8378:, and conceived of motion as always through a medium, rather than through space. In addition, some concepts often termed "Aristotelian" might better be attributed to his followers and commentators upon him. These commentators found that Aristotelian physics had difficulty explaining projectile motion. Aristotle divided motion into two types: "natural" and "violent". The "natural" motion of terrestrial solid matter was to fall downwards, whereas a "violent" motion could push a body sideways. Moreover, in Aristotelian physics, a "violent" motion requires an immediate cause; separated from the cause of its "violent" motion, a body would revert to its "natural" behavior. Yet, a javelin continues moving after it leaves the thrower's hand. Aristotle concluded that the air around the javelin must be imparted with the ability to move the javelin forward.
8353:
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753:
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direction, and its effect is not diminished by horizontal movement. If the cannonball is launched with a greater initial horizontal velocity, then it will travel farther before it hits the ground, but it will still hit the ground in the same amount of time. However, if the cannonball is launched with an even larger initial velocity, then the curvature of the Earth becomes significant: the ground itself will curve away from the falling cannonball. A very fast cannonball will fall away from the inertial straight-line trajectory at the same rate that the Earth curves away beneath it; in other words, it will be in orbit (imagining that it is not slowed by air resistance or obstacles).
905:, is based on the idea of specifying positions using numerical coordinates. Movement is represented by these numbers changing over time: a body's trajectory is represented by a function that assigns to each value of a time variable the values of all the position coordinates. The simplest case is one-dimensional, that is, when a body is constrained to move only along a straight line. Its position can then be given by a single number, indicating where it is relative to some chosen reference point. For example, a body might be free to slide along a track that runs left to right, and so its location can be specified by its distance from a convenient zero point, or
8280:
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1967:
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4347:. Without friction to dissipate a body's energy into heat, the body's energy will trade between potential and (non-thermal) kinetic forms while the total amount remains constant. Any gain of kinetic energy, which occurs when the net force on the body accelerates it to a higher speed, must be accompanied by a loss of potential energy. So, the net force upon the body is determined by the manner in which the potential energy decreases.
7955:
13462:
Aristotelian theory of buoyancy affirms that bodies in a fluid are supported by the resistance of the fluid to being divided by the penetrating object, just as a large piece of wood supports an axe striking it or honey supports a spoon. According to this theory, a boat should sink in shallow water more than in high seas, just as an axe can easily penetrate and even break a small piece of wood, but cannot penetrate a large piece.
8090:
momentum, also holds, as does the conservation of momentum. However, the definition of momentum is modified. Among the consequences of this is the fact that the more quickly a body moves, the harder it is to accelerate, and so, no matter how much force is applied, a body cannot be accelerated to the speed of light. Depending on the problem at hand, momentum in special relativity can be represented as a three-dimensional vector,
8526:
8801:
the total kinetic energy). The question of what is conserved during all other processes, like inelastic collisions and motion slowed by friction, was not resolved until the 19th century. Debates on this topic overlapped with philosophical disputes between the metaphysical views of Newton and
Leibniz, and variants of the term "force" were sometimes used to denote what we would call types of energy. For example, in 1742,
6134:, the dynamics of a system are represented by a function called the Hamiltonian, which in many cases of interest is equal to the total energy of the system. The Hamiltonian is a function of the positions and the momenta of all the bodies making up the system, and it may also depend explicitly upon time. The time derivatives of the position and momentum variables are given by partial derivatives of the Hamiltonian, via
2275:
16045:
16021:
9065:
Kepler's kinematical description of the solar system into a far more powerful dynamical theory because he added concepts from
Galileo's experimental methods β force, mass, momentum, and gravitation. The truly external observer will only get as far as Kepler. Dynamical concepts are formulated on the basis of what we can set up, control, and measure." See, for example, Caspar and Hellman.
16033:
6116:
14654:
and ideas would be meaningfulβthen to give a digest in
English of his great work. Diagrams were added when necessary to the original text and proofs of various problems in physical mechanics and astronomy included. ... or almost a hundred years after its appearance the book continued to serve as a textbook for higher mathematics and astronomy in English schools.
4873:
8649:(1644), Descartes introduced the idea that during a collision between bodies, a "quantity of motion" remains unchanged. Descartes defined this quantity somewhat imprecisely by adding up the products of the speed and "size" of each body, where "size" for him incorporated both volume and surface area. Moreover, Descartes thought of the universe as a
5147:. That is, qualitatively speaking, physical systems obeying Newton's laws can exhibit sensitive dependence upon their initial conditions: a slight change of the position or velocity of one part of a system can lead to the whole system behaving in a radically different way within a short time. Noteworthy examples include the three-body problem, the
4612:. This follows from the fact that the internal forces within the collection, the forces that the objects exert upon each other, occur in balanced pairs by Newton's third law. In a system of two bodies with one much more massive than the other, the center of mass will approximately coincide with the location of the more massive body.
8265:
will vary. The
Ehrenfest theorem says, roughly speaking, that the equations describing how these expectation values change over time have a form reminiscent of Newton's second law. However, the more pronounced quantum effects are in a given situation, the more difficult it is to derive meaningful conclusions from this resemblance.
5059:
12823:...the usual assumption of Newtonian mechanics is that the forces are determined by the simultaneous positions (and possibly their derivatives) of the particles, and that they are related by Newton's third law. No such assumption is possible in special relativity since simultaneity is not an invariant concept in that theory.
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times relative to another. So, in a given observer's frame of reference, action and reaction may not be exactly opposite, and the total momentum of interacting bodies may not be conserved. The conservation of momentum is restored by including the momentum stored in the field that describes the bodies' interaction.
8587:(1673), put forth the hypothesis that "By the action of gravity, whatever its sources, it happens that bodies are moved by a motion composed both of a uniform motion in one direction or another and of a motion downward due to gravity." Newton's second law generalized this hypothesis from gravity to all forces.
7591:
2783:. The speed attained during free fall is proportional to the elapsed time, and the distance traveled is proportional to the square of the elapsed time. Importantly, the acceleration is the same for all bodies, independently of their mass. This follows from combining Newton's second law of motion with his
8200:. A curved path like an orbit, attributed to a gravitational force in Newtonian mechanics, is not the result of a force deflecting a body from an ideal straight-line path, but rather the body's attempt to fall freely through a background that is itself curved by the presence of other masses. A remark by
8683:, and the rule that interactions between bodies do not change the motion of their center of mass. In a later manuscript, Newton added a law of action and reaction, while saying that this law and the law regarding the center of mass implied one another. Newton probably settled on the presentation in the
8979:
an observer who sees one body accelerate without a matching acceleration of some other body to compensate would conclude, not that a force is acting, but that they are not an inertial observer. Landau and
Lifshitz bypass the question by starting with the Lagrangian formalism rather than the Newtonian.
8503:
Galileo recognized that in projectile motion, the Earth's gravity affects vertical but not horizontal motion. However, Galileo's idea of inertia was not exactly the one that would be codified into Newton's first law. Galileo thought that a body moving a long distance inertially would follow the curve
5606:
It is mathematically possible for a collection of point masses, moving in accord with Newton's laws, to launch some of themselves away so forcefully that they fly off to infinity in a finite time. This unphysical behavior, known as a "noncollision singularity", depends upon the masses being pointlike
5039:
The angular momentum of a collection of point masses, and thus of an extended body, is found by adding the contributions from each of the points. This provides a means to characterize a body's rotation about an axis, by adding up the angular momenta of its individual pieces. The result depends on the
4727:
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is that which a body has when it is in actual motion." In modern terminology, "dead force" and "living force" correspond to potential energy and kinetic energy respectively. Conservation of energy was not established as a universal principle until it was understood that the energy of mechanical work
8227:
is a theory of physics originally developed in order to understand microscopic phenomena: behavior at the scale of molecules, atoms or subatomic particles. Generally and loosely speaking, the smaller a system is, the more an adequate mathematical model will require understanding quantum effects. The
7868:
provides an expression for the force upon a charged body that can be plugged into Newton's second law in order to calculate its acceleration. According to the
Lorentz force law, a charged body in an electric field experiences a force in the direction of that field, a force proportional to its charge
7180:
5066:
Newton's law of universal gravitation states that any body attracts any other body along the straight line connecting them. The size of the attracting force is proportional to the product of their masses, and inversely proportional to the square of the distance between them. Finding the shape of the
4293:
upon the body, and the amount of work done is equal to the change in the body's kinetic energy. In many cases of interest, the net work done by a force when a body moves in a closed loop β starting at a point, moving along some trajectory, and returning to the initial point β is zero. If this is the
3391:
that interpolates between projectile motion and uniform circular motion. A cannonball that is lobbed weakly off the edge of a tall cliff will hit the ground in the same amount of time as if it were dropped from rest, because the force of gravity only affects the cannonball's momentum in the downward
14653:
In no sense was it a mere translation of
Laplace's work. Instead it endeavoured to explain his method ". . . by which these results were deduced from one general equation of the motion of matter" and to bring the reader's mathematical skill to the point where the exposition of Laplace's mathematics
13461:
affirmed that solid water should have a greater weight than liquid water for the same volume. We know that this statement is incorrect because the density of ice is lower than that of water (hydrogen bonds create an open crystal structure in the solid phase), and for this reason ice can float. The
8978:
as a definition of "force". See also
Frautschi et al., as well as Feynman, Leighton and Sands, who argue that the second law is incomplete without a specification of a force by another law, like the law of gravity. Kleppner and Kolenkow argue that the second law is incomplete without the third law:
8927:
One textbook observes that a block sliding down an inclined plane is what "some cynics view as the dullest problem in all of physics". Another quips, "Nobody will ever know how many minds, eager to learn the secrets of the universe, found themselves studying inclined planes and pulleys instead, and
8800:
The concept of energy became a key part of
Newtonian mechanics in the post-Newton period. Huygens' solution of the collision of hard spheres showed that in that case, not only is momentum conserved, but kinetic energy is as well (or, rather, a quantity that in retrospect we can identify as one-half
8594:
without requiring physical contact. For example, the Sun and the Earth pull on each other gravitationally, despite being separated by millions of kilometres. This contrasts with the idea, championed by
Descartes among others, that the Sun's gravity held planets in orbit by swirling them in a vortex
8338:
The concepts invoked in Newton's laws of motion β mass, velocity, momentum, force β have predecessors in earlier work, and the content of Newtonian physics was further developed after Newton's time. Newton combined knowledge of celestial motions with the study of events on Earth and showed that one
8264:
is used to calculate the expectation values of a position measurement or a momentum measurement. These expectation values will generally change over time; that is, depending on the time at which (for example) a position measurement is performed, the probabilities for its different possible outcomes
8181:
Newton's third law must be modified in special relativity. The third law refers to the forces between two bodies at the same moment in time, and a key feature of special relativity is that simultaneity is relative. Events that happen at the same time relative to one observer can happen at different
5095:
of the orbit, and thus the type of conic section, is determined by the energy and the angular momentum of the orbiting body. Planets do not have sufficient energy to escape the Sun, and so their orbits are ellipses, to a good approximation; because the planets pull on one another, actual orbits are
4394:
Significant aspects of the motion of an extended body can be understood by imagining the mass of that body concentrated to a single point, known as the center of mass. The location of a body's center of mass depends upon how that body's material is distributed. For a collection of pointlike objects
4077:
Newtonian physics treats matter as being neither created nor destroyed, though it may be rearranged. It can be the case that an object of interest gains or loses mass because matter is added to or removed from it. In such a situation, Newton's laws can be applied to the individual pieces of matter,
5630:
Classical mechanics can be mathematically formulated in multiple different ways, other than the "Newtonian" description (which itself, of course, incorporates contributions from others both before and after Newton). The physical content of these different formulations is the same as the Newtonian,
5209:
that assigns a velocity vector to each point in space and time. A small object being carried along by the fluid flow can change velocity for two reasons: first, because the velocity field at its position is changing over time, and second, because it moves to a new location where the velocity field
4591:
is the total mass of the collection. In the absence of a net external force, the center of mass moves at a constant speed in a straight line. This applies, for example, to a collision between two bodies. If the total external force is not zero, then the center of mass changes velocity as though it
2669:
By Newton's second law, the first term is the total force upon the first body, and the second term is the total force upon the second body. If the two bodies are isolated from outside influences, the only force upon the first body can be that from the second, and vice versa. By Newton's third law,
8393:
thinker active during the sixth century, found this absurd: the same medium, air, was somehow responsible both for sustaining motion and for impeding it. If Aristotle's idea were true, Philoponus said, armies would launch weapons by blowing upon them with bellows. Philoponus argued that setting a
8089:
In special relativity, the rule that Wilczek called "Newton's Zeroth Law" breaks down: the mass of a composite object is not merely the sum of the masses of the individual pieces. Newton's first law, inertial motion, remains true. A form of Newton's second law, that force is the rate of change of
8045:
Collections of charged bodies do not always obey Newton's third law: there can be a change of one body's momentum without a compensatory change in the momentum of another. The discrepancy is accounted for by momentum carried by the electromagnetic field itself. The momentum per unit volume of the
2008:
no motion. The principle expressed by Newton's first law is that there is no way to say which inertial observer is "really" moving and which is "really" standing still. One observer's state of rest is another observer's state of uniform motion in a straight line, and no experiment can deem either
9107:
and modern science. The suggestion has been made that alchemy inspired Newton's notion of "action at a distance", i.e., one body exerting a force upon another without being in direct contact. This suggestion enjoyed considerable support among historians of science until a more extensive study of
9064:
immersed and included in the whole process β because we can act on objects around us. Our ability to intervene in nature clarifies even the motion of the planets around the sun β masses so great and distances so vast that our roles as participants seem insignificant. Newton was able to transform
2727:
has suggested calling attention to this assumption by designating it "Newton's Zeroth Law". Another candidate for a "zeroth law" is the fact that at any instant, a body reacts to the forces applied to it at that instant. Likewise, the idea that forces add like vectors (or in other words obey the
2369:
into Newton's second law, an equation with predictive power can be written. Newton's second law has also been regarded as setting out a research program for physics, establishing that important goals of the subject are to identify the forces present in nature and to catalogue the constituents of
2003:
is privileged over any other. The concept of an inertial observer makes quantitative the everyday idea of feeling no effects of motion. For example, a person standing on the ground watching a train go past is an inertial observer. If the observer on the ground sees the train moving smoothly in a
8204:
that has become proverbial among physicists summarizes the theory: "Spacetime tells matter how to move; matter tells spacetime how to curve." Wheeler himself thought of this reciprocal relationship as a modern, generalized form of Newton's third law. The relation between matter distribution and
897:
masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each. For instance, the Earth and the Sun can both be approximated as
5382:
8062:
and find it to be the value predicted by the Maxwell equations. In other words, light provides an absolute standard for speed, yet the principle of inertia holds that there should be no such standard. This tension is resolved in the theory of special relativity, which revises the notions of
7748:
bodies has much the same mathematical form as Newton's law of universal gravitation: the force is proportional to the product of the charges, inversely proportional to the square of the distance between them, and directed along the straight line between them. The Coulomb force that a charge
1845:. Often, vectors are represented visually as arrows, with the direction of the vector being the direction of the arrow, and the magnitude of the vector indicated by the length of the arrow. Numerically, a vector can be represented as a list; for example, a body's velocity vector might be
8255:
provides a connection between quantum expectation values and Newton's second law, a connection that is necessarily inexact, as quantum physics is fundamentally different from classical. In quantum physics, position and momentum are represented by mathematical entities known as
8488:
Imagine any particle projected along a horizontal plane without friction; then we know, from what has been more fully explained in the preceding pages, that this particle will move along this same plane with a motion which is uniform and perpetual, provided the plane has no
3807:
has a stable equilibrium in the vertical position: if motionless there, it will remain there, and if pushed slightly, it will swing back and forth. Neglecting air resistance and friction in the pivot, the force upon the pendulum is gravity, and Newton's second law becomes
4342:
This is true for many forces including that of gravity, but not for friction; indeed, almost any problem in a mechanics textbook that does not involve friction can be expressed in this way. The fact that the force can be written in this way can be understood from the
8370:, but the history of the concepts involved is obscured by multiple factors. An exact correspondence between Aristotelian and modern concepts is not simple to establish: Aristotle did not clearly distinguish what we would call speed and force, used the same term for
5457:
3510:, the net force upon the body is the zero vector, and by Newton's second law, the body will not accelerate. If the force upon the body is proportional to the displacement from the equilibrium point, and directed to the equilibrium point, then the body will perform
7193:
1799:: a quantity with both magnitude and direction. Velocity and acceleration are vector quantities as well. The mathematical tools of vector algebra provide the means to describe motion in two, three or more dimensions. Vectors are often denoted with an arrow, as in
6008:
7073:
7431:
as mentioned above, in which the first term indicates how the function being differentiated changes over time at a fixed location, and the second term captures how a moving particle will see different values of that function as it travels from place to place:
10128:
Only with this approach, indeed, can the exposition form a logical whole and avoid tautological definitions of the fundamental mechanical quantities. It is, moreover, essentially simpler, and leads to the most complete and direct means of solving problems in
9823:
2722:
Various sources have proposed elevating other ideas used in classical mechanics to the status of Newton's laws. For example, in Newtonian mechanics, the total mass of a body made by bringing together two smaller bodies is the sum of their individual masses.
2667:
8810:
can be dissipated into heat. With the concept of energy given a solid grounding, Newton's laws could then be derived within formulations of classical mechanics that put energy first, as in the Lagrangian and Hamiltonian formulations described above.
1952:
makes quantitative the everyday idea of a push or a pull. Forces in Newtonian mechanics are often due to strings and ropes, friction, muscle effort, gravity, and so forth. Like displacement, velocity, and acceleration, force is a vector quantity.
2412:" might have caused confusion among generations of students: the "action" and "reaction" apply to different bodies. For example, consider a book at rest on a table. The Earth's gravity pulls down upon the book. The "reaction" to that "action" is
7078:
10357:
2306:, and so the total force on a body depends upon both the magnitudes and the directions of the individual forces. When the net force on a body is equal to zero, then by Newton's second law, the body does not accelerate, and it is said to be in
6939:
5288:
1735:
6107:, which relates symmetries and conservation laws. The conservation of momentum can be derived by applying Noether's theorem to a Lagrangian for a multi-particle system, and so, Newton's third law is a theorem rather than an assumption.
1614:
5111:
within a computer's memory; Newton's laws are used to calculate how the velocities will change over a short interval of time, and knowing the velocities, the changes of position over that time interval can be computed. This process is
2032:, which depends upon the amount of matter contained in a body, the speed at which that body is moving, and the direction in which it is moving. In modern notation, the momentum of a body is the product of its mass and its velocity:
8900:
Negative acceleration includes both slowing down (when the current velocity is positive) and speeding up (when the current velocity is negative). For this and other points that students have often found difficult, see McDermott et
4237:
5635:
helps make apparent the connection between symmetries and conservation laws, and it is useful when calculating the motion of constrained bodies, like a mass restricted to move along a curving track or on the surface of a sphere.
1105:
865:), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems. In the time since Newton, new insights, especially around the concept of energy, built the field of
5103:. That is, there is no way to start from the differential equations implied by Newton's laws and, after a finite sequence of standard mathematical operations, obtain equations that express the three bodies' motions over time.
6412:
4355:
A rigid body is an object whose size is too large to neglect and which maintains the same shape over time. In Newtonian mechanics, the motion of a rigid body is often understood by separating it into movement of the body's
4569:
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5906:
is the path for which the integral of the Lagrangian is "stationary". That is, the physical path has the property that small perturbations of it will, to a first approximation, not change the integral of the Lagrangian.
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increases over the interval in question, a negative average velocity indicates a net decrease over that interval, and an average velocity of zero means that the body ends the time interval in the same place as it began.
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7950:
4963:
When the torque is zero, the angular momentum is constant, just as when the force is zero, the momentum is constant. The torque can vanish even when the force is non-zero, if the body is located at the reference point
3885:
8418:. In retrospect, the idea of impetus can be seen as a forerunner of the modern concept of momentum. The intuition that objects move according to some kind of impetus persists in many students of introductory physics.
2203:
4868:{\displaystyle {\frac {d\mathbf {L} }{dt}}=\left({\frac {d\mathbf {r} }{dt}}\right)\times \mathbf {p} +\mathbf {r} \times {\frac {d\mathbf {p} }{dt}}=\mathbf {v} \times m\mathbf {v} +\mathbf {r} \times \mathbf {F} .}
4285:, the energy carried by heat flow, is a type of kinetic energy not associated with the macroscopic motion of objects but instead with the movements of the atoms and molecules of which they are made. According to the
8398:, that would be contained within the body itself. As long as its impetus was sustained, the body would continue to move. In the following centuries, versions of impetus theory were advanced by individuals including
7670:
3136:
8642:
suggested that gravitational attractions were reciprocal β that, for example, the Moon pulls on the Earth while the Earth pulls on the Moon β but he did not argue that such pairs are equal and opposite. In his
8057:
predicts that electromagnetic waves will travel through empty space at a constant, definite speed. Thus, some inertial observers seemingly have a privileged status over the others, namely those who measure the
2270:
5659:
differs from the Newtonian formulation by considering entire trajectories at once rather than predicting a body's motion at a single instant. It is traditional in Lagrangian mechanics to denote position with
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2740:
The study of the behavior of massive bodies using Newton's laws is known as Newtonian mechanics. Some example problems in Newtonian mechanics are particularly noteworthy for conceptual or historical reasons.
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The modern concept of inertia is credited to Galileo. Based on his experiments, Galileo concluded that the "natural" behavior of a moving body was to keep moving, until something else interfered with it. In
1915:
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argue that the Lagrangian formulation makes the conceptual content of classical mechanics more clear than starting with Newton's laws. Lagrangian mechanics provides a convenient framework in which to prove
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3320:, such as that of the Moon around the Earth, can be approximated by uniform circular motion. In such cases, the centripetal force is gravity, and by Newton's law of universal gravitation has magnitude
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107:
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As in the Lagrangian formulation, in Hamiltonian mechanics the conservation of momentum can be derived using Noether's theorem, making Newton's third law an idea that is deduced rather than assumed.
3183:
3148:-shaped trajectories, because gravity affects the body's vertical motion and not its horizontal. At the peak of the projectile's trajectory, its vertical velocity is zero, but its acceleration is
8216:
The Newtonian theory of gravity is a good approximation to the predictions of general relativity when gravitational effects are weak and objects are moving slowly compared to the speed of light.
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charged body in a magnetic field experiences a force that is also proportional to its charge, in a direction perpendicular to both the field and the body's direction of motion. Using the vector
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6555:. This formulation also uses Hamiltonian functions, but in a different way than the formulation described above. The paths taken by bodies or collections of bodies are deduced from a function
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does not change with time, then the derivative acts only upon the velocity, and so the force equals the product of the mass and the time derivative of the velocity, which is the acceleration:
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6096:
which is a restatement of Newton's second law. The left-hand side is the time derivative of the momentum, and the right-hand side is the force, represented in terms of the potential energy.
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6539:
Among the proposals to reform the standard introductory-physics curriculum is one that teaches the concept of energy before that of force, essentially "introductory Hamiltonian mechanics".
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cautions, "Impetus is neither a force, nor a form of energy, nor momentum in the modern sense; it shares something with all these other concepts, but it is identical with none of them."
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observes, "A particle is defined to be an object of insignificant size: e.g. an electron, a tennis ball or a planet. Obviously the validity of this statement depends on the context..."
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1790:
7990:), then the force will be perpendicular to the charge's motion, just as in the case of uniform circular motion studied above, and the charge will circle (or more generally move in a
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2343:β acceleration implies force, force implies acceleration β some other statement about force must also be made. For example, an equation detailing the force might be specified, like
1622:
5567:{\displaystyle {\frac {\partial v}{\partial t}}+(\mathbf {\nabla } \cdot \mathbf {v} )\mathbf {v} =-{\frac {1}{\rho }}\mathbf {\nabla } P+\nu \nabla ^{2}\mathbf {v} +\mathbf {f} ,}
4031:
1160:
velocity, a measure of a body's speed and direction of movement at a single moment of time, rather than over an interval. One notation for the instantaneous velocity is to replace
5766:
5614:
It is not yet known whether or not the Euler and NavierβStokes equations exhibit the analogous behavior of initially smooth solutions "blowing up" in finite time. The question of
4040:
often by friction or viscous drag, in which case energy bleeds out of the oscillator and the amplitude of the oscillations decreases over time. Also, a harmonic oscillator can be
3803:
One reason that the harmonic oscillator is a conceptually important example is that it is good approximation for many systems near a stable mechanical equilibrium. For example, a
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1507:
7287:{\displaystyle -{\frac {\partial }{\partial t}}\mathbf {\nabla } S={\frac {1}{m}}\left(\mathbf {\nabla } S\cdot \mathbf {\nabla } \right)\mathbf {\nabla } S+\mathbf {\nabla } V.}
4439:
1244:
4073:, propel matter in one direction to push the craft in the other. This means that the mass being pushed, the rocket and its remaining onboard fuel supply, is constantly changing.
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Modern presentations of Newton's laws use the mathematics of vectors, a topic that was not developed until the late 19th and early 20th centuries. Vector algebra, pioneered by
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When Newton's laws are applied to rotating extended bodies, they lead to new quantities that are analogous to those invoked in the original laws. The analogue of mass is the
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Second Law of Nature: Each moving thing if left to itself moves in a straight line; so any body moving in a circle always tends to move away from the centre of the circle.
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1917:, indicating that it is moving at 3 metres per second along the horizontal axis and 4 metres per second along the vertical axis. The same motion described in a different
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6713:, analogously to how a light ray propagates in the direction perpendicular to its wavefront. This is simplest to express for the case of a single point mass, in which
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1987:
Every object perseveres in its state of rest, or of uniform motion in a right line, except insofar as it is compelled to change that state by forces impressed thereon.
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8769:
5850:
5592:
4105:
1327:
936:
8244:
of a chosen type is performed. Quantum mechanics allows the physicist to calculate the probability that a chosen measurement will elicit a particular result. The
7900:
3798:
3508:
3482:
2380:
To every action, there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
2324:, which schematically portrays a body of interest and the forces applied to it by outside influences. For example, a free body diagram of a block sitting upon an
1996:: the natural behavior of a body is to move in a straight line at constant speed. A body's motion preserves the status quo, but external forces can perturb this.
3811:
2939:
1294:
1271:
909:, with negative numbers indicating positions to the left and positive numbers indicating positions to the right. If the body's location as a function of time is
8196:
is a theory of gravity that advances beyond that of Newton. In general relativity, the gravitational force of Newtonian mechanics is reimagined as curvature of
8144:
7887:
7312:
6812:
6788:
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6711:
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6667:
6196:
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3212:
3166:
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3019:
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2896:
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2143:
2138:
1414:
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1347:
1198:
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15303:
7175:{\displaystyle -\mathbf {\nabla } {\frac {\partial S}{\partial t}}={\frac {1}{2m}}\mathbf {\nabla } \left(\mathbf {\nabla } S\right)^{2}+\mathbf {\nabla } V.}
8279:
5104:
7624:
is a special case of Newton's second law, adapted for the case of describing a small object bombarded stochastically by even smaller ones. It can be written
2023:
The change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed.
8512:, who recognized that inertial motion should be motion in a straight line. Descartes published his laws of nature (laws of motion) with this correction in
7627:
5709:. The simplest example is a massive point particle, the Lagrangian for which can be written as the difference between its kinetic and potential energies:
3194:
When a body is in uniform circular motion, the force on it changes the direction of its motion but not its speed. For a body moving in a circle of radius
3064:
14925:
9905:
7718:
is a force that varies randomly from instant to instant, representing the net effect of collisions with the surrounding particles. This is used to model
13109:
Schaffer, Kathryn; Barreto Lemos, Gabriela (24 May 2019). "Obliterating Thingness: An Introduction to the "What" and the "So What" of Quantum Physics".
8609:
forces, and unable to find a quantitatively satisfactory explanation of his law of gravity in terms of an aetherial model, Newton eventually declared, "
8038:
works by applying electric and/or magnetic fields to moving charges and measuring the resulting acceleration, which by the Lorentz force law yields the
5377:{\displaystyle {\frac {\partial v}{\partial t}}+(\mathbf {\nabla } \cdot \mathbf {v} )\mathbf {v} =-{\frac {1}{\rho }}\mathbf {\nabla } P+\mathbf {f} ,}
2779:
If a body falls from rest near the surface of the Earth, then in the absence of air resistance, it will accelerate at a constant rate. This is known as
2208:
12621:
4925:
8551:
had worked out his own, concise version of the law in 1656. It was not published until 1703, eight years after his death, in the opening paragraph of
1619:
is to velocity as velocity is to position: it is the derivative of the velocity with respect to time. Acceleration can likewise be defined as a limit:
15933:
9710:
6817:
6017:
5107:
can be applied to obtain useful, albeit approximate, results for the three-body problem. The positions and velocities of the bodies can be stored in
5075:
is constant, or by applying a duality transformation to a 2-dimensional harmonic oscillator. However it is solved, the result is that orbits will be
8910:
Per Cohen and Whitman. For other phrasings, see Eddington and Frautschi et al. Andrew Motte's 1729 translation rendered Newton's "nisi quatenus" as
8617:'s theories of motion and gravity, the first grounds for judging them must be the successful predictions they made. And indeed, since Newton's time
7317:
3381:
is the mass of the larger body being orbited. Therefore, the mass of a body can be calculated from observations of another body orbiting around it.
2069:
where all three quantities can change over time. Newton's second law, in modern form, states that the time derivative of the momentum is the force:
11635:
6201:
4686:
8722:
Newton expressed his second law by saying that the force on a body is proportional to its change of motion, or momentum. By the time he wrote the
8656:
During the 1650s, Huygens studied collisions between hard spheres and deduced a principle that is now identified as the conservation of momentum.
5648:. Due to the breadth of these topics, the discussion here will be confined to concise treatments of how they reformulate Newton's laws of motion.
2072:
898:
pointlike when considering the orbit of the former around the latter, but the Earth is not pointlike when considering activities on its surface.
14619:
14521:
8779:
would employ it as a basic premise in the 1740s. Euler pioneered the study of rigid bodies and established the basic theory of fluid dynamics.
6467:
which reproduces the familiar statement that a body's momentum is the product of its mass and velocity. The time derivative of the momentum is
5116:
to calculate, approximately, the bodies' trajectories. Generally speaking, the shorter the time interval, the more accurate the approximation.
15271:
8327:
8302:
869:
on his foundations. Limitations to Newton's laws have also been discovered; new theories are necessary when objects move at very high speeds (
857:
15068:
15054:
15037:
10756:
8679:, he listed four laws: the principle of inertia, the change of motion by force, a statement about relative motion that would today be called
797:
13170:"Investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics"
8534:
First Law of Nature: Each thing when left to itself continues in the same state; so any moving body goes on moving until something stops it.
4273:
after Newton's time, but it has become an inseparable part of what is considered "Newtonian" physics. Energy can broadly be classified into
11706:
8559:
Hypothesis I: Any body already in motion will continue to move perpetually with the same speed and in a straight line unless it is impeded.
5156:
4305:
3619:
10794:
6470:
2918:
is the distance from the center of the Earth to the body's location, which is very nearly the radius of the Earth. Setting this equal to
386:
15360:
13664:
13560:
11953:
10684:
8858:
5615:
505:
6417:
5911:
provides the mathematical tools for finding this path. Applying the calculus of variations to the task of finding the path yields the
3549:
1848:
7617:
that a gas exerts upon the container holding it as the aggregate of many impacts of atoms, each imparting a tiny amount of momentum.
5771:
3140:
If the body is not released from rest but instead launched upwards and/or horizontally with nonzero velocity, then free fall becomes
2339:
of force, i.e., a force is that which exists when an inertial observer sees a body accelerating. In order for this to be more than a
11947:
LeGresley, Sarah E.; Delgado, Jennifer A.; Bruner, Christopher R.; Murray, Michael J.; Fischer, Christopher J. (13 September 2019).
6558:
2492:
1250:
of the position with respect to time. It can roughly be thought of as the ratio between an infinitesimally small change in position
15483:
14903:
from 1799 to 1805, a work collecting in one place all the theoretical and empirical results of the research predicated on Newton's
13097:
It is a fundamental quantum doctrine that a measurement does not, in general, reveal a pre-existing value of the measured property.
11949:"Calculus-enhanced energy-first curriculum for introductory physics improves student performance locally and in downstream courses"
8853:
2784:
2344:
2035:
478:
7435:
15908:
15885:
15641:
15589:
4635:
Angular momentum is calculated with respect to a reference point. If the displacement vector from a reference point to a body is
10680:"Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context"
9108:
Newton's papers became possible, after which it fell out of favor. However, it does appear that Newton's alchemy influenced his
8185:
Newtonian mechanics is a good approximation to special relativity when the speeds involved are small compared to that of light.
5210:
has a different value. Consequently, when Newton's second law is applied to an infinitesimal portion of fluid, the acceleration
2004:
straight line at a constant speed, then a passenger sitting on the train will also be an inertial observer: the train passenger
17:
15493:
15231:
12424:
Chu, Caroline S.; Lebrilla, Carlito B. (2010). "Introduction to Modern Techniques in Mass Spectrometry". In Jue, Thomas (ed.).
11344:
8618:
4444:
1446:
63:
11291:
10379:
8789:(1798β1825) forsook geometry and developed mechanics purely through algebraic expressions, while resolving questions that the
5170:
is an expression of Newton's second law adapted to fluid dynamics. A fluid is described by a velocity field, i.e., a function
15151:
14856:
14680:
14589:
14365:
14269:
14182:
14072:
13866:
13527:
13483:
13344:
13307:
13024:
12986:
12887:
12846:
12785:"Four-Dimensional Formulations of Newtonian Mechanics and Their Relation to the Special and the General Theory of Relativity"
12689:
12443:
12253:
11923:
11883:
11796:
11747:
11605:
11354:
11309:
11059:
10804:
10766:
10495:
10470:
10154:
10113:
9977:
9793:
9648:
9568:
9429:
9330:
9285:
9206:
9074:
Aristotelian physics also had difficulty explaining buoyancy, a point that Galileo tried to resolve without complete success.
8245:
7594:
A simulation of a larger, but still microscopic, particle (in yellow) surrounded by a gas of smaller particles, illustrating
6126:
was a key development in modern physics and can be conveniently stated in the language of Lagrangian or Hamiltonian mechanics
2790:
2314:
if, when the position of the body is changed slightly, the body remains near that equilibrium. Otherwise, the equilibrium is
15520:
14614:
13807:
13259:
8715:
833:
A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force.
11378:
Breen, Barbara J.; Weidert, Christine E.; Lindner, John F.; Walker, Lisa May; Kelly, Kasey; Heidtmann, Evan (April 2008).
9042:
Discussions can be found in, for example, Frautschi et al., Panofsky and Phillips, Goldstein, Poole and Safko, and Werner.
8407:
5712:
3237:
15619:
15330:
14886:
14763:
14395:
6533:
which, upon identifying the negative derivative of the potential with the force, is just Newton's second law once again.
2775:, deviating from a parabolic arc because of air resistance, spin, and deformation into a non-spherical shape upon impact.
1203:
460:
8785:
8248:
for a measurement is the average of the possible results it might yield, weighted by their probabilities of occurrence.
16105:
15532:
13812:
13556:"Exploring the preinstruction and postinstruction non-Newtonian world views as measured by the Force Concept Inventory"
8093:
6003:{\displaystyle {\frac {d}{dt}}\left({\frac {\partial L}{\partial {\dot {q}}}}\right)={\frac {\partial L}{\partial q}}.}
5099:
If a third mass is added, the Kepler problem becomes the three-body problem, which in general has no exact solution in
3168:
downwards, as it is at all times. Setting the wrong vector equal to zero is a common confusion among physics students.
15510:
7068:{\displaystyle -{\frac {\partial S}{\partial t}}={\frac {1}{2m}}\left(\mathbf {\nabla } S\right)^{2}+V(\mathbf {q} ).}
15322:
15189:
14141:
14108:
13273:
13239:
12767:
12731:
12595:
12487:
12400:
11838:
10899:
10182:
10142:
10058:
9144:
8084:
5072:
790:
15918:
15743:
11869:
8988:
See, for instance, Moebs et al., Gonick and Huffman, Low and Wilson, Stocklmayer et al., Hellingman, and Hodanbosi.
8241:
5167:
1921:
will be represented by different numbers, and vector algebra can be used to translate between these alternatives.
1796:
1296:
over which it occurs. More carefully, the velocity and all other derivatives can be defined using the concept of a
31:
15996:
5173:
2416:
the support force from the table holding up the book, but the gravitational pull of the book acting on the Earth.
1928:
are used with a technical meaning. Moreover, words which are synonymous in everyday speech are not so in physics:
752:
16085:
15938:
15840:
15738:
15559:
14899:
These advances in our understanding of planetary motion led Laplace to produce the four principal volumes of his
12585:
10048:
8771:. This form of the second law was written (for the special case of constant force) at least as early as 1716, by
5250:
126:
8948:
4062:
1504:
Instantaneous velocity can be defined as the limit of the average velocity as the time interval shrinks to zero:
16095:
8843:
8415:
8352:
381:
121:
38:
10515:
8742:
does not express acceleration as the second derivative of position, and so it does not give the second law as
8698:
5166:
by considering a fluid as composed of infinitesimal pieces, each exerting forces upon neighboring pieces. The
2009:
point of view to be correct or incorrect. There is no absolute standard of rest. Newton himself believed that
1744:
1131:) is used, per tradition, to mean "change in". A positive average velocity means that the position coordinate
16090:
16080:
15823:
13770:
10097:
6941:
The relation to Newton's laws can be seen by considering a point mass moving in a time-independent potential
6099:
5247:, and there is a net force upon it if the fluid pressure varies from one side of it to another. Accordingly,
3274:
and is directed toward the center of the circle. The force required to sustain this acceleration, called the
8601:. Newton considered aetherial explanations of force but ultimately rejected them. The study of magnetism by
6693:. Bodies move over time in such a way that their trajectories are perpendicular to the surfaces of constant
4078:
keeping track of which pieces belong to the object of interest over time. For instance, if a rocket of mass
2662:{\displaystyle {\frac {d\mathbf {p} }{dt}}={\frac {d\mathbf {p} _{1}}{dt}}+{\frac {d\mathbf {p} _{2}}{dt}}.}
2303:
16065:
15733:
10199:
7857:, and it points in the exact opposite direction. Coulomb's law is thus consistent with Newton's third law.
6548:
3998:
783:
770:
531:
454:
376:
219:
8493:
15928:
15787:
15584:
15096:
14791:
14423:
13966:
13413:
13174:
12517:
12335:
12286:
12193:
12144:
12074:
11824:
11547:
11477:
11433:
11384:
11236:
11187:
11138:
10984:
10932:
10834:
10204:
10006:
9363:
8602:
5912:
5108:
4398:
450:
251:
15678:
14572:
Smith, George E. (December 2020). "Newton's Laws of Motion". In Schliesser, Eric; Smeenk, Chris (eds.).
9824:
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
8232:. Instead of thinking about quantities like position, momentum, and energy as properties that an object
6551:
provides yet another formulation of classical mechanics, one which makes it mathematically analogous to
2205:
As the acceleration is the second derivative of position with respect to time, this can also be written
229:
15975:
15728:
15723:
15646:
15549:
15478:
15337:
15224:
11875:
8311:
6736:
5451:
5139:
Three double pendulums, initialized with almost exactly the same initial conditions, diverge over time.
847:
If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.
670:
559:
278:
13891:
10678:
Carli, Marta; Lippiello, Stefania; Pantano, Ornella; Perona, Mario; Tormen, Giuseppe (19 March 2020).
10519:
6623:
2463:
2434:
16013:
15693:
15609:
15263:
13053:
12789:
12386:
8838:
8805:
wrote, "Dead force consists of a simple tendency to motion: such is that of a spring ready to relax;
8734:
he made no explicit use of it, perhaps because he believed geometrical arguments in the tradition of
8676:
7699:
6944:
5619:
4110:
3995:), and so this expression simplifies to the equation for a simple harmonic oscillator with frequency
3774:
can be calculated knowing, for example, the position and velocity the body has at a given time, like
2732:), and the idea that forces change the energy of a body, have both been described as a "fourth law".
424:
15142:(1996). "The Emergence of Vector Calculus in Physics: The Early Decades". In Schubring, Gert (ed.).
14211:"William R. Newman. Newton the Alchemist: Science, Enigma, and the Quest for Nature's "Secret Fire""
10200:"The role of competing knowledge structures in undermining learning: Newton's second and third laws"
7965:
4967:
16100:
15564:
15505:
15488:
15473:
15418:
14786:
12972:
12330:
9024:
Among the many textbook treatments of this point are Hand and Finch and also Kleppner and Kolenkow.
8645:
8583:
8514:
8206:
7958:
The Lorentz force law in effect: electrons are bent into a circular trajectory by a magnetic field.
6934:{\displaystyle -{\frac {\partial S}{\partial t}}=H\left(\mathbf {q} ,\mathbf {\nabla } S,t\right).}
4900:
3705:
2420:
700:
544:
14921:"Γmilie Du ChΓ’telet's interpretation of the laws of motion in the light of 18th century mechanics"
8000:
5644:, leads to further insight about symmetry, and can be developed into sophisticated techniques for
5427:
5213:
5017:
4995:
4878:
4660:
4638:
4289:, when a force acts upon a body while that body moves along the line of the force, the force does
4242:
4141:
2787:. The latter states that the magnitude of the gravitational force from the Earth upon the body is
2695:
2673:
2544:
2350:
1802:
16075:
15542:
15295:
14920:
10790:
9818:
9638:
8802:
7606:
6135:
5631:
but they provide different insights and facilitate different types of calculations. For example,
2729:
2714:
is known to be constant, it follows that the forces have equal magnitude and opposite direction.
2010:
650:
414:
15144:
Hermann GΓΌnther GraΓmann (1809β1877): Visionary Mathematician, Scientist and Neohumanist Scholar
14977:
11791:. Providence, RI: American Mathematical Society and Clay Mathematics Institute. pp. 57β67.
11783:
11630:
11472:
11231:
11182:
10829:
10300:
9454:
8653:, that is, filled with matter, so all motion required a body to displace a medium as it moved.
5683:
690:
15913:
15903:
15668:
15631:
15604:
15498:
14706:"The mathematical form of measurement and the argument for Proposition I in Newton's Principia"
13227:
13111:
12873:
12717:
11037:
9265:
9230:
8888:
8848:
8826:
8672:. Newton cited the work of Huygens, Wren, and Wallis to support the validity of his third law.
8201:
8174:, which depends upon the body's speed. Alternatively, momentum and force can be represented as
8080:
8054:
5908:
5100:
4344:
4067:
3511:
3411:
3384:
3323:
2307:
1824:
1730:{\displaystyle a={\frac {dv}{dt}}=\lim _{\Delta t\to 0}{\frac {v(t+\Delta t)-v(t)}{\Delta t}}.}
695:
512:
13234:. Translated by Hemley, Susan Reid; Ostrowsky, Nicole; Ostrowsky, Dan. John Wiley & Sons.
12877:
3281:
16070:
15960:
15867:
15753:
15748:
15537:
15450:
15425:
15217:
14096:
12675:
9134:
8399:
8153:
7675:
6670:
6131:
5637:
5135:
3974:
3954:
3930:
3910:
3685:
2424:
2423:. The latter remains true even in cases where Newton's statement does not, for instance when
1609:{\displaystyle {\frac {ds}{dt}}=\lim _{\Delta t\to 0}{\frac {s(t+\Delta t)-s(t)}{\Delta t}}.}
1163:
1110:
705:
680:
366:
184:
14581:
9006:
For the former, see Greiner, or Wachter and Hoeber. For the latter, see Tait and Heaviside.
2298:
along the direction of the plane that could be applied, for example, by friction or a string
2013:
existed, but that the only measures of space or time accessible to experiment are relative.
15874:
15594:
15351:
15105:
14991:
14934:
14800:
14481:
14432:
13975:
13673:
13569:
13422:
13183:
13072:
12918:
12798:
12630:
12536:
12344:
12295:
12202:
12153:
12093:
12034:
11962:
11556:
11496:
11393:
11297:
11245:
11147:
11098:
10993:
10941:
10843:
10693:
10606:
10553:
10425:
10314:
10265:
10213:
9923:
9832:
9517:
9468:
9372:
9354:
9312:
8814:
8780:
8610:
8591:
8544:
8039:
7833:
7806:
7779:
7752:
6123:
6104:
5882:
5855:
5656:
5632:
5387:
5092:
4057:
3517:
1419:
1352:
968:
941:
906:
725:
685:
593:
589:
581:
571:
361:
354:
110:
14467:
13016:
Einstein's Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity
8745:
5826:
5577:
4081:
1966:
1303:
912:
720:
8:
16049:
15683:
15663:
15579:
15569:
15430:
14785:
Marquina, J. E.; Marquina, M. L.; Marquina, V.; HernΓ‘ndez-GΓ³mez, J. J. (1 January 2017).
13686:
13659:
13617:
13582:
13555:
13010:
12642:
11975:
11948:
11089:
11041:
10706:
10679:
10416:
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8680:
8669:
8571:
8427:
7995:
7602:
7421:
5645:
5641:
5595:
5233:
5152:
5071:. The Kepler problem can be solved in multiple ways, including by demonstrating that the
4286:
3777:
3487:
3461:
3401:
2670:
these forces have equal magnitude but opposite direction, so they cancel when added, and
1297:
866:
500:
441:
419:
164:
159:
154:
54:
15146:. Boston Studies in the Philosophy of Science. Vol. 187. Kluwer. pp. 197β210.
15109:
14995:
14938:
14812:
14804:
14485:
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14390:
13979:
13677:
13573:
13426:
13187:
13076:
12922:
12802:
12634:
12540:
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12348:
12299:
12206:
12157:
12097:
12038:
11966:
11560:
11500:
11397:
11301:
11249:
11151:
11102:
10997:
10945:
10847:
10697:
10653:
10557:
10429:
10318:
10269:
10217:
9927:
9836:
9521:
9472:
9376:
9234:
8563:
According to Huygens, this law was already known by Galileo and Descartes among others.
8071:
in such a way that all inertial observers will agree upon the speed of light in vacuum.
7182:
Interchanging the order of the partial derivatives on the left-hand side, and using the
5446:
stands for an external influence like a gravitational pull. Incorporating the effect of
4232:{\displaystyle \mathbf {F} =M{\frac {d\mathbf {v} }{dt}}-\mathbf {u} {\frac {dM}{dt}}\,}
3041:
can be taken to be constant. This particular value of acceleration is typically denoted
2921:
1276:
1253:
15989:
15898:
15614:
15527:
15255:
15194:
15015:
14958:
14824:
14754:
14735:
14644:
14554:
14546:
14335:
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14240:
14210:
14043:
13942:
13934:
13837:
13751:
13743:
13699:
13642:
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13489:
13389:
13209:
13165:
13146:
13120:
13088:
13062:
12954:
12713:
12654:
12560:
12526:
12368:
12117:
12083:
12050:
12025:
11998:
11912:
11733:
11672:
11644:
11520:
11486:
11269:
11212:
11019:
10867:
10729:
10631:
10579:
10511:
10338:
10040:
9848:
9681:
9634:
9484:
9320:
9179:
9103:
called him "the last of the magicians" to describe his place in the transition between
8687:
with three primary laws and then other statements reduced to corollaries, during 1685.
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246:
214:
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10460:
7420:
This is another re-expression of Newton's second law. The expression in brackets is a
1100:{\displaystyle {\frac {\Delta s}{\Delta t}}={\frac {s(t_{1})-s(t_{0})}{t_{1}-t_{0}}}.}
15984:
15857:
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15554:
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14907:. From that time forward, Newtonian science sprang from Laplace's work, not Newton's.
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11792:
11774:(2006). "Existence and smoothness of the NavierβStokes equation". In Carlson, James;
11771:
11753:
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11676:
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9459:
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9202:
9167:. Translated by Cohen, I.B.; Whitman, A. Los Angeles: University of California Press.
9140:
8661:
8459:
8395:
8252:
8229:
8224:
8053:
There is subtle conceptual conflict between electromagnetism and Newton's first law:
8035:
7865:
7621:
7610:
4621:
3275:
3141:
2754:
2428:
2427:
as well as material bodies carry momentum, and when momentum is defined properly, in
2340:
2321:
2279:
2000:
1918:
878:
640:
597:
554:
549:
490:
266:
256:
149:
15178:
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11524:
8433:
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15793:
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15113:
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14719:
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12806:
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12352:
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12069:
12042:
11980:
11970:
11654:
11564:
11504:
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11155:
11106:
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10949:
10924:
10851:
10711:
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10597:
10583:
10561:
10544:
10535:
10433:
10411:
10322:
10273:
10221:
10015:
10001:
9931:
9881:
Resnick, Robert; Halliday, David (1966). "Section 5-4: Mass; Newton's Second Law".
9840:
9691:
9626:
9525:
9476:
9380:
8942:
8868:
8818:
8657:
8650:
8613:": whether or not a model like Descartes's vortices could be found to underlie the
8438:
7741:
7693:
5113:
5049:
4679:, then the body's angular momentum with respect to that point is, using the vector
4625:
4299:
4278:
2961:
cancels from both sides of the equation, leaving an acceleration that depends upon
735:
715:
660:
655:
601:
576:
431:
289:
234:
209:
15091:
13961:
13408:
12512:
12281:
12188:
12139:
11728:(2021). "Struggles with the Continuum". In Anel, Mathieu; Catren, Gabriel (eds.).
11542:
11428:
11379:
11133:
10251:
9936:
9909:
9779:
9530:
9503:
8945:) take the conservation of momentum as a fundamental physical principle and treat
3182:
2771:. In between bounces, the ball's height as a function of time is close to being a
15805:
15574:
15468:
13515:
13048:
12978:
The Disordered Cosmos: A Journey into Dark Matter, Spacetime, and Dreams Deferred
12277:
11690:
11543:"A unit on oscillations, determinism and chaos for introductory physics students"
11084:
10252:"Changing the Order of Newton's LawsβWhy & How the Third Law Should be First"
10089:
10036:
9967:
9359:"Student difficulties in connecting graphs and physics: Examples from kinematics"
9083:
9051:
Details can be found in the textbooks by, e.g., Cohen-Tannoudji et al. and Peres.
8707:
8639:
8597:
8509:
8455:
8390:
8386:
8286:
8210:
8047:
7745:
7719:
7595:
6158:
constrained to move in a straight line, under the effect of a potential. Writing
5148:
3948:
3177:
2385:
730:
675:
625:
620:
539:
14946:
14848:
Forces and Fields: The Concept of Action at a Distance in the History of Physics
14418:
12435:
11698:
9844:
9358:
9178:
Newton, Isaac; Chittenden, N. W.; Motte, Andrew; Hill, Theodore Preston (1846).
7609:
applies Newton's laws of motion to large numbers (typically on the order of the
6407:{\displaystyle {\frac {dp}{dt}}=-{\frac {\partial {\mathcal {H}}}{\partial q}}.}
16001:
15848:
15673:
15656:
15626:
15413:
14666:
14302:
14215:
13196:
13169:
13134:
12931:
12904:
12755:
12473:
11820:
11538:
11332:
10925:"Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks"
10649:
10105:
9728:
9711:"Mistranslation of Newton's First Law Discovered after Nearly Nearly 300 Years"
9630:
9316:
8776:
8505:
8171:
8059:
5608:
5607:
and able to approach one another arbitrarily closely, as well as the lack of a
5068:
5058:
4564:{\displaystyle \mathbf {R} =\sum _{i=1}^{N}{\frac {m_{i}\mathbf {r} _{i}}{M}},}
4383:
4369:
4357:
4282:
4274:
3278:, is therefore also directed toward the center of the circle and has magnitude
2325:
1128:
757:
665:
566:
283:
14723:
14632:
14534:
14279:
14118:
13084:
13034:
12996:
12905:"Free fall in curved spacetimeβhow to visualise gravity in general relativity"
12856:
12810:
12425:
11933:
11757:
11615:
9740:
9216:
6337:{\displaystyle {\frac {dq}{dt}}={\frac {\partial {\mathcal {H}}}{\partial p}}}
16059:
15893:
15775:
15717:
15161:
15125:
15011:
14881:
14820:
14731:
14690:
14640:
14599:
14542:
14501:
14472:
14452:
14323:
14236:
14206:
14192:
14082:
14039:
14009:
13995:
13876:
13833:
13695:
13655:
13638:
13608:
13591:
13537:
13501:
13452:
13385:
13354:
13317:
13205:
13142:
12950:
12818:
12699:
12650:
12556:
12364:
12315:
12263:
12222:
12173:
12113:
11994:
11893:
11865:
11806:
11668:
11576:
11516:
11454:
11413:
11364:
11265:
11208:
11167:
11118:
11069:
11015:
10980:"A unified, contemporary approach to teaching energy in introductory physics"
10961:
10863:
10814:
10725:
10627:
10619:
10575:
10445:
10407:
10375:
10334:
10285:
10233:
10123:
10044:
9987:
9945:
9803:
9658:
9578:
9539:
9455:"Students' use of the principle of energy conservation in problem situations"
9439:
9392:
9340:
9295:
8772:
8451:
7894:
5076:
4680:
3992:
2764:
2724:
2397:
814:
645:
472:
14866:
14375:
14031:
13374:
Annali della Scuola Normale Superiore di Pisa. Classe di Lettere e Filosofia
13283:
12741:
12605:
12497:
11848:
10909:
10776:
7945:{\displaystyle \mathbf {F} =q\mathbf {E} +q\mathbf {v} \times \mathbf {B} .}
6790:
changes most steeply. In other words, the momentum of the point mass is the
2759:
1924:
The study of mechanics is complicated by the fact that household words like
16037:
15781:
15651:
15460:
15435:
15398:
15240:
14954:
14259:
14151:
13014:
12976:
12239:
12135:
12046:
12020:
11779:
11775:
11725:
10752:
10601:
10170:
9196:
9104:
9015:
Among the many textbook explanations of this are Frautschi et al. and Boas.
8411:
8307:
6119:
5144:
5130:
3880:{\displaystyle {\frac {d^{2}\theta }{dt^{2}}}=-{\frac {g}{L}}\sin \theta ,}
2329:
2283:
852:
837:
710:
635:
324:
204:
14851:(Dover reprint ed.). Mineola, N.Y.: Dover Publications. p. 189.
14670:
14062:
13856:
12679:
12410:
12243:
11232:"Bohlin transformation: the hidden symmetry that connects Hooke to Newton"
11049:
10068:
9783:
9419:
8462:. Descartes knew about this controversy and did not wish to get involved.
2198:{\displaystyle \mathbf {F} =m{\frac {d\mathbf {v} }{dt}}=m\mathbf {a} \,.}
15799:
15408:
15287:
15185:
15139:
14846:
14101:
The Foundations of Newton's Alchemy: Or, "the Hunting of the Greene Lyon"
13255:
12721:
12477:
12016:
11828:
11694:
11659:
11593:
11340:
10975:
10889:
10716:
9235:"Classical Dynamics: University of Cambridge Part II Mathematical Tripos"
9198:
Techniques of Classical Mechanics: from Lagrangian to Newtonian mechanics
8665:
8454:
worldview, and in 1633 this view had given rise a great conflict between
8175:
7731:
6552:
5852:. The physical path that the particle will take between an initial point
2768:
1416:
can be made arbitrarily small by choosing an input sufficiently close to
15090:
Silva, Cibelle Celestino; de Andrade Martins, Roberto (September 2002).
15069:"History of the Conservation of Energy: Booms, Blood, and Beer (Part 3)"
15055:"History of the Conservation of Energy: Booms, Blood, and Beer (Part 2)"
15038:"History of the Conservation of Energy: Booms, Blood, and Beer (Part 1)"
14550:
14516:
13789:
Two new sciences, including centers of gravity & force of percussion
13493:
13393:
13369:
13019:. Providence, Rhode Island: American Mathematical Society. p. 143.
12513:"Self-torque and angular momentum balance for a spinning charged sphere"
9695:
9553:
Urone, Paul Peter; Hinrichs, Roger; Dirks, Kim; Sharma, Manjula (2021).
7590:
15923:
15811:
14842:
14784:
14353:
13841:
13792:. Translated by Drake, S. University of Wisconsin Press. pp. 217 .
13630:
13443:
13409:"Experiments on buoyancy and surface tension following Galileo Galilei"
12941:
12838:
Curvature of Space and Time, with an Introduction to Geometric Analysis
12390:
12105:
11907:
10085:
8938:
8822:
7187:
7183:
6669:. The Hamiltonian is incorporated into the HamiltonβJacobi equation, a
3406:
3187:
2401:
1795:
Position, when thought of as a displacement from an origin point, is a
1247:
902:
836:
At any instant of time, the net force on a body is equal to the body's
495:
169:
15117:
14493:
14331:
14297:
13987:
13938:
13914:
13747:
13723:
13554:
Eaton, Philip; Vavruska, Kinsey; Willoughby, Shannon (25 April 2019).
13478:(2nd ed.). Institute of Classical Studies, University of London.
13434:
12548:
12307:
12214:
12165:
11985:
11568:
11446:
11405:
11159:
11134:"Student understanding of the angular momentum of classical particles"
11006:
10979:
10437:
10277:
10225:
10019:
5625:
2400:. This pushes the rocket upwards, without regard to the ground or the
840:
multiplied by its mass or, equivalently, the rate at which the body's
15033:
11110:
11036:
10566:
10539:
9415:
9264:
9181:
Newton's Principia: The Mathematical Principles of Natural Philosophy
8590:
One important characteristic of Newtonian physics is that forces can
8469:
8375:
8367:
8261:
8197:
8147:
7735:
5447:
5088:
5067:
orbits that an inverse-square force law will produce is known as the
4387:
4045:
2780:
2750:
517:
14444:
13825:
12619:
Werner, Reinhard F. (9 October 2014). "Comment on "What Bell did"".
10953:
9384:
8629:
8436:
introduced the concept of inertia by way of his "laws of nature" in
7665:{\displaystyle m\mathbf {a} =-\gamma \mathbf {v} +\mathbf {\xi } \,}
3131:{\displaystyle g={\frac {GM}{r^{2}}}\approx \mathrm {9.8~m/s^{2}} .}
15445:
15386:
15209:
15183:
14710:
14315:
14261:
Dutch Light: Christiaan Huygens and the Making of Science in Europe
14228:
13930:
13739:
13125:
13067:
12531:
12088:
11830:
The Conceptual Foundations of the Statistical Approach in Mechanics
11738:
11649:
9686:
9560:
9033:
Treatments can be found in, e.g., Chabay et al. and McCallum et al.
8806:
8403:
7954:
7614:
6791:
5084:
4295:
3804:
3145:
2772:
2029:
1153:
841:
436:
319:
294:
13660:"University student conceptual resources for understanding forces"
11914:
Out of the Shadows: Contributions of 20th Century Women to Physics
11491:
8529:
Ball in circular motion has string cut and flies off tangentially.
8525:
6414:
Evaluating these partial derivatives, the former equation becomes
6124:
a celebrated theorem that relates symmetries and conservation laws
2320:
A common visual representation of forces acting in concert is the
2265:{\displaystyle \mathbf {F} =m{\frac {d^{2}\mathbf {s} }{dt^{2}}}.}
15403:
15391:
15279:
11631:"From Newton's second law to Euler's equations of perfect fluids"
9096:
9060:
As one physicist writes, "Physical theory is possible because we
8727:
8371:
8325:
Newton's first and second laws, in Latin, from the original 1687
5244:
5080:
4956:{\displaystyle \mathbf {\tau } =\mathbf {r} \times \mathbf {F} .}
4261:
is the net external force (e.g., a planet's gravitational pull).
1993:
1975:
409:
262:
179:
14064:
Science and Culture in the Nineteenth Century: Recreating Newton
9890:
9625:
9165:
The Principia, The Mathematical Principles of Natural Philosophy
9112:, in particular, how he thought about the combination of colors.
8714:
Here, Somerville deduces the inverse-square law of gravity from
2419:
Newton's third law relates to a more fundamental principle, the
1910:{\displaystyle \mathbf {v} =(\mathrm {3~m/s} ,\mathrm {4~m/s} )}
15957:
13265:
11910:(2006). "Emmy Noether". In Byers, Nina; Williams, Gary (eds.).
9672:
Hoek, D. (2023). "Forced Changes Only: A New Take on Inertia".
9109:
8735:
8306:, with hand-written corrections for the second edition, in the
6853:{\displaystyle \mathbf {v} ={\frac {1}{m}}\mathbf {\nabla } S.}
6089:{\displaystyle {\frac {d}{dt}}(m{\dot {q}})=-{\frac {dV}{dq}},}
4922:
point in the same direction. The remaining term is the torque,
4629:
4270:
2408:
Overly brief paraphrases of the third law, like "action equals
2389:
2274:
818:
468:
314:
224:
14177:(2nd ed.). Cambridge University Press. pp. 454β484.
13051:(1993). "Hidden variables and the two theorems of John Bell".
10412:"Newton's Zeroth Law: Learning from Listening to Our Students"
8864:
List of textbooks on classical mechanics and quantum mechanics
7413:{\displaystyle \left\mathbf {\nabla } S=-\mathbf {\nabla } V.}
7294:
Gathering together the terms that depend upon the gradient of
6613:{\displaystyle S(\mathbf {q} _{1},\mathbf {q} _{2},\ldots ,t)}
5243:. The mass of an infinitesimal portion depends upon the fluid
5040:
chosen axis, the shape of the body, and the rate of rotation.
4374:
3458:
axis, and suppose an equilibrium point exists at the position
2534:{\displaystyle \mathbf {p} =\mathbf {p} _{1}+\mathbf {p} _{2}}
14468:"The vis viva dispute: A controversy at the dawn of dynamics"
13613:"Impetus-Like Reasoning as Continuous with Newtonian Physics"
9643:(Advanced ed.). Cambridge : Cambridge University Press.
7991:
7613:) of particles. Kinetic theory can explain, for example, the
6273:{\displaystyle {\mathcal {H}}(p,q)={\frac {p^{2}}{2m}}+V(q).}
5163:
4717:{\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} .}
3317:
1971:
822:
304:
299:
241:
15184:
Chakrabarty, Deepto; Dourmashkin, Peter; Tomasik, Michelle;
14419:"The young Huygens solves the problem of elastic collisions"
14298:"The First English Version of Newton's Hypotheses non fingo"
13407:
Straulino, S.; Gambi, C. M. C.; Righini, A. (January 2011).
12511:
Bonga, BΓ©atrice; Poisson, Eric; Yang, Huan (November 2018).
11946:
10356:
Hodanbosi, Carol (August 1996). Fairman, Jonathan G. (ed.).
9903:
8821:, stemmed from and largely supplanted the earlier system of
8675:
Newton arrived at his set of three laws incrementally. In a
5062:
Animation of three points or bodies attracting to each other
3186:
Two objects in uniform circular motion, orbiting around the
2431:
as well. In Newtonian mechanics, if two bodies have momenta
15179:
Newtonβs Laws of Dynamics - The Feynman Lectures on Physics
13653:
13606:
12841:. Providence, Rhode Island: American Mathematical Society.
10677:
9915:
Physical Review Special Topics - Physics Education Research
9509:
Physical Review Special Topics - Physics Education Research
8794:
8347:
5823:
and the potential energy is some function of the position,
4379:
3144:. When air resistance can be neglected, projectiles follow
2113:{\displaystyle \mathbf {F} ={\frac {d\mathbf {p} }{dt}}\,.}
309:
272:
16032:
14173:(2016). "A preliminary reassessment of Newton's alchemy".
13861:. New York: Cambridge University Press. pp. 175β180.
12392:
The principles of electromagnetic theory and of relativity
9353:
8710:'s expanded version of the first two volumes of Laplace's
8624:
7889:
and to the strength of the electric field. In addition, a
7730:
Newton's three laws can be applied to phenomena involving
6115:
1999:
The modern understanding of Newton's first law is that no
14358:
Concepts of Force: A Study in the Foundations of Dynamics
11918:. Cambridge: Cambridge University Press. pp. 83β96.
11377:
9177:
8466:
was not published until 1664, ten years after his death.
8359:
7585:
4724:
Taking the time derivative of the angular momentum gives
4484:{\displaystyle \mathbf {r} _{1},\ldots ,\mathbf {r} _{N}}
4044:
by an applied force, which can lead to the phenomenon of
102:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
13858:
Pierre Gassendi and the Birth of Early Modern Philosophy
12331:"Breaking Newton's third law: electromagnetic instances"
11730:
New Spaces in Physics: Formal and Conceptual Reflections
11427:
McCandlish, David (July 1973). Shirer, Donald L. (ed.).
10923:
Billah, K. Yusuf; Scanlan, Robert H. (1 February 1991).
9868:
An Introduction to the Physics of Mass, Length, and Time
9552:
9421:
Mathematical Methods for Optical Physics and Engineering
6770:, and the point mass moves in the direction along which
4615:
1974:, rather than in straight lines, because of the Earth's
938:, then its average velocity over the time interval from
37:"F=ma" redirects here. For the physics competition, see
15089:
14360:. Mineola, N.Y.: Dover Publications. pp. 91, 127.
13553:
13226:
12879:
Geons, Black Holes, and Quantum Foam: A Life in Physics
12070:"The HamiltonβJacobi equation: An alternative approach"
9972:(2nd ed.). Cambridge: Cambridge University Press.
8928:
decided to switch to some more interesting profession."
2328:
can illustrate the combination of gravitational force,
12189:"Hydrodynamic Analogy to the HamiltonβJacobi Equation"
9357:; Rosenquist, Mark L.; van Zee, Emily H. (June 1987).
7580:
825:
acting on it. These laws, which provide the basis for
15973:
13769:
Galilei, G. (1954) . Crew, H.; De Salvio, A. (eds.).
13406:
13108:
11629:
Han-Kwan, Daniel; Iacobelli, Mikaela (7 April 2021).
11132:
Close, Hunter G.; Heron, Paula R. L. (October 2011).
10602:"Galileo and Oresme: Who Is Modern? Who Is Medieval?"
10246:
9870:. United Kingdom: University Press. pp. 126β128.
8951:
8748:
8156:
8132:
8096:
8003:
7968:
7903:
7875:
7836:
7809:
7782:
7755:
7702:
7678:
7630:
7438:
7320:
7300:
7196:
7081:
6978:
6972:, in which case the HamiltonβJacobi equation becomes
6947:
6866:
6820:
6800:
6776:
6739:
6719:
6699:
6679:
6655:
6626:
6561:
6473:
6420:
6350:
6286:
6204:
6184:
6164:
6144:
6020:
5921:
5885:
5858:
5829:
5774:
5715:
5686:
5666:
5580:
5460:
5430:
5410:
5390:
5291:
5253:
5216:
5176:
5020:
4998:
4970:
4928:
4903:
4881:
4730:
4689:
4663:
4641:
4598:
4577:
4497:
4447:
4401:
4308:
4245:
4166:
4144:
4113:
4084:
4001:
3977:
3957:
3933:
3913:
3893:
3814:
3780:
3760:
3740:
3708:
3688:
3622:
3552:
3520:
3490:
3464:
3444:
3424:
3367:
3326:
3284:
3240:
3220:
3200:
3154:
3067:
3047:
3027:
3007:
2987:
2967:
2947:
2924:
2904:
2884:
2864:
2844:
2793:
2698:
2676:
2569:
2547:
2495:
2489:
respectively, then the total momentum of the pair is
2466:
2437:
2353:
2211:
2146:
2126:
2075:
2038:
1851:
1827:
1805:
1747:
1625:
1510:
1449:
1422:
1402:
1382:
1355:
1335:
1306:
1279:
1256:
1206:
1186:
1166:
1137:
1113:
998:
971:
944:
915:
66:
13915:"Christiaan Huygens' The Motion of Colliding Bodies"
13476:
Philoponus and the Rejection of Aristotelian Science
11473:"Integrability and chaos: the classical uncertainty"
10250:; Rayner, John P.; Gore, Michael M. (October 2012).
10035:
9910:"Do students use and understand free-body diagrams?"
9280:(6th ed.). Hoboken, NJ: Wiley. pp. 76β78.
8726:
he had already developed calculus (which he called "
8342:
4335:{\displaystyle \mathbf {F} =-\mathbf {\nabla } U\,.}
4294:
case, then the force can be written in terms of the
3675:{\displaystyle x(t)=A\cos \omega t+B\sin \omega t\,}
1246:
This denotes that the instantaneous velocity is the
30:"Newton's laws" redirects here. For other uses, see
14926:
Studies in History and Philosophy of Science Part A
13913:Blackwell, Richard J.; Huygens, Christiaan (1977).
12580:
12482:(2nd ed.). Mineola, N.Y.: Dover Publications.
11323:
11321:
10974:
10462:
Classical Mechanics: Point Particles and Relativity
9502:Brookes, David T.; Etkina, Eugenia (25 June 2009).
9453:Driver, Rosalind; Warrington, Lynda (1 July 1985).
9158:
9156:
6526:{\displaystyle {\frac {dp}{dt}}=-{\frac {dV}{dq}},}
5626:
Relation to other formulations of classical physics
5616:
existence and smoothness of NavierβStokes solutions
2282:for a block on an inclined plane, illustrating the
14787:"Leonhard Euler and the mechanics of rigid bodies"
12622:Journal of Physics A: Mathematical and Theoretical
11911:
11819:
9184:. University of California Libraries. Daniel Adee.
8970:
8763:
8522:) in 1644, with the heliocentric part toned down.
8162:
8138:
8118:
8026:
7982:
7944:
7881:
7849:
7822:
7795:
7768:
7710:
7684:
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7412:
7306:
7286:
7174:
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6852:
6806:
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6725:
6705:
6685:
6661:
6641:
6612:
6525:
6459:
6406:
6336:
6272:
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6150:
6088:
6002:
5898:
5871:
5844:
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5566:
5438:
5416:
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5277:
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4889:
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4649:
4604:
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4334:
4253:
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4099:
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2555:
2533:
2481:
2452:
2361:
2264:
2197:
2132:
2112:
2061:
2028:By "motion", Newton meant the quantity now called
1909:
1837:
1813:
1784:
1729:
1608:
1496:
1435:
1408:
1388:
1368:
1341:
1321:
1288:
1265:
1238:
1192:
1172:
1143:
1119:
1099:
984:
957:
930:
101:
15934:Statal Institute of Higher Education Isaac Newton
14257:
12971:
12726:(2nd ed.). Oxford: Oxford University Press.
11628:
11429:"Solutions to the Three-Body Problem by Computer"
11380:"Invitation to embarrassingly parallel computing"
9819:"A note on rods and clocks in Newton's Principia"
8119:{\displaystyle \mathbf {p} =m\gamma \mathbf {v} }
6860:The HamiltonβJacobi equation for a point mass is
5143:Newton's laws of motion allow the possibility of
4350:
2717:
1982:Translated from Latin, Newton's first law reads,
16057:
14576:. Oxford University Press. Online before print.
14103:. Cambridge University Press. pp. 211β212.
13912:
13302:. Cambridge University Press. pp. 310β311.
13220:
12510:
12468:
11732:. Cambridge University Press. pp. 281β326.
11636:Proceedings of the American Mathematical Society
11600:. Princeton University Press. pp. 363β364.
11349:. Princeton University Press. pp. 726β728.
11318:
11296:. American Mathematical Society. pp. 8β12.
11280:
10524:. Vol. 15 (9th ed.). pp. 715β716.
9965:
9452:
9260:
9258:
9153:
8285:Isaac Newton (1643β1727), in a 1689 portrait by
7075:Taking the gradient of both sides, this becomes
6460:{\displaystyle {\frac {dq}{dt}}={\frac {p}{m}},}
3609:{\displaystyle m{\frac {d^{2}x}{dt^{2}}}=-kx\,.}
2335:Newton's second law is sometimes presented as a
1656:
1535:
1451:
14067:. New York: Taylor & Francis. p. 147.
12590:(3rd ed.). San Francisco: Addison Wesley.
12464:
12462:
11183:"Another comment on "Eccentricity as a vector""
10654:"Frequently Asked Questions: Projectile Motion"
10198:Low, David J.; Wilson, Kate F. (January 2017).
9880:
9424:. Cambridge, U.K.: Cambridge University Press.
9311:
9133:Thornton, Stephen T.; Marion, Jerry B. (2004).
8605:and others created a precedent for thinking of
8366:The subject of physics is often traced back to
7744:for the electric force between two stationary,
5816:{\displaystyle T={\frac {1}{2}}m{\dot {q}}^{2}}
4281:, due to a body's position relative to others.
3927:is its angle from the vertical. When the angle
2744:
14620:The British Journal for the History of Science
14522:The British Journal for the History of Science
14165:
14163:
14161:
12674:
12430:. Totowa, NJ: Humana Press. pp. 137β154.
12248:(4th ed.). Weinheim, Germany: Wiley-VCH.
12067:
10799:(1st ed.). New York: Spiegel & Grau.
10084:
9966:Kleppner, Daniel; Kolenkow, Robert J. (2014).
9132:
8228:conceptual underpinning of quantum physics is
7860:Electromagnetism treats forces as produced by
1992:Newton's first law expresses the principle of
851:The three laws of motion were first stated by
15225:
14918:
13163:
12712:
12681:General Relativity and the Einstein Equations
10978:; Sherwood, Bruce; Titus, Aaron (July 2019).
10922:
10883:
10881:
10828:Topper, D.; Vincent, D. E. (1 January 1999).
10827:
10758:Mathematical Methods in the Physical Sciences
10485:
10169:
9501:
9255:
8230:very different from that of classical physics
8046:electromagnetic field is proportional to the
5119:
4051:
2767:photographed at 25 frames per second using a
2062:{\displaystyle \mathbf {p} =m\mathbf {v} \,,}
863:Mathematical Principles of Natural Philosophy
791:
15092:"Polar and axial vectors versus quaternions"
14757:Philosophiae Naturalis Principia Mathematica
13474:Sorabji, Richard (2010). "John Philoponus".
12584:; Poole, Charles P.; Safko, John L. (2002).
12459:
11833:. New York: Dover Publications. p. 18.
11707:Notices of the American Mathematical Society
11470:
11327:
11286:
11082:
10830:"An analysis of Newton's projectile diagram"
10406:
8421:
7571:{\displaystyle \left=\left={\frac {d}{dt}}.}
6198:for the body's momentum, the Hamiltonian is
5202:{\displaystyle \mathbf {v} (\mathbf {x} ,t)}
3616:This differential equation has the solution
14158:
14136:. Cambridge University Press. p. 390.
12423:
11471:Masoliver, Jaume; Ros, Ana (1 March 2011).
10796:How I Killed Pluto and Why It Had It Coming
10100:. Vol. 1. Translated by Sykes, J. B.;
10004:(1958). "On the Classical Laws of Motion".
9961:
9959:
9957:
9955:
9785:Classical dynamics: A Contemporary Approach
9778:
9640:The Mechanical Universe: Mechanics and Heat
9136:Classical Dynamics of Particles and Systems
8668:would apply momentum conservation to study
8566:
5278:{\displaystyle \mathbf {a} =\mathbf {F} /m}
1273:to the infinitesimally small time interval
901:The mathematical description of motion, or
889:Newton's laws are often stated in terms of
858:Philosophiæ Naturalis Principia Mathematica
817:that describe the relationship between the
15232:
15218:
14517:"Some Reflections on Newton's "Principia""
13890:Descartes, R. (2008) . Bennett, J. (ed.).
13665:Physical Review Physics Education Research
13561:Physical Review Physics Education Research
12868:
12866:
11954:Physical Review Physics Education Research
11588:
11586:
11426:
11131:
10878:
10685:Physical Review Physics Education Research
10298:
10053:. Reading, Mass.: Addison-Wesley Pub. Co.
9788:. Cambridge : Cambridge University Press.
9307:
9305:
8971:{\displaystyle \mathbf {F} =m\mathbf {a} }
8859:List of scientific laws named after people
8339:theory of mechanics could encompass both.
7190:on the first term on the right-hand side,
6280:In this example, Hamilton's equations are
3171:
798:
784:
14613:Patterson, Elizabeth C. (December 1969).
14612:
14416:
13962:"Is Newton's second law really Newton's?"
13889:
13721:
13685:
13581:
13442:
13195:
13124:
13066:
13009:
12940:
12930:
12762:. W. W. Norton and Company. p. 224.
12530:
12087:
11984:
11974:
11770:
11737:
11658:
11648:
11490:
11005:
10894:. Cambridge: Cambridge University Press.
10887:
10715:
10705:
10648:
10565:
10534:
10355:
10197:
10080:
10078:
10050:The Feynman Lectures on Physics, Volume 1
9935:
9685:
9591:
9529:
9139:(5th ed.). Brooke Cole. p. 49.
8937:For example, JosΓ© and Saletan (following
8793:had left open, like a full theory of the
8504:of the Earth. This idea was corrected by
8381:
7994:) around the magnetic field lines at the
7661:
4328:
4228:
3671:
3602:
2191:
2106:
2055:
1497:{\displaystyle \lim _{t\to t_{0}}f(t)=L.}
14975:
14675:(1st ed.). Oxford: Pergamon Press.
14205:
13959:
13298:Fuchs, Christopher A. (6 January 2011).
12902:
12385:
11689:
10888:Hand, Louis N.; Finch, Janet D. (1998).
10596:
10540:"The Transverse Momentum of an Electron"
10486:Wachter, Armin; Hoeber, Henning (2006).
10000:
9952:
9596:. New York: Macmillan. pp. 123β125.
9546:
8854:List of equations in classical mechanics
8697:
8628:
8619:every attempt at such a model has failed
8570:
8524:
8492:
8468:
8351:
7953:
7803:is equal in magnitude to the force that
7589:
6114:
5232:has two terms, a combination known as a
5134:
5057:
4373:
4360:and movement around the center of mass.
4061:
3405:
3181:
2758:
2384:
2273:
1970:Artificial satellites move along curved
1965:
1785:{\displaystyle {\frac {d^{2}s}{dt^{2}}}}
14060:
13854:
13802:
13785:
13768:
13473:
13367:
12872:
12863:
12834:
12329:Kneubil, Fabiana B. (1 November 2016).
12328:
11583:
11083:Lyublinskaya, Irina E. (January 1998).
10747:
10745:
10743:
10458:
10374:
9865:
9816:
9727:
9302:
9126:
8738:to be more rigorous. Consequently, the
8625:Momentum conservation and the third law
7738:, though subtleties and caveats exist.
6138:. The simplest example is a point mass
2831:{\displaystyle F={\frac {GMm}{r^{2}}},}
2310:. A state of mechanical equilibrium is
14:
16058:
14703:
14514:
14388:
14352:
14169:
13908:
13906:
13808:"Science in the Renaissance: A Survey"
13775:. Dover Publications Inc. p. 268.
13717:
13715:
13658:; Heron, Paula R. L. (30 March 2021).
13330:
13300:Coming of Age with Quantum Information
13230:; Diu, Bernard; LaloΓ«, Franck (2005).
13047:
12754:
12618:
12276:
12245:A Modern Course in Statistical Physics
12238:
12186:
11864:
11346:The Princeton Companion to Mathematics
11230:Saggio, Maria Luisa (1 January 2013).
11229:
11180:
10410:; Redish, Edward F. (1 January 2005).
10075:
10031:
10029:
9774:
9772:
9770:
9709:Pappas, Stephanie (5 September 2023).
9708:
9162:
8690:
8660:would later deduce the same rules for
7586:Thermodynamics and statistical physics
2347:. By inserting such an expression for
1737:Consequently, the acceleration is the
27:Laws in physics about force and motion
15484:Newton's law of universal gravitation
15213:
15138:
14978:"History of physical terms: "energy""
14879:
14841:
14752:
14672:The Origins of Infinitesimal Calculus
14665:
14582:10.1093/oxfordhb/9780199930418.013.35
14571:
14465:
14292:
14095:
13772:Dialogues Concerning Two New Sciences
13654:Robertson, Amy D.; Goodhew, Lisa M.;
13607:Robertson, Amy D.; Goodhew, Lisa M.;
13514:
13297:
13254:
12782:
12670:
12668:
12576:
12574:
12427:Biomedical Applications of Biophysics
12234:
12232:
12140:"Mixed States in Classical Mechanics"
12134:
11906:
11860:
11858:
11466:
11464:
11331:(2008). "The Three-Body Problem". In
11085:"Central collisionsβThe general case"
10789:
10140:
9768:
9766:
9764:
9762:
9760:
9758:
9756:
9754:
9752:
9750:
9621:
9619:
9617:
9615:
9613:
9611:
9609:
9607:
9605:
9603:
9410:
9408:
9406:
9404:
9402:
8394:body into motion imparted a quality,
8188:
8074:
5124:
4616:Rotational analogues of Newton's laws
4026:{\displaystyle \omega ={\sqrt {g/L}}}
2345:Newton's law of universal gravitation
480:Newton's law of universal gravitation
15642:Newton's theorem of revolving orbits
15239:
15032:
14131:
14008:
13883:
13687:10.1103/PhysRevPhysEducRes.17.010121
13583:10.1103/PhysRevPhysEducRes.15.010123
13522:. University of Pennsylvania Press.
13261:Quantum Theory: Concepts and Methods
12015:
11976:10.1103/PhysRevPhysEducRes.15.020126
11724:
11537:
11054:(6th ed.). Hoboken, NJ: Wiley.
10761:(3rd ed.). Hoboken, NJ: Wiley.
10751:
10740:
10707:10.1103/PhysRevPhysEducRes.16.010111
10510:
10141:Moebs, William; et al. (2023).
9671:
9414:
9229:
9194:
8219:
8205:spacetime curvature is given by the
8055:Maxwell's theory of electromagnetism
5761:{\displaystyle L(q,{\dot {q}})=T-V,}
4269:Physicists developed the concept of
3267:{\displaystyle a={\frac {v^{2}}{r}}}
15590:LeibnizβNewton calculus controversy
15331:standing on the shoulders of giants
14919:Reichenberger, Andrea (June 2018).
14887:Stanford Encyclopedia of Philosophy
14764:Stanford Encyclopedia of Philosophy
14417:Erlichson, Herman (February 1997).
14396:Stanford Encyclopedia of Philosophy
13903:
13712:
13611:; Heron, Paula R. L. (March 2021).
13370:"Aristotle's Hydrostatical Physics"
12684:. Oxford: Oxford University Press.
12479:Classical Electricity and Magnetism
12068:Houchmandzadeh, Bahram (May 2020).
11592:
11293:PoincarΓ© and the Three Body Problem
10465:. New York: Springer. p. 135.
10026:
9095:Newton himself was an enthusiastic
7725:
7581:Relation to other physical theories
4491:, the center of mass is located at
4434:{\displaystyle m_{1},\ldots ,m_{N}}
1239:{\displaystyle v={\frac {ds}{dt}}.}
461:Mechanics of planar particle motion
69:
24:
15172:
14976:Frontali, Clara (September 2014).
14880:Smith, George (19 December 2007).
14753:Smith, George (20 December 2007).
14389:Slowik, Edward (15 October 2021).
13518:(1982). Sargent, Steven D. (ed.).
12665:
12571:
12229:
11855:
11461:
11051:Calculus: Single and Multivariable
9817:Brading, Katherine (August 2019).
9747:
9733:Introduction to Special Relativity
9600:
9399:
9278:Calculus: Single and Multivariable
8997:See, for example, Frautschi et al.
8677:1684 manuscript written to Huygens
8543:According to American philosopher
8236:, one considers what result might
7538:
7517:
7513:
7489:
7478:
7450:
7446:
7400:
7386:
7371:
7360:
7332:
7328:
7274:
7263:
7253:
7242:
7216:
7206:
7202:
7162:
7140:
7129:
7101:
7093:
7086:
7027:
6993:
6985:
6910:
6881:
6873:
6840:
6542:
6392:
6385:
6380:
6325:
6318:
6313:
6207:
5988:
5980:
5952:
5944:
5539:
5525:
5488:
5472:
5464:
5356:
5319:
5303:
5295:
5036:are directed along the same line.
4628:, and the counterpart of force is
4321:
4264:
3907:is the length of the pendulum and
3395:
3234:, its acceleration has a magnitude
3115:
3106:
2290:), the downward force of gravity (
1900:
1892:
1878:
1870:
1715:
1689:
1660:
1594:
1568:
1539:
1167:
1114:
1010:
1002:
25:
16117:
14466:Smith, George E. (October 2006).
14175:The Cambridge Companion to Newton
13520:On the Threshold of Exact Science
12981:. New York, NY: Bold Type Books.
10490:. New York: Springer. p. 6.
10488:Compendium of theoretical physics
9908:; Etkina, Eugenia (1 June 2009).
9504:""Force," ontology, and language"
8716:Kepler's laws of planetary motion
8343:Antiquity and medieval background
8085:Acceleration (special relativity)
6763:{\displaystyle S(\mathbf {q} ,t)}
4624:, the counterpart of momentum is
4363:
3414:undergoes simple harmonic motion.
2858:is the mass of the falling body,
829:, can be paraphrased as follows:
16043:
16031:
16019:
16007:
15995:
15983:
15919:Isaac Newton Group of Telescopes
15132:
15083:
15026:
14969:
14912:
14873:
14835:
14778:
14746:
14697:
14659:
14606:
14565:
14508:
14459:
14410:
14382:
14346:
14286:
14258:Aldersey-Williams, Hugh (2020).
14251:
14199:
14125:
14089:
14054:
14002:
13960:Pourciau, Bruce (October 2011).
13953:
13848:
13796:
13779:
13762:
13544:
13508:
13467:
13400:
13361:
13324:
13290:
13248:
13157:
13102:
13041:
13003:
12965:
12903:Kersting, Magdalena (May 2019).
11871:Statistical Physics of Particles
11699:"Off to infinity in finite time"
11181:Mungan, Carl E. (1 March 2005).
9594:The Nature of the Physical World
9089:
9077:
9068:
9054:
9045:
8964:
8953:
8918:which Hoek argues was erroneous.
8444:Traité du monde et de la lumière
8318:
8293:
8278:
8112:
8098:
7970:
7962:If the electric field vanishes (
7935:
7927:
7916:
7905:
7649:
7635:
7530:
7055:
6955:
6902:
6822:
6747:
6642:{\displaystyle \mathbf {q} _{i}}
6629:
6585:
6570:
6178:for the position coordinate and
5601:
5557:
5549:
5504:
5496:
5450:turns the Euler equation into a
5432:
5367:
5335:
5327:
5263:
5255:
5218:
5186:
5178:
5162:Newton's laws can be applied to
5157:FermiβPastaβUlamβTsingou problem
5022:
5000:
4972:
4946:
4938:
4908:
4883:
4875:The first term vanishes because
4858:
4850:
4842:
4831:
4812:
4798:
4790:
4767:
4738:
4707:
4699:
4691:
4665:
4643:
4542:
4499:
4471:
4450:
4378:The total center of mass of the
4310:
4247:
4204:
4185:
4168:
4146:
4115:
3190:(center of mass of both objects)
2700:
2678:
2635:
2603:
2577:
2549:
2521:
2506:
2497:
2482:{\displaystyle \mathbf {p} _{2}}
2469:
2453:{\displaystyle \mathbf {p} _{1}}
2440:
2355:
2332:, friction, and string tension.
2237:
2213:
2187:
2165:
2148:
2091:
2077:
2051:
2040:
1853:
1830:
1807:
884:
765:
764:
751:
84:
15939:Newton International Fellowship
15620:generalized GaussβNewton method
15533:Newton's method in optimization
12896:
12828:
12783:Havas, Peter (1 October 1964).
12776:
12748:
12706:
12612:
12504:
12417:
12379:
12322:
12282:"Two Models of Brownian Motion"
12270:
12187:Weiner, J. H. (November 1974).
12180:
12128:
12061:
12021:"Teaching Energy Before Forces"
12009:
11940:
11900:
11813:
11764:
11718:
11683:
11622:
11531:
11420:
11371:
11223:
11174:
11125:
11076:
11030:
10968:
10916:
10821:
10783:
10671:
10642:
10590:
10528:
10504:
10479:
10452:
10400:
10368:
10349:
10292:
10240:
10191:
10177:. HarperPerennial. p. 50.
10163:
10134:
9994:
9897:
9874:
9859:
9810:
9721:
9702:
9665:
9585:
9495:
9446:
9036:
9027:
9018:
9009:
9000:
8991:
8982:
8931:
8921:
8904:
8894:
8553:De Motu Corporum ex Percussione
7711:{\displaystyle \mathbf {\xi } }
6965:{\displaystyle V(\mathbf {q} )}
5044:Multi-body gravitational system
4131:{\displaystyle \mathbf {v} (t)}
2692:is constant. Alternatively, if
1821:, or in bold typeface, such as
14704:Dunlop, Katherine (May 2012).
13722:Blackwell, Richard J. (1966).
12882:. W. W. Norton & Company.
12643:10.1088/1751-8113/47/42/424011
10301:"Newton's third law revisited"
9347:
9223:
9188:
9171:
8881:
8844:History of classical mechanics
8428:Galileo Galilei Β§ Inertia
8348:Aristotle and "violent" motion
7983:{\displaystyle \mathbf {E} =0}
7059:
7051:
6959:
6951:
6757:
6743:
6607:
6565:
6264:
6258:
6224:
6212:
6110:
6054:
6036:
5839:
5833:
5740:
5719:
5500:
5484:
5331:
5315:
5196:
5182:
4985:{\displaystyle \mathbf {r} =0}
4351:Rigid-body motion and rotation
4277:, due to a body's motion, and
4138:, ejects matter at a velocity
4125:
4119:
4094:
4088:
3632:
3626:
3546:, Newton's second law becomes
2718:Candidates for additional laws
1904:
1860:
1710:
1704:
1695:
1680:
1666:
1589:
1583:
1574:
1559:
1545:
1482:
1476:
1458:
1316:
1310:
1063:
1050:
1041:
1028:
925:
919:
39:United States Physics Olympiad
13:
1:
14813:10.1088/0143-0807/38/1/015001
14574:The Oxford Handbook of Newton
12357:10.1088/0143-0807/37/6/065201
11785:The Millennium Prize Problems
10299:Hellingman, C. (March 1992).
10098:Course of Theoretical Physics
9937:10.1103/PhysRevSTPER.5.010108
9782:; Saletan, Eugene J. (1998).
9531:10.1103/PhysRevSTPER.5.010110
9325:. Macmillan. pp. 84β85.
9119:
5651:
4915:{\displaystyle m\mathbf {v} }
4160:relative to the rocket, then
4036:A harmonic oscillator can be
3727:{\displaystyle {\sqrt {k/m}}}
2016:
1944:has a different meaning than
1156:gives the means to define an
387:Koopmanβvon Neumann mechanics
15560:Newton's theorem about ovals
10175:The Cartoon Guide to Physics
10147:University Physics, Volume 1
9969:An introduction to mechanics
8712:TraitΓ© de mΓ©canique cΓ©leste.
8446:) written 1629β33. However,
8027:{\displaystyle \omega =qB/m}
5768:where the kinetic energy is
5439:{\displaystyle \mathbf {f} }
5225:{\displaystyle \mathbf {a} }
5096:not exactly conic sections.
5029:{\displaystyle \mathbf {r} }
5014:and the displacement vector
5007:{\displaystyle \mathbf {F} }
4890:{\displaystyle \mathbf {v} }
4672:{\displaystyle \mathbf {p} }
4650:{\displaystyle \mathbf {r} }
4254:{\displaystyle \mathbf {F} }
4153:{\displaystyle \mathbf {u} }
2785:law of universal gravitation
2745:Uniformly accelerated motion
2707:{\displaystyle \mathbf {p} }
2685:{\displaystyle \mathbf {p} }
2556:{\displaystyle \mathbf {p} }
2541:, and the rate of change of
2373:
2362:{\displaystyle \mathbf {F} }
2302:The forces acting on a body
2286:perpendicular to the plane (
1961:
1814:{\displaystyle \mathbf {s} }
455:Non-inertial reference frame
7:
15929:Sir Isaac Newton Sixth Form
15585:Corpuscular theory of light
15511:SchrΓΆdingerβNewton equation
15097:American Journal of Physics
14947:10.1016/j.shpsa.2018.01.006
14901:TraitΓ© de mΓ©canique cΓ©leste
14792:European Journal of Physics
14424:American Journal of Physics
13967:American Journal of Physics
13724:"Descartes' Laws of Motion"
13414:American Journal of Physics
13175:European Journal of Physics
12723:Flat and Curved Space-times
12518:American Journal of Physics
12436:10.1007/978-1-60327-233-9_6
12336:European Journal of Physics
12287:American Journal of Physics
12194:American Journal of Physics
12145:American Journal of Physics
12075:American Journal of Physics
11548:American Journal of Physics
11478:European Journal of Physics
11434:American Journal of Physics
11385:American Journal of Physics
11237:European Journal of Physics
11188:European Journal of Physics
11139:American Journal of Physics
10985:American Journal of Physics
10933:American Journal of Physics
10835:European Journal of Physics
10205:American Journal of Physics
10007:American Journal of Physics
9845:10.1016/j.shpsb.2017.07.004
9364:American Journal of Physics
8832:
8786:TraitΓ© de mΓ©canique cΓ©leste
8581:Christiaan Huygens, in his
4390:is on top of the pen's tip.
2735:
2392:work by producing a strong
1741:of position, often written
382:Appell's equation of motion
252:Inertial frame of reference
10:
16122:
15338:Notes on the Jewish Temple
15188:; Vuletic, Vladan (2016).
15004:10.1088/0031-9120/49/5/564
13135:10.1007/s10699-019-09608-5
12387:Tonnelat, Marie-Antoinette
11876:Cambridge University Press
11509:10.1088/0143-0807/32/2/016
11258:10.1088/0143-0807/34/1/129
11201:10.1088/0143-0807/26/2/L01
10856:10.1088/0143-0807/20/1/018
10327:10.1088/0031-9120/27/2/011
9592:Eddington, Arthur (1929).
9481:10.1088/0031-9120/20/4/308
8460:Roman Catholic Inquisition
8425:
8312:Trinity College, Cambridge
8268:
8078:
5702:{\displaystyle {\dot {q}}}
5128:
5120:Chaos and unpredictability
5047:
4657:and the body has momentum
4592:were a point body of mass
4367:
4055:
4052:Objects with variable mass
3399:
3175:
2898:is Newton's constant, and
2878:is the mass of the Earth,
2748:
1376:if the difference between
36:
29:
16106:Eponymous laws of physics
15947:
15884:
15839:
15762:
15704:
15459:
15379:
15314:
15247:
14724:10.1007/s11229-011-9983-8
14633:10.1017/S0007087400010232
14535:10.1017/S000708740800188X
14061:Higgitt, Rebekah (2015).
14014:"Was Newton a Newtonian?"
13855:LoLordo, Antonia (2007).
13085:10.1103/RevModPhys.65.803
13054:Reviews of Modern Physics
12973:Prescod-Weinstein, Chanda
12811:10.1103/RevModPhys.36.938
12790:Reviews of Modern Physics
10149:. OpenStax. p. 220.
9885:. John Wiley & Sons.
8422:Inertia and the first law
8408:Abu'l-BarakΔt al-BaghdΔdΔ«
8300:Newton's own copy of his
7864:acting upon charges. The
5620:Millennium Prize Problems
5073:LaplaceβRungeβLenz vector
3354:{\displaystyle GMm/r^{2}}
1948:. The physics concept of
1838:{\displaystyle {\bf {s}}}
15489:post-Newtonian expansion
15369:Corruptions of Scripture
15361:Ancient Kingdoms Amended
13893:Principles of philosophy
13368:Ugaglia, Monica (2015).
13197:10.1088/1361-6404/aa57d1
12932:10.1088/1361-6552/ab08f5
12470:Panofsky, Wolfgang K. H.
12395:. Dordrecht: D. Reidel.
10620:10.4169/002557010X479965
10459:Greiner, Walter (2003).
10143:"5.5 Newton's Third Law"
9866:Feather, Norman (1959).
9735:. Wiley. pp. 8β16.
9201:. Institute of Physics.
8887:See, for example, Zain.
8874:
8704:Mechanism of the Heavens
8646:Principles of Philosophy
8584:Horologium Oscillatorium
8567:Force and the second law
8515:Principles of Philosophy
8207:Einstein field equations
6549:HamiltonβJacobi equation
6014:of the Lagrangian gives
5609:relativistic speed limit
3418:Consider a body of mass
3309:{\displaystyle mv^{2}/r}
2421:conservation of momentum
545:Rotating reference frame
377:HamiltonβJacobi equation
18:Newton's second law
15679:Absolute space and time
15543:truncated Newton method
15516:Newton's laws of motion
15479:Newton's law of cooling
14032:10.1126/science.1088786
13296:D. Bilodeau, quoted in
13228:Cohen-Tannoudji, Claude
12874:Wheeler, John Archibald
11038:Hughes-Hallett, Deborah
10521:Encyclopædia Britannica
10387:MIT Physics Annual 2003
10173:; Huffman, Art (1991).
9629:; Olenick, Richard P.;
9266:Hughes-Hallett, Deborah
9242:University of Cambridge
8728:the science of fluxions
8595:of transparent matter,
8432:The French philosopher
8163:{\displaystyle \gamma }
7685:{\displaystyle \gamma }
7607:kinetic theory of gases
5913:EulerβLagrange equation
5168:Euler momentum equation
4298:of a function called a
3984:{\displaystyle \theta }
3964:{\displaystyle \theta }
3940:{\displaystyle \theta }
3920:{\displaystyle \theta }
3695:{\displaystyle \omega }
3514:. Writing the force as
3438:able to move along the
3172:Uniform circular motion
2730:superposition principle
2011:absolute space and time
1956:
1349:at a given input value
1173:{\displaystyle \Delta }
1120:{\displaystyle \Delta }
1107:Here, the Greek letter
811:Newton's laws of motion
486:Newton's laws of motion
346:Newton's laws of motion
16086:Scientific observation
15914:Isaac Newton Telescope
15904:Isaac Newton Institute
15674:NewtonβPuiseux theorem
15669:Parallelogram of force
15657:kissing number problem
15647:NewtonβEuler equations
15550:GaussβNewton algorithm
15499:gravitational constant
14515:Davies, E. B. (2009).
14132:West, Richard (1980).
14097:Dobbs, Betty Jo Teeter
13339:. Dover. p. 178.
13112:Foundations of Science
12676:Choquet-Bruhat, Yvonne
12047:10.1103/Physics.12.100
11048:; et al. (2013).
9276:; et al. (2013).
8972:
8849:List of eponymous laws
8839:Euler's laws of motion
8827:William Rowan Hamilton
8765:
8719:
8664:that Huygens had, and
8636:
8578:
8561:
8541:
8536:
8530:
8520:Principia Philosophiae
8500:
8491:
8476:
8382:Philoponus and impetus
8363:
8202:John Archibald Wheeler
8164:
8140:
8120:
8081:Relativistic mechanics
8028:
7984:
7959:
7946:
7883:
7851:
7824:
7797:
7770:
7712:
7686:
7666:
7598:
7572:
7414:
7308:
7288:
7176:
7069:
6966:
6935:
6854:
6808:
6784:
6764:
6727:
6707:
6687:
6663:
6643:
6614:
6527:
6461:
6408:
6338:
6274:
6192:
6172:
6152:
6127:
6122:, whose 1915 proof of
6090:
6004:
5909:Calculus of variations
5900:
5873:
5846:
5817:
5762:
5703:
5674:
5611:in Newtonian physics.
5588:
5568:
5452:NavierβStokes equation
5440:
5418:
5398:
5378:
5279:
5226:
5203:
5140:
5063:
5030:
5008:
4986:
4957:
4916:
4891:
4869:
4718:
4673:
4651:
4606:
4585:
4565:
4526:
4485:
4435:
4391:
4345:conservation of energy
4336:
4255:
4233:
4154:
4132:
4101:
4074:
4027:
3985:
3965:
3941:
3921:
3901:
3881:
3794:
3768:
3748:
3728:
3696:
3676:
3610:
3540:
3512:simple harmonic motion
3504:
3478:
3452:
3432:
3415:
3375:
3355:
3310:
3268:
3228:
3208:
3191:
3162:
3132:
3055:
3035:
3015:
2995:
2975:
2955:
2935:
2912:
2892:
2872:
2852:
2832:
2776:
2708:
2686:
2663:
2557:
2535:
2483:
2454:
2405:
2363:
2308:mechanical equilibrium
2299:
2266:
2199:
2134:
2114:
2063:
1979:
1911:
1839:
1815:
1786:
1731:
1610:
1498:
1437:
1410:
1390:
1370:
1343:
1323:
1290:
1267:
1240:
1194:
1174:
1145:
1121:
1101:
986:
959:
932:
877:), or are very small (
844:is changing with time.
513:Simple harmonic motion
426:Euler's laws of motion
220:D'Alembert's principle
103:
16096:Copernican Revolution
15868:Isaac Newton Gargoyle
15778: (nephew-in-law)
15754:Copernican Revolution
15749:Scientific Revolution
15610:NewtonβCotes formulas
15474:Newton's inequalities
15451:Structural coloration
15190:"Classical Mechanics"
13786:Galilei, G. (1974) .
13331:Caspar, Max (2012) .
12835:Stavrov, Iva (2020).
12019:(13 September 2019).
11772:Fefferman, Charles L.
10358:"Third Law of Motion"
9674:Philosophy of Science
9355:McDermott, Lillian C.
9313:Thompson, Silvanus P.
8973:
8766:
8701:
8632:
8611:I feign no hypotheses
8574:
8557:
8537:
8532:
8528:
8496:
8486:
8484:(1638) Galileo wrote:
8472:
8400:Nur ad-Din al-Bitruji
8355:
8328:Principia Mathematica
8165:
8141:
8121:
8079:Further information:
8029:
7985:
7957:
7947:
7884:
7852:
7850:{\displaystyle q_{1}}
7825:
7823:{\displaystyle q_{2}}
7798:
7796:{\displaystyle q_{2}}
7776:exerts upon a charge
7771:
7769:{\displaystyle q_{1}}
7713:
7687:
7667:
7593:
7573:
7415:
7309:
7289:
7177:
7070:
6967:
6936:
6855:
6809:
6785:
6765:
6728:
6708:
6688:
6671:differential equation
6664:
6644:
6615:
6528:
6462:
6409:
6339:
6275:
6193:
6173:
6153:
6132:Hamiltonian mechanics
6118:
6091:
6005:
5901:
5899:{\displaystyle q_{f}}
5874:
5872:{\displaystyle q_{i}}
5847:
5818:
5763:
5704:
5675:
5638:Hamiltonian mechanics
5589:
5569:
5441:
5424:is the pressure, and
5419:
5399:
5397:{\displaystyle \rho }
5379:
5280:
5227:
5204:
5138:
5083:(including circles),
5061:
5031:
5009:
4987:
4958:
4917:
4892:
4870:
4719:
4674:
4652:
4607:
4586:
4566:
4506:
4486:
4436:
4377:
4337:
4256:
4234:
4155:
4133:
4107:, moving at velocity
4102:
4065:
4028:
3986:
3966:
3942:
3922:
3902:
3882:
3795:
3769:
3749:
3729:
3697:
3677:
3611:
3541:
3539:{\displaystyle F=-kx}
3505:
3479:
3453:
3433:
3409:
3376:
3356:
3311:
3269:
3229:
3209:
3185:
3163:
3133:
3056:
3036:
3016:
2996:
2976:
2956:
2936:
2913:
2893:
2873:
2853:
2833:
2762:
2709:
2687:
2664:
2558:
2536:
2484:
2455:
2388:
2364:
2277:
2267:
2200:
2135:
2115:
2064:
1969:
1912:
1840:
1816:
1787:
1732:
1611:
1499:
1438:
1436:{\displaystyle t_{0}}
1411:
1391:
1371:
1369:{\displaystyle t_{0}}
1344:
1324:
1291:
1268:
1241:
1195:
1175:
1146:
1122:
1102:
987:
985:{\displaystyle t_{1}}
960:
958:{\displaystyle t_{0}}
933:
873:), are very massive (
821:of an object and the
367:Hamiltonian mechanics
185:Statistical mechanics
104:
16091:Experimental physics
16081:Equations of physics
15875:Astronomers Monument
15565:NewtonβPepys problem
15538:Apollonius's problem
15506:NewtonβCartan theory
15419:NewtonβOkounkov body
15352:hypotheses non fingo
15341: (c. 1680)
15036:(10 December 2018).
14391:"Descartes' Physics"
13899:. Part II, Β§ 37, 39.
13011:Goodstein, Judith R.
11598:Fly by Night Physics
11042:McCallum, William G.
10891:Analytical Mechanics
10607:Mathematics Magazine
10380:"The Origin of Mass"
9627:Frautschi, Steven C.
9270:McCallum, William G.
9195:Zain, Samya (2019).
8949:
8815:Josiah Willard Gibbs
8781:Pierre-Simon Laplace
8764:{\displaystyle F=ma}
8746:
8670:inelastic collisions
8545:Richard J. Blackwell
8154:
8130:
8094:
8040:mass-to-charge ratio
8001:
7966:
7901:
7873:
7834:
7807:
7780:
7753:
7746:electrically charged
7700:
7676:
7628:
7436:
7318:
7298:
7194:
7079:
6976:
6945:
6864:
6818:
6798:
6774:
6737:
6717:
6697:
6677:
6653:
6624:
6559:
6471:
6418:
6348:
6284:
6202:
6182:
6162:
6142:
6136:Hamilton's equations
6018:
5919:
5883:
5856:
5845:{\displaystyle V(q)}
5827:
5772:
5713:
5684:
5664:
5657:Lagrangian mechanics
5633:Lagrangian mechanics
5587:{\displaystyle \nu }
5578:
5458:
5428:
5408:
5388:
5289:
5251:
5214:
5174:
5018:
4996:
4968:
4926:
4901:
4879:
4728:
4687:
4661:
4639:
4596:
4575:
4495:
4445:
4399:
4306:
4243:
4164:
4142:
4111:
4100:{\displaystyle M(t)}
4082:
4058:Variable-mass system
3999:
3975:
3955:
3931:
3911:
3891:
3812:
3778:
3758:
3738:
3734:, and the constants
3706:
3686:
3682:where the frequency
3620:
3550:
3518:
3488:
3462:
3442:
3422:
3365:
3324:
3282:
3238:
3218:
3214:at a constant speed
3198:
3152:
3065:
3045:
3025:
3005:
2985:
2965:
2945:
2922:
2902:
2882:
2862:
2842:
2791:
2696:
2674:
2567:
2545:
2493:
2464:
2435:
2351:
2209:
2144:
2124:
2073:
2036:
1849:
1825:
1803:
1745:
1623:
1508:
1447:
1420:
1400:
1380:
1353:
1333:
1322:{\displaystyle f(t)}
1304:
1277:
1254:
1204:
1184:
1164:
1135:
1111:
996:
969:
942:
931:{\displaystyle s(t)}
913:
590:Angular acceleration
582:Rotational frequency
362:Lagrangian mechanics
355:Analytical mechanics
111:Second law of motion
64:
16066:Classical mechanics
15684:Luminiferous aether
15632:Newton's identities
15605:Newton's cannonball
15580:Classical mechanics
15570:Newtonian potential
15431:Newtonian telescope
15110:2002AmJPh..70..958S
15042:Skulls in the Stars
14996:2014PhyEd..49..564F
14939:2018SHPSA..69....1R
14805:2017EJPh...38a5001M
14486:2006PhT....59j..31S
14437:1997AmJPh..65..149E
14264:. London: Picador.
13980:2011AmJPh..79.1015P
13678:2021PRPER..17a0121R
13618:The Physics Teacher
13574:2019PRPER..15a0123E
13427:2011AmJPh..79...32S
13188:2017EJPh...38b5705M
13166:Singh, Chandralekha
13077:1993RvMP...65..803M
12923:2019PhyEd..54c5008K
12803:1964RvMP...36..938H
12714:Ellis, George F. R.
12635:2014JPhA...47P4011W
12587:Classical Mechanics
12541:2018AmJPh..86..839B
12349:2016EJPh...37f5201K
12300:1961AmJPh..29..510M
12207:1974AmJPh..42.1026W
12158:1965AmJPh..33..146R
12098:2020AmJPh..88..353H
12039:2019PhyOJ..12..100B
11967:2019PRPER..15b0126L
11561:2004AmJPh..72..446L
11501:2011EJPh...32..431M
11398:2008AmJPh..76..347B
11302:1997ptbp.book.....B
11250:2013EJPh...34..129S
11152:2011AmJPh..79.1068C
11103:1998PhTea..36...18L
11090:The Physics Teacher
10998:2019AmJPh..87..504C
10946:1991AmJPh..59..118B
10848:1999EJPh...20...59T
10698:2020PRPER..16a0111C
10600:(1 February 2010).
10558:1905Natur..72Q.429H
10512:Tait, Peter Guthrie
10430:2005PhTea..43...41S
10417:The Physics Teacher
10319:1992PhyEd..27..112H
10270:2012PhTea..50..406S
10257:The Physics Teacher
10218:2017AmJPh..85...54L
10090:Lifshitz, Evgeny M.
10041:Leighton, Robert B.
10037:Feynman, Richard P.
9928:2009PRPER...5a0108R
9904:Rosengrant, David;
9837:2019SHPMP..67..160B
9715:Scientific American
9696:10.1017/psa.2021.38
9635:Goodstein, David L.
9522:2009PRPER...5a0110B
9473:1985PhyEd..20..171D
9377:1987AmJPh..55..503M
9163:Newton, I. (1999).
9101:John Maynard Keynes
8681:Galilean invariance
8575:Christiaan Huygens
8258:Hermitian operators
7996:cyclotron frequency
7603:statistical physics
6100:Landau and Lifshitz
6012:partial derivatives
5646:perturbation theory
5642:statistical physics
5596:kinematic viscosity
5153:dynamical billiards
4287:work-energy theorem
3971:is nearly equal to
3793:{\displaystyle t=0}
3503:{\displaystyle x=0}
3477:{\displaystyle x=0}
3402:Harmonic oscillator
3385:Newton's cannonball
1940:, for example, and
1932:is not the same as
867:classical mechanics
827:Newtonian mechanics
442:Harmonic oscillator
420:Equations of motion
55:Classical mechanics
49:Part of a series on
16014:History of science
15909:Isaac Newton Medal
15714: (birthplace)
15528:Newtonian dynamics
15426:Newton's reflector
15195:MIT OpenCourseWare
15057:. 29 December 2018
14667:Baron, Margaret E.
14171:Newman, William R.
14012:(15 August 2003).
13631:10.1119/10.0003660
13550:See, for example:
12760:Special Relativity
12582:Goldstein, Herbert
12106:10.1119/10.0000781
11825:Ehrenfest, Tatiana
11660:10.1090/proc/15349
11539:Laws, Priscilla W.
11337:Barrow-Green, June
11329:Barrow-Green, June
11288:Barrow-Green, June
11046:Gleason, Andrew M.
9906:Van Heuvelen, Alan
9322:Calculus Made Easy
9274:Gleason, Andrew M.
8968:
8803:Γmilie du ChΓ’telet
8761:
8720:
8662:elastic collisions
8637:
8579:
8549:Christiaan Huygens
8547:, Dutch scientist
8531:
8501:
8477:
8364:
8194:General relativity
8189:General relativity
8160:
8136:
8116:
8075:Special relativity
8024:
7980:
7960:
7942:
7879:
7847:
7820:
7793:
7766:
7708:
7682:
7662:
7599:
7568:
7410:
7304:
7284:
7172:
7065:
6962:
6931:
6850:
6804:
6780:
6760:
6723:
6703:
6683:
6659:
6639:
6610:
6523:
6457:
6404:
6334:
6270:
6188:
6168:
6148:
6128:
6086:
6000:
5915:for the particle,
5896:
5879:and a final point
5869:
5842:
5813:
5758:
5699:
5680:and velocity with
5670:
5640:is convenient for
5584:
5564:
5436:
5414:
5394:
5374:
5275:
5222:
5199:
5141:
5125:Nonlinear dynamics
5064:
5054:Three-body problem
5026:
5004:
4992:) or if the force
4982:
4953:
4912:
4887:
4865:
4714:
4669:
4647:
4602:
4581:
4561:
4481:
4431:
4392:
4332:
4251:
4229:
4150:
4128:
4097:
4075:
4066:Rockets, like the
4023:
3981:
3961:
3937:
3917:
3897:
3877:
3790:
3764:
3744:
3724:
3692:
3672:
3606:
3536:
3500:
3474:
3448:
3428:
3416:
3412:springβmass system
3389:thought experiment
3371:
3351:
3306:
3264:
3224:
3204:
3192:
3158:
3128:
3051:
3031:
3011:
2991:
2971:
2951:
2941:, the body's mass
2934:{\displaystyle ma}
2931:
2908:
2888:
2868:
2848:
2828:
2777:
2769:stroboscopic flash
2704:
2682:
2659:
2553:
2531:
2479:
2450:
2406:
2359:
2300:
2262:
2195:
2130:
2110:
2059:
1980:
1907:
1835:
1811:
1782:
1727:
1673:
1606:
1552:
1494:
1472:
1433:
1406:
1386:
1366:
1339:
1319:
1289:{\displaystyle dt}
1286:
1266:{\displaystyle ds}
1263:
1236:
1190:
1170:
1141:
1117:
1097:
982:
955:
928:
875:general relativity
871:special relativity
758:Physics portal
372:Routhian mechanics
247:Frame of reference
99:
15971:
15970:
15863: (sculpture)
15830:Abraham de Moivre
15784: (professor)
15712:Woolsthorpe Manor
15664:Newton's quotient
15637:Newton polynomial
15595:Newton's notation
15326: (1661β1665)
15153:978-9-048-14758-8
15118:10.1119/1.1475326
14983:Physics Education
14858:978-0-486-44240-2
14682:978-1-483-28092-9
14615:"Mary Somerville"
14591:978-0-199-93041-8
14494:10.1063/1.2387086
14367:978-0-486-40689-3
14294:Cohen, I. Bernard
14271:978-1-5098-9333-1
14184:978-1-107-01546-3
14074:978-1-317-31495-0
13988:10.1119/1.3607433
13974:(10): 1015β1022.
13868:978-0-511-34982-9
13804:Hellman, C. Doris
13656:Scherr, Rachel E.
13609:Scherr, Rachel E.
13529:978-0-812-27831-6
13485:978-1-905-67018-5
13457:Aristotle in his
13435:10.1119/1.3492721
13346:978-0-486-15175-5
13337:Hellman, C. Doris
13309:978-0-521-19926-1
13232:Quantum Mechanics
13164:Marshman, Emily;
13026:978-1-4704-2846-4
12988:978-1-5417-2470-9
12910:Physics Education
12889:978-0-393-07948-7
12848:978-1-4704-6313-7
12718:Williams, Ruth M.
12691:978-0-19-155226-7
12549:10.1119/1.5054590
12445:978-1-60327-233-9
12308:10.1119/1.1937823
12255:978-3-527-69048-0
12215:10.1119/1.1987920
12201:(11): 1026β1028.
12166:10.1119/1.1971282
12138:(February 1965).
11925:978-0-521-82197-1
11885:978-0-521-87342-0
11798:978-0-821-83679-8
11749:978-1-108-49062-7
11607:978-0-691-18254-4
11569:10.1119/1.1649964
11447:10.1119/1.1987423
11406:10.1119/1.2834738
11356:978-0-691-11880-2
11311:978-0-8218-0367-7
11160:10.1119/1.3579141
11146:(10): 1068β1078.
11061:978-0-470-88861-2
11007:10.1119/1.5109519
10806:978-0-385-53108-5
10768:978-0-471-19826-0
10598:Nicodemi, Olympia
10536:Heaviside, Oliver
10497:978-0-387-25799-0
10472:978-0-387-21851-9
10438:10.1119/1.1845990
10408:Scherr, Rachel E.
10306:Physics Education
10278:10.1119/1.4752043
10226:10.1119/1.4972041
10156:978-1-947172-20-3
10115:978-0-080-06466-6
10045:Sands, Matthew L.
10020:10.1119/1.1934608
10002:Eisenbud, Leonard
9979:978-0-521-19811-0
9795:978-1-139-64890-5
9650:978-0-521-71590-4
9570:978-1-947172-01-2
9460:Physics Education
9431:978-0-511-91510-9
9332:978-0-312-18548-0
9287:978-0-470-88861-2
9208:978-0-750-32076-4
8592:act at a distance
8508:, Descartes, and
8253:Ehrenfest theorem
8246:expectation value
8225:Quantum mechanics
8220:Quantum mechanics
8139:{\displaystyle m}
8036:Mass spectrometry
7882:{\displaystyle q}
7866:Lorentz force law
7622:Langevin equation
7563:
7524:
7470:
7457:
7352:
7339:
7307:{\displaystyle S}
7234:
7213:
7126:
7108:
7018:
7000:
6888:
6837:
6807:{\displaystyle S}
6783:{\displaystyle S}
6726:{\displaystyle S}
6706:{\displaystyle S}
6686:{\displaystyle S}
6662:{\displaystyle t}
6518:
6492:
6452:
6439:
6399:
6369:
6332:
6305:
6250:
6191:{\displaystyle p}
6171:{\displaystyle q}
6151:{\displaystyle m}
6105:Noether's theorem
6081:
6051:
6034:
5995:
5968:
5964:
5935:
5804:
5789:
5737:
5696:
5673:{\displaystyle q}
5522:
5479:
5417:{\displaystyle P}
5353:
5310:
5105:Numerical methods
4825:
4780:
4751:
4622:moment of inertia
4605:{\displaystyle M}
4584:{\displaystyle M}
4556:
4226:
4198:
4021:
3900:{\displaystyle L}
3863:
3847:
3767:{\displaystyle B}
3747:{\displaystyle A}
3722:
3588:
3451:{\displaystyle x}
3431:{\displaystyle m}
3374:{\displaystyle M}
3276:centripetal force
3262:
3227:{\displaystyle v}
3207:{\displaystyle r}
3161:{\displaystyle g}
3142:projectile motion
3105:
3094:
3054:{\displaystyle g}
3034:{\displaystyle r}
3014:{\displaystyle r}
2994:{\displaystyle M}
2974:{\displaystyle G}
2954:{\displaystyle m}
2911:{\displaystyle r}
2891:{\displaystyle G}
2871:{\displaystyle M}
2851:{\displaystyle m}
2823:
2755:Projectile motion
2654:
2622:
2590:
2429:quantum mechanics
2322:free body diagram
2280:free body diagram
2257:
2178:
2133:{\displaystyle m}
2104:
2001:inertial observer
1919:coordinate system
1891:
1869:
1780:
1739:second derivative
1722:
1655:
1650:
1601:
1534:
1529:
1450:
1409:{\displaystyle L}
1389:{\displaystyle f}
1342:{\displaystyle L}
1231:
1193:{\displaystyle d}
1144:{\displaystyle s}
1092:
1017:
879:quantum mechanics
808:
807:
555:Centrifugal force
550:Centripetal force
506:Euler's equations
491:Relative velocity
267:Moment of inertia
97:
71:
16:(Redirected from
16113:
16048:
16047:
16046:
16036:
16035:
16024:
16023:
16022:
16012:
16011:
16010:
16000:
15999:
15988:
15987:
15979:
15959:
15854: (monotype)
15818:William Stukeley
15814: (disciple)
15794:Benjamin Pulleyn
15770:Catherine Barton
15689:Newtonian series
15600:Rotating spheres
15346:General Scholium
15241:Sir Isaac Newton
15234:
15227:
15220:
15211:
15210:
15206:
15204:
15202:
15166:
15165:
15136:
15130:
15129:
15087:
15081:
15080:
15078:
15076:
15071:. 25 August 2019
15066:
15064:
15062:
15052:
15050:
15048:
15030:
15024:
15023:
14973:
14967:
14966:
14916:
14910:
14909:
14896:
14894:
14877:
14871:
14870:
14839:
14833:
14832:
14782:
14776:
14775:
14773:
14771:
14750:
14744:
14743:
14701:
14695:
14694:
14663:
14657:
14656:
14610:
14604:
14603:
14569:
14563:
14562:
14512:
14506:
14505:
14463:
14457:
14456:
14414:
14408:
14407:
14405:
14403:
14386:
14380:
14379:
14350:
14344:
14343:
14290:
14284:
14283:
14255:
14249:
14248:
14203:
14197:
14196:
14167:
14156:
14155:
14129:
14123:
14122:
14093:
14087:
14086:
14058:
14052:
14051:
14006:
14000:
13999:
13957:
13951:
13950:
13910:
13901:
13900:
13898:
13887:
13881:
13880:
13852:
13846:
13845:
13813:Renaissance News
13800:
13794:
13793:
13783:
13777:
13776:
13766:
13760:
13759:
13719:
13710:
13707:
13689:
13650:
13603:
13585:
13548:
13542:
13541:
13516:Maier, Anneliese
13512:
13506:
13505:
13471:
13465:
13464:
13446:
13404:
13398:
13397:
13365:
13359:
13358:
13335:. Translated by
13328:
13322:
13321:
13294:
13288:
13287:
13252:
13246:
13245:
13224:
13218:
13217:
13199:
13168:(1 March 2017).
13161:
13155:
13154:
13128:
13106:
13100:
13099:
13070:
13049:Mermin, N. David
13045:
13039:
13038:
13007:
13001:
13000:
12969:
12963:
12962:
12944:
12934:
12900:
12894:
12893:
12876:(18 June 2010).
12870:
12861:
12860:
12832:
12826:
12825:
12780:
12774:
12773:
12752:
12746:
12745:
12710:
12704:
12703:
12672:
12663:
12662:
12616:
12610:
12609:
12578:
12569:
12568:
12534:
12508:
12502:
12501:
12466:
12457:
12456:
12454:
12452:
12421:
12415:
12414:
12383:
12377:
12376:
12326:
12320:
12319:
12278:Mermin, N. David
12274:
12268:
12267:
12240:Reichl, Linda E.
12236:
12227:
12226:
12184:
12178:
12177:
12132:
12126:
12125:
12091:
12065:
12059:
12058:
12013:
12007:
12006:
11988:
11978:
11944:
11938:
11937:
11917:
11904:
11898:
11897:
11862:
11853:
11852:
11817:
11811:
11810:
11790:
11768:
11762:
11761:
11741:
11722:
11716:
11715:
11703:
11691:Saari, Donald G.
11687:
11681:
11680:
11662:
11652:
11643:(7): 3045β3061.
11626:
11620:
11619:
11590:
11581:
11580:
11535:
11529:
11528:
11494:
11468:
11459:
11458:
11424:
11418:
11417:
11375:
11369:
11368:
11325:
11316:
11315:
11284:
11278:
11277:
11227:
11221:
11220:
11178:
11172:
11171:
11129:
11123:
11122:
11111:10.1119/1.879949
11080:
11074:
11073:
11034:
11028:
11027:
11009:
10972:
10966:
10965:
10929:
10920:
10914:
10913:
10885:
10876:
10875:
10825:
10819:
10818:
10787:
10781:
10780:
10749:
10738:
10737:
10719:
10709:
10675:
10669:
10668:
10666:
10664:
10646:
10640:
10639:
10594:
10588:
10587:
10569:
10567:10.1038/072429a0
10532:
10526:
10525:
10508:
10502:
10501:
10483:
10477:
10476:
10456:
10450:
10449:
10404:
10398:
10397:
10395:
10393:
10384:
10372:
10366:
10365:
10362:www.grc.nasa.gov
10353:
10347:
10346:
10296:
10290:
10289:
10248:Stocklmayer, Sue
10244:
10238:
10237:
10195:
10189:
10188:
10167:
10161:
10160:
10138:
10132:
10131:
10104:(2nd ed.).
10082:
10073:
10072:
10033:
10024:
10023:
9998:
9992:
9991:
9963:
9950:
9949:
9939:
9901:
9895:
9894:
9878:
9872:
9871:
9863:
9857:
9856:
9814:
9808:
9807:
9776:
9745:
9744:
9725:
9719:
9718:
9706:
9700:
9699:
9689:
9669:
9663:
9662:
9623:
9598:
9597:
9589:
9583:
9582:
9550:
9544:
9543:
9533:
9499:
9493:
9492:
9450:
9444:
9443:
9412:
9397:
9396:
9351:
9345:
9344:
9309:
9300:
9299:
9262:
9253:
9252:
9250:
9248:
9239:
9233:(January 2015).
9227:
9221:
9220:
9192:
9186:
9185:
9175:
9169:
9168:
9160:
9151:
9150:
9130:
9113:
9093:
9087:
9081:
9075:
9072:
9066:
9058:
9052:
9049:
9043:
9040:
9034:
9031:
9025:
9022:
9016:
9013:
9007:
9004:
8998:
8995:
8989:
8986:
8980:
8977:
8975:
8974:
8969:
8967:
8956:
8935:
8929:
8925:
8919:
8908:
8902:
8898:
8892:
8885:
8819:Oliver Heaviside
8770:
8768:
8767:
8762:
8658:Christopher Wren
8633:Johannes Kepler
8482:Two New Sciences
8473:Galileo Galilei
8416:Albert of Saxony
8322:
8297:
8282:
8209:, which require
8169:
8167:
8166:
8161:
8145:
8143:
8142:
8137:
8125:
8123:
8122:
8117:
8115:
8101:
8033:
8031:
8030:
8025:
8020:
7989:
7987:
7986:
7981:
7973:
7951:
7949:
7948:
7943:
7938:
7930:
7919:
7908:
7888:
7886:
7885:
7880:
7856:
7854:
7853:
7848:
7846:
7845:
7829:
7827:
7826:
7821:
7819:
7818:
7802:
7800:
7799:
7794:
7792:
7791:
7775:
7773:
7772:
7767:
7765:
7764:
7726:Electromagnetism
7717:
7715:
7714:
7709:
7707:
7694:drag coefficient
7691:
7689:
7688:
7683:
7671:
7669:
7668:
7663:
7660:
7652:
7638:
7577:
7575:
7574:
7569:
7564:
7562:
7551:
7546:
7542:
7541:
7533:
7525:
7523:
7512:
7502:
7498:
7497:
7493:
7492:
7481:
7471:
7463:
7458:
7456:
7445:
7419:
7417:
7416:
7411:
7403:
7389:
7384:
7380:
7379:
7375:
7374:
7363:
7353:
7345:
7340:
7338:
7327:
7313:
7311:
7310:
7305:
7293:
7291:
7290:
7285:
7277:
7266:
7261:
7257:
7256:
7245:
7235:
7227:
7219:
7214:
7212:
7201:
7181:
7179:
7178:
7173:
7165:
7157:
7156:
7151:
7147:
7143:
7132:
7127:
7125:
7114:
7109:
7107:
7099:
7091:
7089:
7074:
7072:
7071:
7066:
7058:
7044:
7043:
7038:
7034:
7030:
7019:
7017:
7006:
7001:
6999:
6991:
6983:
6971:
6969:
6968:
6963:
6958:
6940:
6938:
6937:
6932:
6927:
6923:
6913:
6905:
6889:
6887:
6879:
6871:
6859:
6857:
6856:
6851:
6843:
6838:
6830:
6825:
6813:
6811:
6810:
6805:
6789:
6787:
6786:
6781:
6769:
6767:
6766:
6761:
6750:
6732:
6730:
6729:
6724:
6712:
6710:
6709:
6704:
6692:
6690:
6689:
6684:
6668:
6666:
6665:
6660:
6648:
6646:
6645:
6640:
6638:
6637:
6632:
6619:
6617:
6616:
6611:
6594:
6593:
6588:
6579:
6578:
6573:
6532:
6530:
6529:
6524:
6519:
6517:
6509:
6501:
6493:
6491:
6483:
6475:
6466:
6464:
6463:
6458:
6453:
6445:
6440:
6438:
6430:
6422:
6413:
6411:
6410:
6405:
6400:
6398:
6390:
6389:
6388:
6378:
6370:
6368:
6360:
6352:
6343:
6341:
6340:
6335:
6333:
6331:
6323:
6322:
6321:
6311:
6306:
6304:
6296:
6288:
6279:
6277:
6276:
6271:
6251:
6249:
6241:
6240:
6231:
6211:
6210:
6197:
6195:
6194:
6189:
6177:
6175:
6174:
6169:
6157:
6155:
6154:
6149:
6095:
6093:
6092:
6087:
6082:
6080:
6072:
6064:
6053:
6052:
6044:
6035:
6033:
6022:
6009:
6007:
6006:
6001:
5996:
5994:
5986:
5978:
5973:
5969:
5967:
5966:
5965:
5957:
5950:
5942:
5936:
5934:
5923:
5905:
5903:
5902:
5897:
5895:
5894:
5878:
5876:
5875:
5870:
5868:
5867:
5851:
5849:
5848:
5843:
5822:
5820:
5819:
5814:
5812:
5811:
5806:
5805:
5797:
5790:
5782:
5767:
5765:
5764:
5759:
5739:
5738:
5730:
5708:
5706:
5705:
5700:
5698:
5697:
5689:
5679:
5677:
5676:
5671:
5593:
5591:
5590:
5585:
5573:
5571:
5570:
5565:
5560:
5552:
5547:
5546:
5528:
5523:
5515:
5507:
5499:
5491:
5480:
5478:
5470:
5462:
5445:
5443:
5442:
5437:
5435:
5423:
5421:
5420:
5415:
5404:is the density,
5403:
5401:
5400:
5395:
5383:
5381:
5380:
5375:
5370:
5359:
5354:
5346:
5338:
5330:
5322:
5311:
5309:
5301:
5293:
5284:
5282:
5281:
5276:
5271:
5266:
5258:
5231:
5229:
5228:
5223:
5221:
5208:
5206:
5205:
5200:
5189:
5181:
5050:Two-body problem
5035:
5033:
5032:
5027:
5025:
5013:
5011:
5010:
5005:
5003:
4991:
4989:
4988:
4983:
4975:
4962:
4960:
4959:
4954:
4949:
4941:
4933:
4921:
4919:
4918:
4913:
4911:
4896:
4894:
4893:
4888:
4886:
4874:
4872:
4871:
4866:
4861:
4853:
4845:
4834:
4826:
4824:
4816:
4815:
4806:
4801:
4793:
4785:
4781:
4779:
4771:
4770:
4761:
4752:
4750:
4742:
4741:
4732:
4723:
4721:
4720:
4715:
4710:
4702:
4694:
4678:
4676:
4675:
4670:
4668:
4656:
4654:
4653:
4648:
4646:
4626:angular momentum
4611:
4609:
4608:
4603:
4590:
4588:
4587:
4582:
4570:
4568:
4567:
4562:
4557:
4552:
4551:
4550:
4545:
4539:
4538:
4528:
4525:
4520:
4502:
4490:
4488:
4487:
4482:
4480:
4479:
4474:
4459:
4458:
4453:
4440:
4438:
4437:
4432:
4430:
4429:
4411:
4410:
4341:
4339:
4338:
4333:
4324:
4313:
4300:scalar potential
4260:
4258:
4257:
4252:
4250:
4238:
4236:
4235:
4230:
4227:
4225:
4217:
4209:
4207:
4199:
4197:
4189:
4188:
4179:
4171:
4159:
4157:
4156:
4151:
4149:
4137:
4135:
4134:
4129:
4118:
4106:
4104:
4103:
4098:
4032:
4030:
4029:
4024:
4022:
4017:
4009:
3990:
3988:
3987:
3982:
3970:
3968:
3967:
3962:
3946:
3944:
3943:
3938:
3926:
3924:
3923:
3918:
3906:
3904:
3903:
3898:
3886:
3884:
3883:
3878:
3864:
3856:
3848:
3846:
3845:
3844:
3831:
3827:
3826:
3816:
3799:
3797:
3796:
3791:
3773:
3771:
3770:
3765:
3753:
3751:
3750:
3745:
3733:
3731:
3730:
3725:
3723:
3718:
3710:
3701:
3699:
3698:
3693:
3681:
3679:
3678:
3673:
3615:
3613:
3612:
3607:
3589:
3587:
3586:
3585:
3572:
3568:
3567:
3557:
3545:
3543:
3542:
3537:
3509:
3507:
3506:
3501:
3483:
3481:
3480:
3475:
3457:
3455:
3454:
3449:
3437:
3435:
3434:
3429:
3380:
3378:
3377:
3372:
3360:
3358:
3357:
3352:
3350:
3349:
3340:
3315:
3313:
3312:
3307:
3302:
3297:
3296:
3273:
3271:
3270:
3265:
3263:
3258:
3257:
3248:
3233:
3231:
3230:
3225:
3213:
3211:
3210:
3205:
3167:
3165:
3164:
3159:
3137:
3135:
3134:
3129:
3124:
3123:
3122:
3113:
3103:
3095:
3093:
3092:
3083:
3075:
3060:
3058:
3057:
3052:
3040:
3038:
3037:
3032:
3020:
3018:
3017:
3012:
3000:
2998:
2997:
2992:
2980:
2978:
2977:
2972:
2960:
2958:
2957:
2952:
2940:
2938:
2937:
2932:
2917:
2915:
2914:
2909:
2897:
2895:
2894:
2889:
2877:
2875:
2874:
2869:
2857:
2855:
2854:
2849:
2837:
2835:
2834:
2829:
2824:
2822:
2821:
2812:
2801:
2713:
2711:
2710:
2705:
2703:
2691:
2689:
2688:
2683:
2681:
2668:
2666:
2665:
2660:
2655:
2653:
2645:
2644:
2643:
2638:
2628:
2623:
2621:
2613:
2612:
2611:
2606:
2596:
2591:
2589:
2581:
2580:
2571:
2562:
2560:
2559:
2554:
2552:
2540:
2538:
2537:
2532:
2530:
2529:
2524:
2515:
2514:
2509:
2500:
2488:
2486:
2485:
2480:
2478:
2477:
2472:
2459:
2457:
2456:
2451:
2449:
2448:
2443:
2396:downwards using
2368:
2366:
2365:
2360:
2358:
2271:
2269:
2268:
2263:
2258:
2256:
2255:
2254:
2241:
2240:
2235:
2234:
2224:
2216:
2204:
2202:
2201:
2196:
2190:
2179:
2177:
2169:
2168:
2159:
2151:
2139:
2137:
2136:
2131:
2119:
2117:
2116:
2111:
2105:
2103:
2095:
2094:
2085:
2080:
2068:
2066:
2065:
2060:
2054:
2043:
1916:
1914:
1913:
1908:
1903:
1899:
1889:
1881:
1877:
1867:
1856:
1844:
1842:
1841:
1836:
1834:
1833:
1820:
1818:
1817:
1812:
1810:
1791:
1789:
1788:
1783:
1781:
1779:
1778:
1777:
1764:
1760:
1759:
1749:
1736:
1734:
1733:
1728:
1723:
1721:
1713:
1675:
1672:
1651:
1649:
1641:
1633:
1615:
1613:
1612:
1607:
1602:
1600:
1592:
1554:
1551:
1530:
1528:
1520:
1512:
1503:
1501:
1500:
1495:
1471:
1470:
1469:
1442:
1440:
1439:
1434:
1432:
1431:
1415:
1413:
1412:
1407:
1395:
1393:
1392:
1387:
1375:
1373:
1372:
1367:
1365:
1364:
1348:
1346:
1345:
1340:
1328:
1326:
1325:
1320:
1295:
1293:
1292:
1287:
1272:
1270:
1269:
1264:
1245:
1243:
1242:
1237:
1232:
1230:
1222:
1214:
1199:
1197:
1196:
1191:
1180:with the symbol
1179:
1177:
1176:
1171:
1150:
1148:
1147:
1142:
1126:
1124:
1123:
1118:
1106:
1104:
1103:
1098:
1093:
1091:
1090:
1089:
1077:
1076:
1066:
1062:
1061:
1040:
1039:
1023:
1018:
1016:
1008:
1000:
991:
989:
988:
983:
981:
980:
964:
962:
961:
956:
954:
953:
937:
935:
934:
929:
800:
793:
786:
773:
768:
767:
760:
756:
755:
661:Johann Bernoulli
656:Daniel Bernoulli
577:Tangential speed
481:
457:
432:Fictitious force
427:
279:Mechanical power
269:
210:Angular momentum
108:
106:
105:
100:
98:
96:
88:
87:
78:
73:
72:
46:
45:
21:
16121:
16120:
16116:
16115:
16114:
16112:
16111:
16110:
16101:Scientific laws
16056:
16055:
16054:
16044:
16042:
16030:
16020:
16018:
16008:
16006:
15994:
15982:
15974:
15972:
15967:
15966:
15965:
15964:
15963:
15956:
15943:
15899:Newton's cradle
15880:
15835:
15808: (student)
15806:William Whiston
15802: (student)
15758:
15739:Religious views
15700:
15615:Newton's method
15575:Newtonian fluid
15469:Bucket argument
15455:
15375:
15310:
15243:
15238:
15200:
15198:
15175:
15173:Further reading
15170:
15169:
15154:
15137:
15133:
15088:
15084:
15074:
15072:
15067:
15060:
15058:
15053:
15046:
15044:
15031:
15027:
14974:
14970:
14917:
14913:
14892:
14890:
14878:
14874:
14859:
14840:
14836:
14783:
14779:
14769:
14767:
14751:
14747:
14702:
14698:
14683:
14664:
14660:
14611:
14607:
14592:
14570:
14566:
14513:
14509:
14464:
14460:
14445:10.1119/1.18659
14415:
14411:
14401:
14399:
14387:
14383:
14368:
14351:
14347:
14291:
14287:
14272:
14256:
14252:
14209:(1 June 2020).
14204:
14200:
14185:
14168:
14159:
14144:
14130:
14126:
14111:
14094:
14090:
14075:
14059:
14055:
14007:
14003:
13958:
13954:
13911:
13904:
13896:
13888:
13884:
13869:
13853:
13849:
13826:10.2307/2858681
13801:
13797:
13784:
13780:
13767:
13763:
13720:
13713:
13549:
13545:
13530:
13513:
13509:
13486:
13472:
13468:
13405:
13401:
13366:
13362:
13347:
13329:
13325:
13310:
13295:
13291:
13276:
13253:
13249:
13242:
13225:
13221:
13162:
13158:
13107:
13103:
13046:
13042:
13027:
13008:
13004:
12989:
12970:
12966:
12901:
12897:
12890:
12871:
12864:
12849:
12833:
12829:
12781:
12777:
12770:
12753:
12749:
12734:
12711:
12707:
12692:
12673:
12666:
12617:
12613:
12598:
12579:
12572:
12525:(11): 839β848.
12509:
12505:
12490:
12474:Phillips, Melba
12467:
12460:
12450:
12448:
12446:
12422:
12418:
12403:
12384:
12380:
12327:
12323:
12280:(August 1961).
12275:
12271:
12256:
12237:
12230:
12185:
12181:
12133:
12129:
12066:
12062:
12014:
12010:
11945:
11941:
11926:
11905:
11901:
11886:
11863:
11856:
11841:
11821:Ehrenfest, Paul
11818:
11814:
11799:
11788:
11769:
11765:
11750:
11723:
11719:
11701:
11688:
11684:
11627:
11623:
11608:
11591:
11584:
11536:
11532:
11469:
11462:
11425:
11421:
11376:
11372:
11357:
11333:Gowers, Timothy
11326:
11319:
11312:
11285:
11281:
11228:
11224:
11179:
11175:
11130:
11126:
11081:
11077:
11062:
11035:
11031:
10973:
10969:
10954:10.1119/1.16590
10927:
10921:
10917:
10902:
10886:
10879:
10826:
10822:
10807:
10788:
10784:
10769:
10750:
10741:
10676:
10672:
10662:
10660:
10650:Scholberg, Kate
10647:
10643:
10595:
10591:
10538:(August 1905).
10533:
10529:
10509:
10505:
10498:
10484:
10480:
10473:
10457:
10453:
10405:
10401:
10391:
10389:
10382:
10373:
10369:
10354:
10350:
10297:
10293:
10245:
10241:
10196:
10192:
10185:
10168:
10164:
10157:
10139:
10135:
10116:
10108:. p. vii.
10083:
10076:
10061:
10034:
10027:
9999:
9995:
9980:
9964:
9953:
9902:
9898:
9879:
9875:
9864:
9860:
9815:
9811:
9796:
9777:
9748:
9729:Resnick, Robert
9726:
9722:
9707:
9703:
9670:
9666:
9651:
9631:Apostol, Tom M.
9624:
9601:
9590:
9586:
9571:
9556:College Physics
9551:
9547:
9500:
9496:
9451:
9447:
9432:
9413:
9400:
9385:10.1119/1.15104
9352:
9348:
9333:
9317:Gardner, Martin
9310:
9303:
9288:
9263:
9256:
9246:
9244:
9237:
9228:
9224:
9209:
9193:
9189:
9176:
9172:
9161:
9154:
9147:
9131:
9127:
9122:
9117:
9116:
9094:
9090:
9084:Anneliese Maier
9082:
9078:
9073:
9069:
9059:
9055:
9050:
9046:
9041:
9037:
9032:
9028:
9023:
9019:
9014:
9010:
9005:
9001:
8996:
8992:
8987:
8983:
8963:
8952:
8950:
8947:
8946:
8936:
8932:
8926:
8922:
8916:except insofar,
8909:
8905:
8899:
8895:
8886:
8882:
8877:
8835:
8783:'s five-volume
8747:
8744:
8743:
8730:"), but in the
8708:Mary Somerville
8696:
8640:Johannes Kepler
8634:
8627:
8603:William Gilbert
8576:
8569:
8510:Pierre Gassendi
8498:
8497:RenΓ© Descartes
8474:
8456:Galileo Galilei
8430:
8424:
8391:Byzantine Greek
8387:John Philoponus
8384:
8357:
8350:
8345:
8336:
8335:
8334:
8331:
8323:
8314:
8298:
8289:
8287:Godfrey Kneller
8283:
8271:
8222:
8211:tensor calculus
8191:
8155:
8152:
8151:
8131:
8128:
8127:
8111:
8097:
8095:
8092:
8091:
8087:
8077:
8048:Poynting vector
8016:
8002:
7999:
7998:
7969:
7967:
7964:
7963:
7934:
7926:
7915:
7904:
7902:
7899:
7898:
7874:
7871:
7870:
7841:
7837:
7835:
7832:
7831:
7814:
7810:
7808:
7805:
7804:
7787:
7783:
7781:
7778:
7777:
7760:
7756:
7754:
7751:
7750:
7728:
7720:Brownian motion
7703:
7701:
7698:
7697:
7677:
7674:
7673:
7656:
7648:
7634:
7629:
7626:
7625:
7611:Avogadro number
7596:Brownian motion
7588:
7583:
7555:
7550:
7537:
7529:
7516:
7511:
7510:
7506:
7488:
7477:
7476:
7472:
7462:
7449:
7444:
7443:
7439:
7437:
7434:
7433:
7399:
7385:
7370:
7359:
7358:
7354:
7344:
7331:
7326:
7325:
7321:
7319:
7316:
7315:
7299:
7296:
7295:
7273:
7262:
7252:
7241:
7240:
7236:
7226:
7215:
7205:
7200:
7195:
7192:
7191:
7161:
7152:
7139:
7138:
7134:
7133:
7128:
7118:
7113:
7100:
7092:
7090:
7085:
7080:
7077:
7076:
7054:
7039:
7026:
7025:
7021:
7020:
7010:
7005:
6992:
6984:
6982:
6977:
6974:
6973:
6954:
6946:
6943:
6942:
6909:
6901:
6900:
6896:
6880:
6872:
6870:
6865:
6862:
6861:
6839:
6829:
6821:
6819:
6816:
6815:
6799:
6796:
6795:
6775:
6772:
6771:
6746:
6738:
6735:
6734:
6718:
6715:
6714:
6698:
6695:
6694:
6678:
6675:
6674:
6654:
6651:
6650:
6633:
6628:
6627:
6625:
6622:
6621:
6589:
6584:
6583:
6574:
6569:
6568:
6560:
6557:
6556:
6545:
6543:HamiltonβJacobi
6510:
6502:
6500:
6484:
6476:
6474:
6472:
6469:
6468:
6444:
6431:
6423:
6421:
6419:
6416:
6415:
6391:
6384:
6383:
6379:
6377:
6361:
6353:
6351:
6349:
6346:
6345:
6324:
6317:
6316:
6312:
6310:
6297:
6289:
6287:
6285:
6282:
6281:
6242:
6236:
6232:
6230:
6206:
6205:
6203:
6200:
6199:
6183:
6180:
6179:
6163:
6160:
6159:
6143:
6140:
6139:
6113:
6073:
6065:
6063:
6043:
6042:
6026:
6021:
6019:
6016:
6015:
6010:Evaluating the
5987:
5979:
5977:
5956:
5955:
5951:
5943:
5941:
5937:
5927:
5922:
5920:
5917:
5916:
5890:
5886:
5884:
5881:
5880:
5863:
5859:
5857:
5854:
5853:
5828:
5825:
5824:
5807:
5796:
5795:
5794:
5781:
5773:
5770:
5769:
5729:
5728:
5714:
5711:
5710:
5688:
5687:
5685:
5682:
5681:
5665:
5662:
5661:
5654:
5628:
5604:
5579:
5576:
5575:
5556:
5548:
5542:
5538:
5524:
5514:
5503:
5495:
5487:
5471:
5463:
5461:
5459:
5456:
5455:
5431:
5429:
5426:
5425:
5409:
5406:
5405:
5389:
5386:
5385:
5366:
5355:
5345:
5334:
5326:
5318:
5302:
5294:
5292:
5290:
5287:
5286:
5267:
5262:
5254:
5252:
5249:
5248:
5217:
5215:
5212:
5211:
5185:
5177:
5175:
5172:
5171:
5149:double pendulum
5133:
5127:
5122:
5056:
5048:Main articles:
5046:
5021:
5019:
5016:
5015:
4999:
4997:
4994:
4993:
4971:
4969:
4966:
4965:
4945:
4937:
4929:
4927:
4924:
4923:
4907:
4902:
4899:
4898:
4882:
4880:
4877:
4876:
4857:
4849:
4841:
4830:
4817:
4811:
4807:
4805:
4797:
4789:
4772:
4766:
4762:
4760:
4756:
4743:
4737:
4733:
4731:
4729:
4726:
4725:
4706:
4698:
4690:
4688:
4685:
4684:
4664:
4662:
4659:
4658:
4642:
4640:
4637:
4636:
4618:
4597:
4594:
4593:
4576:
4573:
4572:
4546:
4541:
4540:
4534:
4530:
4529:
4527:
4521:
4510:
4498:
4496:
4493:
4492:
4475:
4470:
4469:
4454:
4449:
4448:
4446:
4443:
4442:
4425:
4421:
4406:
4402:
4400:
4397:
4396:
4372:
4366:
4353:
4320:
4309:
4307:
4304:
4303:
4267:
4265:Work and energy
4246:
4244:
4241:
4240:
4218:
4210:
4208:
4203:
4190:
4184:
4180:
4178:
4167:
4165:
4162:
4161:
4145:
4143:
4140:
4139:
4114:
4112:
4109:
4108:
4083:
4080:
4079:
4060:
4054:
4013:
4008:
4000:
3997:
3996:
3976:
3973:
3972:
3956:
3953:
3952:
3932:
3929:
3928:
3912:
3909:
3908:
3892:
3889:
3888:
3855:
3840:
3836:
3832:
3822:
3818:
3817:
3815:
3813:
3810:
3809:
3779:
3776:
3775:
3759:
3756:
3755:
3739:
3736:
3735:
3714:
3709:
3707:
3704:
3703:
3687:
3684:
3683:
3621:
3618:
3617:
3581:
3577:
3573:
3563:
3559:
3558:
3556:
3551:
3548:
3547:
3519:
3516:
3515:
3489:
3486:
3485:
3463:
3460:
3459:
3443:
3440:
3439:
3423:
3420:
3419:
3404:
3398:
3396:Harmonic motion
3366:
3363:
3362:
3345:
3341:
3336:
3325:
3322:
3321:
3298:
3292:
3288:
3283:
3280:
3279:
3253:
3249:
3247:
3239:
3236:
3235:
3219:
3216:
3215:
3199:
3196:
3195:
3180:
3178:Circular motion
3174:
3153:
3150:
3149:
3118:
3114:
3109:
3099:
3088:
3084:
3076:
3074:
3066:
3063:
3062:
3046:
3043:
3042:
3026:
3023:
3022:
3006:
3003:
3002:
2986:
2983:
2982:
2966:
2963:
2962:
2946:
2943:
2942:
2923:
2920:
2919:
2903:
2900:
2899:
2883:
2880:
2879:
2863:
2860:
2859:
2843:
2840:
2839:
2817:
2813:
2802:
2800:
2792:
2789:
2788:
2757:
2749:Main articles:
2747:
2738:
2720:
2699:
2697:
2694:
2693:
2677:
2675:
2672:
2671:
2646:
2639:
2634:
2633:
2629:
2627:
2614:
2607:
2602:
2601:
2597:
2595:
2582:
2576:
2572:
2570:
2568:
2565:
2564:
2548:
2546:
2543:
2542:
2525:
2520:
2519:
2510:
2505:
2504:
2496:
2494:
2491:
2490:
2473:
2468:
2467:
2465:
2462:
2461:
2444:
2439:
2438:
2436:
2433:
2432:
2376:
2354:
2352:
2349:
2348:
2294:), and a force
2250:
2246:
2242:
2236:
2230:
2226:
2225:
2223:
2212:
2210:
2207:
2206:
2186:
2170:
2164:
2160:
2158:
2147:
2145:
2142:
2141:
2125:
2122:
2121:
2096:
2090:
2086:
2084:
2076:
2074:
2071:
2070:
2050:
2039:
2037:
2034:
2033:
2019:
1964:
1959:
1895:
1885:
1873:
1863:
1852:
1850:
1847:
1846:
1829:
1828:
1826:
1823:
1822:
1806:
1804:
1801:
1800:
1773:
1769:
1765:
1755:
1751:
1750:
1748:
1746:
1743:
1742:
1714:
1676:
1674:
1659:
1642:
1634:
1632:
1624:
1621:
1620:
1593:
1555:
1553:
1538:
1521:
1513:
1511:
1509:
1506:
1505:
1465:
1461:
1454:
1448:
1445:
1444:
1427:
1423:
1421:
1418:
1417:
1401:
1398:
1397:
1381:
1378:
1377:
1360:
1356:
1354:
1351:
1350:
1334:
1331:
1330:
1329:has a limit of
1305:
1302:
1301:
1278:
1275:
1274:
1255:
1252:
1251:
1223:
1215:
1213:
1205:
1202:
1201:
1185:
1182:
1181:
1165:
1162:
1161:
1136:
1133:
1132:
1112:
1109:
1108:
1085:
1081:
1072:
1068:
1067:
1057:
1053:
1035:
1031:
1024:
1022:
1009:
1001:
999:
997:
994:
993:
976:
972:
970:
967:
966:
949:
945:
943:
940:
939:
914:
911:
910:
887:
804:
763:
750:
749:
742:
741:
740:
615:
607:
606:
586:
540:Circular motion
534:
524:
523:
522:
479:
449:
446:
425:
404:
396:
395:
392:
391:
349:
339:
331:
330:
329:
288:
284:Mechanical work
277:
261:
199:
191:
190:
189:
144:
136:
113:
89:
83:
79:
77:
68:
67:
65:
62:
61:
42:
35:
28:
23:
22:
15:
12:
11:
5:
16119:
16109:
16108:
16103:
16098:
16093:
16088:
16083:
16078:
16076:Texts in Latin
16073:
16068:
16053:
16052:
16040:
16028:
16016:
16004:
15992:
15969:
15968:
15955:
15954:
15952:
15951:
15949:
15945:
15944:
15942:
15941:
15936:
15931:
15926:
15921:
15916:
15911:
15906:
15901:
15896:
15890:
15888:
15882:
15881:
15879:
15878:
15871:
15864:
15855:
15845:
15843:
15837:
15836:
15834:
15833:
15832: (friend)
15827:
15826: (friend)
15821:
15820: (friend)
15815:
15809:
15803:
15797:
15791:
15790: (mentor)
15788:William Clarke
15785:
15779:
15773:
15766:
15764:
15760:
15759:
15757:
15756:
15751:
15746:
15744:Occult studies
15741:
15736:
15731:
15726:
15721:
15715:
15708:
15706:
15702:
15701:
15699:
15698:
15697:
15696:
15686:
15681:
15676:
15671:
15666:
15661:
15660:
15659:
15649:
15644:
15639:
15634:
15629:
15627:Newton fractal
15624:
15623:
15622:
15612:
15607:
15602:
15597:
15592:
15587:
15582:
15577:
15572:
15567:
15562:
15557:
15555:Newton's rings
15552:
15547:
15546:
15545:
15540:
15530:
15525:
15524:
15523:
15513:
15508:
15503:
15502:
15501:
15496:
15491:
15481:
15476:
15471:
15465:
15463:
15457:
15456:
15454:
15453:
15448:
15443:
15441:Newton's metal
15438:
15433:
15428:
15423:
15422:
15421:
15414:Newton polygon
15411:
15406:
15401:
15396:
15395:
15394:
15383:
15381:
15377:
15376:
15374:
15373:
15365:
15357:
15348:" (1713;
15342:
15334:
15327:
15318:
15316:
15315:Other writings
15312:
15311:
15309:
15308:
15300:
15292:
15284:
15276:
15268:
15260:
15251:
15249:
15245:
15244:
15237:
15236:
15229:
15222:
15214:
15208:
15207:
15181:
15174:
15171:
15168:
15167:
15152:
15131:
15104:(9): 958β963.
15082:
15025:
14990:(5): 564β573.
14968:
14911:
14882:"Isaac Newton"
14872:
14857:
14843:Hesse, Mary B.
14834:
14777:
14745:
14718:(1): 191β229.
14696:
14681:
14658:
14627:(4): 311β339.
14605:
14590:
14564:
14529:(2): 211β224.
14507:
14458:
14431:(2): 149β154.
14409:
14381:
14366:
14345:
14316:10.1086/349598
14310:(3): 379β388.
14285:
14270:
14250:
14229:10.1086/709344
14223:(2): 395β396.
14207:Nummedal, Tara
14198:
14183:
14157:
14142:
14124:
14109:
14088:
14073:
14053:
14010:Fara, Patricia
14001:
13952:
13931:10.1086/351876
13925:(4): 574β597.
13902:
13882:
13867:
13847:
13820:(4): 186β200.
13795:
13778:
13761:
13740:10.1086/350115
13734:(2): 220β234.
13711:
13709:
13708:
13651:
13625:(3): 185β188.
13604:
13543:
13528:
13507:
13484:
13466:
13399:
13380:(1): 169β199.
13360:
13345:
13323:
13308:
13289:
13274:
13247:
13240:
13219:
13156:
13101:
13061:(3): 803β815.
13040:
13025:
13002:
12987:
12964:
12895:
12888:
12862:
12847:
12827:
12797:(4): 938β965.
12775:
12768:
12747:
12732:
12705:
12690:
12664:
12629:(42): 424011.
12611:
12596:
12570:
12503:
12488:
12458:
12444:
12416:
12401:
12378:
12321:
12294:(8): 510β517.
12269:
12254:
12228:
12179:
12152:(2): 146β150.
12127:
12082:(5): 353β359.
12060:
12008:
11939:
11924:
11899:
11884:
11866:Kardar, Mehran
11854:
11839:
11812:
11797:
11763:
11748:
11717:
11682:
11621:
11606:
11582:
11555:(4): 446β452.
11541:(April 2004).
11530:
11485:(2): 431β458.
11460:
11441:(7): 928β929.
11419:
11392:(4): 347β352.
11370:
11355:
11317:
11310:
11279:
11244:(1): 129β137.
11222:
11173:
11124:
11075:
11060:
11029:
10992:(7): 504β509.
10967:
10940:(2): 118β124.
10915:
10900:
10877:
10820:
10805:
10782:
10767:
10739:
10670:
10641:
10589:
10527:
10503:
10496:
10478:
10471:
10451:
10399:
10376:Wilczek, Frank
10367:
10348:
10313:(2): 112β115.
10291:
10264:(7): 406β409.
10239:
10190:
10183:
10162:
10155:
10133:
10114:
10106:Pergamon Press
10086:Landau, Lev D.
10074:
10059:
10025:
9993:
9978:
9951:
9896:
9873:
9858:
9809:
9794:
9780:JosΓ©, Jorge V.
9746:
9720:
9701:
9664:
9649:
9599:
9584:
9569:
9545:
9494:
9467:(4): 171β176.
9445:
9430:
9398:
9371:(6): 503β513.
9346:
9331:
9301:
9286:
9254:
9222:
9207:
9187:
9170:
9152:
9145:
9124:
9123:
9121:
9118:
9115:
9114:
9088:
9076:
9067:
9053:
9044:
9035:
9026:
9017:
9008:
8999:
8990:
8981:
8966:
8962:
8959:
8955:
8930:
8920:
8903:
8893:
8879:
8878:
8876:
8873:
8872:
8871:
8866:
8861:
8856:
8851:
8846:
8841:
8834:
8831:
8777:Leonhard Euler
8760:
8757:
8754:
8751:
8702:Page 157 from
8695:
8689:
8626:
8623:
8568:
8565:
8506:Isaac Beeckman
8434:RenΓ© Descartes
8423:
8420:
8383:
8380:
8349:
8346:
8344:
8341:
8333:
8332:
8324:
8317:
8315:
8299:
8292:
8290:
8284:
8277:
8274:
8273:
8272:
8270:
8267:
8221:
8218:
8190:
8187:
8172:Lorentz factor
8159:
8146:is the body's
8135:
8114:
8110:
8107:
8104:
8100:
8076:
8073:
8060:speed of light
8023:
8019:
8015:
8012:
8009:
8006:
7979:
7976:
7972:
7941:
7937:
7933:
7929:
7925:
7922:
7918:
7914:
7911:
7907:
7878:
7844:
7840:
7817:
7813:
7790:
7786:
7763:
7759:
7727:
7724:
7706:
7681:
7659:
7655:
7651:
7647:
7644:
7641:
7637:
7633:
7587:
7584:
7582:
7579:
7567:
7561:
7558:
7554:
7549:
7545:
7540:
7536:
7532:
7528:
7522:
7519:
7515:
7509:
7505:
7501:
7496:
7491:
7487:
7484:
7480:
7475:
7469:
7466:
7461:
7455:
7452:
7448:
7442:
7409:
7406:
7402:
7398:
7395:
7392:
7388:
7383:
7378:
7373:
7369:
7366:
7362:
7357:
7351:
7348:
7343:
7337:
7334:
7330:
7324:
7303:
7283:
7280:
7276:
7272:
7269:
7265:
7260:
7255:
7251:
7248:
7244:
7239:
7233:
7230:
7225:
7222:
7218:
7211:
7208:
7204:
7199:
7171:
7168:
7164:
7160:
7155:
7150:
7146:
7142:
7137:
7131:
7124:
7121:
7117:
7112:
7106:
7103:
7098:
7095:
7088:
7084:
7064:
7061:
7057:
7053:
7050:
7047:
7042:
7037:
7033:
7029:
7024:
7016:
7013:
7009:
7004:
6998:
6995:
6990:
6987:
6981:
6961:
6957:
6953:
6950:
6930:
6926:
6922:
6919:
6916:
6912:
6908:
6904:
6899:
6895:
6892:
6886:
6883:
6878:
6875:
6869:
6849:
6846:
6842:
6836:
6833:
6828:
6824:
6803:
6779:
6759:
6756:
6753:
6749:
6745:
6742:
6733:is a function
6722:
6702:
6682:
6658:
6636:
6631:
6609:
6606:
6603:
6600:
6597:
6592:
6587:
6582:
6577:
6572:
6567:
6564:
6544:
6541:
6522:
6516:
6513:
6508:
6505:
6499:
6496:
6490:
6487:
6482:
6479:
6456:
6451:
6448:
6443:
6437:
6434:
6429:
6426:
6403:
6397:
6394:
6387:
6382:
6376:
6373:
6367:
6364:
6359:
6356:
6330:
6327:
6320:
6315:
6309:
6303:
6300:
6295:
6292:
6269:
6266:
6263:
6260:
6257:
6254:
6248:
6245:
6239:
6235:
6229:
6226:
6223:
6220:
6217:
6214:
6209:
6187:
6167:
6147:
6112:
6109:
6085:
6079:
6076:
6071:
6068:
6062:
6059:
6056:
6050:
6047:
6041:
6038:
6032:
6029:
6025:
5999:
5993:
5990:
5985:
5982:
5976:
5972:
5963:
5960:
5954:
5949:
5946:
5940:
5933:
5930:
5926:
5893:
5889:
5866:
5862:
5841:
5838:
5835:
5832:
5810:
5803:
5800:
5793:
5788:
5785:
5780:
5777:
5757:
5754:
5751:
5748:
5745:
5742:
5736:
5733:
5727:
5724:
5721:
5718:
5695:
5692:
5669:
5653:
5650:
5627:
5624:
5618:is one of the
5603:
5600:
5583:
5563:
5559:
5555:
5551:
5545:
5541:
5537:
5534:
5531:
5527:
5521:
5518:
5513:
5510:
5506:
5502:
5498:
5494:
5490:
5486:
5483:
5477:
5474:
5469:
5466:
5434:
5413:
5393:
5373:
5369:
5365:
5362:
5358:
5352:
5349:
5344:
5341:
5337:
5333:
5329:
5325:
5321:
5317:
5314:
5308:
5305:
5300:
5297:
5274:
5270:
5265:
5261:
5257:
5220:
5198:
5195:
5192:
5188:
5184:
5180:
5129:Main article:
5126:
5123:
5121:
5118:
5077:conic sections
5069:Kepler problem
5045:
5042:
5024:
5002:
4981:
4978:
4974:
4952:
4948:
4944:
4940:
4936:
4932:
4910:
4906:
4885:
4864:
4860:
4856:
4852:
4848:
4844:
4840:
4837:
4833:
4829:
4823:
4820:
4814:
4810:
4804:
4800:
4796:
4792:
4788:
4784:
4778:
4775:
4769:
4765:
4759:
4755:
4749:
4746:
4740:
4736:
4713:
4709:
4705:
4701:
4697:
4693:
4667:
4645:
4617:
4614:
4601:
4580:
4560:
4555:
4549:
4544:
4537:
4533:
4524:
4519:
4516:
4513:
4509:
4505:
4501:
4478:
4473:
4468:
4465:
4462:
4457:
4452:
4428:
4424:
4420:
4417:
4414:
4409:
4405:
4370:Center of mass
4368:Main article:
4365:
4364:Center of mass
4362:
4358:center of mass
4352:
4349:
4331:
4327:
4323:
4319:
4316:
4312:
4283:Thermal energy
4266:
4263:
4249:
4224:
4221:
4216:
4213:
4206:
4202:
4196:
4193:
4187:
4183:
4177:
4174:
4170:
4148:
4127:
4124:
4121:
4117:
4096:
4093:
4090:
4087:
4068:Space Shuttle
4056:Main article:
4053:
4050:
4020:
4016:
4012:
4007:
4004:
3980:
3960:
3947:is small, the
3936:
3916:
3896:
3876:
3873:
3870:
3867:
3862:
3859:
3854:
3851:
3843:
3839:
3835:
3830:
3825:
3821:
3789:
3786:
3783:
3763:
3743:
3721:
3717:
3713:
3691:
3670:
3667:
3664:
3661:
3658:
3655:
3652:
3649:
3646:
3643:
3640:
3637:
3634:
3631:
3628:
3625:
3605:
3601:
3598:
3595:
3592:
3584:
3580:
3576:
3571:
3566:
3562:
3555:
3535:
3532:
3529:
3526:
3523:
3499:
3496:
3493:
3484:. That is, at
3473:
3470:
3467:
3447:
3427:
3400:Main article:
3397:
3394:
3370:
3348:
3344:
3339:
3335:
3332:
3329:
3305:
3301:
3295:
3291:
3287:
3261:
3256:
3252:
3246:
3243:
3223:
3203:
3176:Main article:
3173:
3170:
3157:
3127:
3121:
3117:
3112:
3108:
3102:
3098:
3091:
3087:
3082:
3079:
3073:
3070:
3050:
3030:
3010:
2990:
2970:
2950:
2930:
2927:
2907:
2887:
2867:
2847:
2827:
2820:
2816:
2811:
2808:
2805:
2799:
2796:
2746:
2743:
2737:
2734:
2719:
2716:
2702:
2680:
2658:
2652:
2649:
2642:
2637:
2632:
2626:
2620:
2617:
2610:
2605:
2600:
2594:
2588:
2585:
2579:
2575:
2551:
2528:
2523:
2518:
2513:
2508:
2503:
2499:
2476:
2471:
2447:
2442:
2398:rocket engines
2394:reaction force
2383:
2382:
2375:
2372:
2357:
2330:"normal" force
2326:inclined plane
2304:add as vectors
2261:
2253:
2249:
2245:
2239:
2233:
2229:
2222:
2219:
2215:
2194:
2189:
2185:
2182:
2176:
2173:
2167:
2163:
2157:
2154:
2150:
2129:
2109:
2102:
2099:
2093:
2089:
2083:
2079:
2058:
2053:
2049:
2046:
2042:
2026:
2025:
2018:
2015:
1990:
1989:
1963:
1960:
1958:
1955:
1906:
1902:
1898:
1894:
1888:
1884:
1880:
1876:
1872:
1866:
1862:
1859:
1855:
1832:
1809:
1776:
1772:
1768:
1763:
1758:
1754:
1726:
1720:
1717:
1712:
1709:
1706:
1703:
1700:
1697:
1694:
1691:
1688:
1685:
1682:
1679:
1671:
1668:
1665:
1662:
1658:
1654:
1648:
1645:
1640:
1637:
1631:
1628:
1605:
1599:
1596:
1591:
1588:
1585:
1582:
1579:
1576:
1573:
1570:
1567:
1564:
1561:
1558:
1550:
1547:
1544:
1541:
1537:
1533:
1527:
1524:
1519:
1516:
1493:
1490:
1487:
1484:
1481:
1478:
1475:
1468:
1464:
1460:
1457:
1453:
1443:. One writes,
1430:
1426:
1405:
1385:
1363:
1359:
1338:
1318:
1315:
1312:
1309:
1285:
1282:
1262:
1259:
1235:
1229:
1226:
1221:
1218:
1212:
1209:
1200:, for example,
1189:
1169:
1140:
1116:
1096:
1088:
1084:
1080:
1075:
1071:
1065:
1060:
1056:
1052:
1049:
1046:
1043:
1038:
1034:
1030:
1027:
1021:
1015:
1012:
1007:
1004:
979:
975:
952:
948:
927:
924:
921:
918:
886:
883:
849:
848:
845:
834:
806:
805:
803:
802:
795:
788:
780:
777:
776:
775:
774:
761:
744:
743:
739:
738:
733:
728:
723:
718:
713:
708:
703:
698:
693:
688:
683:
678:
673:
668:
663:
658:
653:
648:
643:
638:
633:
628:
623:
617:
616:
613:
612:
609:
608:
605:
604:
585:
584:
579:
574:
569:
567:Coriolis force
564:
563:
562:
552:
547:
542:
536:
535:
530:
529:
526:
525:
521:
520:
515:
510:
509:
508:
503:
493:
488:
483:
476:
465:
464:
463:
458:
445:
444:
439:
434:
429:
422:
417:
412:
406:
405:
402:
401:
398:
397:
394:
393:
390:
389:
384:
379:
374:
369:
364:
358:
352:
350:
343:
340:
337:
336:
333:
332:
328:
327:
322:
317:
312:
307:
302:
297:
292:
286:
281:
275:
270:
259:
254:
249:
244:
239:
238:
237:
232:
222:
217:
212:
207:
201:
200:
197:
196:
193:
192:
188:
187:
182:
177:
172:
167:
162:
157:
152:
146:
145:
142:
141:
138:
137:
135:
134:
129:
124:
118:
115:
114:
109:
95:
92:
86:
82:
76:
58:
57:
51:
50:
26:
9:
6:
4:
3:
2:
16118:
16107:
16104:
16102:
16099:
16097:
16094:
16092:
16089:
16087:
16084:
16082:
16079:
16077:
16074:
16072:
16069:
16067:
16064:
16063:
16061:
16051:
16041:
16039:
16034:
16029:
16027:
16017:
16015:
16005:
16003:
15998:
15993:
15991:
15986:
15981:
15980:
15977:
15962:
15958:
15950:
15946:
15940:
15937:
15935:
15932:
15930:
15927:
15925:
15922:
15920:
15917:
15915:
15912:
15910:
15907:
15905:
15902:
15900:
15897:
15895:
15894:Newton (unit)
15892:
15891:
15889:
15887:
15883:
15877:
15876:
15872:
15870:
15869:
15865:
15862:
15860:
15856:
15853:
15851:
15847:
15846:
15844:
15842:
15838:
15831:
15828:
15825:
15824:William Jones
15822:
15819:
15816:
15813:
15810:
15807:
15804:
15801:
15798:
15796: (tutor)
15795:
15792:
15789:
15786:
15783:
15780:
15777:
15776:John Conduitt
15774:
15772: (niece)
15771:
15768:
15767:
15765:
15761:
15755:
15752:
15750:
15747:
15745:
15742:
15740:
15737:
15735:
15732:
15730:
15727:
15725:
15722:
15719:
15718:Cranbury Park
15716:
15713:
15710:
15709:
15707:
15705:Personal life
15703:
15695:
15692:
15691:
15690:
15687:
15685:
15682:
15680:
15677:
15675:
15672:
15670:
15667:
15665:
15662:
15658:
15655:
15654:
15653:
15652:Newton number
15650:
15648:
15645:
15643:
15640:
15638:
15635:
15633:
15630:
15628:
15625:
15621:
15618:
15617:
15616:
15613:
15611:
15608:
15606:
15603:
15601:
15598:
15596:
15593:
15591:
15588:
15586:
15583:
15581:
15578:
15576:
15573:
15571:
15568:
15566:
15563:
15561:
15558:
15556:
15553:
15551:
15548:
15544:
15541:
15539:
15536:
15535:
15534:
15531:
15529:
15526:
15522:
15521:Kepler's laws
15519:
15518:
15517:
15514:
15512:
15509:
15507:
15504:
15500:
15497:
15495:
15494:parameterized
15492:
15490:
15487:
15486:
15485:
15482:
15480:
15477:
15475:
15472:
15470:
15467:
15466:
15464:
15462:
15458:
15452:
15449:
15447:
15444:
15442:
15439:
15437:
15434:
15432:
15429:
15427:
15424:
15420:
15417:
15416:
15415:
15412:
15410:
15407:
15405:
15402:
15400:
15397:
15393:
15390:
15389:
15388:
15385:
15384:
15382:
15380:Contributions
15378:
15371:
15370:
15366:
15363:
15362:
15358:
15355:
15353:
15347:
15343:
15340:
15339:
15335:
15333:" (1675)
15332:
15328:
15325:
15324:
15320:
15319:
15317:
15313:
15306:
15305:
15301:
15298:
15297:
15293:
15290:
15289:
15285:
15282:
15281:
15277:
15274:
15273:
15269:
15266:
15265:
15261:
15258:
15257:
15253:
15252:
15250:
15246:
15242:
15235:
15230:
15228:
15223:
15221:
15216:
15215:
15212:
15197:
15196:
15191:
15187:
15182:
15180:
15177:
15176:
15163:
15159:
15155:
15149:
15145:
15141:
15135:
15127:
15123:
15119:
15115:
15111:
15107:
15103:
15099:
15098:
15093:
15086:
15070:
15056:
15043:
15039:
15035:
15029:
15021:
15017:
15013:
15009:
15005:
15001:
14997:
14993:
14989:
14985:
14984:
14979:
14972:
14964:
14960:
14956:
14952:
14948:
14944:
14940:
14936:
14932:
14928:
14927:
14922:
14915:
14908:
14906:
14902:
14889:
14888:
14883:
14876:
14868:
14864:
14860:
14854:
14850:
14849:
14844:
14838:
14830:
14826:
14822:
14818:
14814:
14810:
14806:
14802:
14799:(1): 015001.
14798:
14794:
14793:
14788:
14781:
14766:
14765:
14760:
14758:
14749:
14741:
14737:
14733:
14729:
14725:
14721:
14717:
14713:
14712:
14707:
14700:
14692:
14688:
14684:
14678:
14674:
14673:
14668:
14662:
14655:
14650:
14646:
14642:
14638:
14634:
14630:
14626:
14622:
14621:
14616:
14609:
14601:
14597:
14593:
14587:
14583:
14579:
14575:
14568:
14560:
14556:
14552:
14548:
14544:
14540:
14536:
14532:
14528:
14524:
14523:
14518:
14511:
14503:
14499:
14495:
14491:
14487:
14483:
14480:(10): 31β36.
14479:
14475:
14474:
14473:Physics Today
14469:
14462:
14454:
14450:
14446:
14442:
14438:
14434:
14430:
14426:
14425:
14420:
14413:
14398:
14397:
14392:
14385:
14377:
14373:
14369:
14363:
14359:
14355:
14349:
14341:
14337:
14333:
14329:
14325:
14321:
14317:
14313:
14309:
14305:
14304:
14299:
14295:
14289:
14281:
14277:
14273:
14267:
14263:
14262:
14254:
14246:
14242:
14238:
14234:
14230:
14226:
14222:
14218:
14217:
14212:
14208:
14202:
14194:
14190:
14186:
14180:
14176:
14172:
14166:
14164:
14162:
14153:
14149:
14145:
14143:9780521231435
14139:
14135:
14134:Never at Rest
14128:
14120:
14116:
14112:
14110:9780521273817
14106:
14102:
14098:
14092:
14084:
14080:
14076:
14070:
14066:
14065:
14057:
14049:
14045:
14041:
14037:
14033:
14029:
14026:(5635): 920.
14025:
14021:
14020:
14015:
14011:
14005:
13997:
13993:
13989:
13985:
13981:
13977:
13973:
13969:
13968:
13963:
13956:
13948:
13944:
13940:
13936:
13932:
13928:
13924:
13920:
13916:
13909:
13907:
13895:
13894:
13886:
13878:
13874:
13870:
13864:
13860:
13859:
13851:
13843:
13839:
13835:
13831:
13827:
13823:
13819:
13815:
13814:
13809:
13805:
13799:
13791:
13790:
13782:
13774:
13773:
13765:
13757:
13753:
13749:
13745:
13741:
13737:
13733:
13729:
13725:
13718:
13716:
13705:
13701:
13697:
13693:
13688:
13683:
13679:
13675:
13672:(1): 010121.
13671:
13667:
13666:
13661:
13657:
13652:
13648:
13644:
13640:
13636:
13632:
13628:
13624:
13620:
13619:
13614:
13610:
13605:
13601:
13597:
13593:
13589:
13584:
13579:
13575:
13571:
13568:(1): 010123.
13567:
13563:
13562:
13557:
13552:
13551:
13547:
13539:
13535:
13531:
13525:
13521:
13517:
13511:
13503:
13499:
13495:
13491:
13487:
13481:
13477:
13470:
13463:
13460:
13454:
13450:
13445:
13440:
13436:
13432:
13428:
13424:
13420:
13416:
13415:
13410:
13403:
13395:
13391:
13387:
13383:
13379:
13375:
13371:
13364:
13356:
13352:
13348:
13342:
13338:
13334:
13327:
13319:
13315:
13311:
13305:
13301:
13293:
13285:
13281:
13277:
13275:0-7923-2549-4
13271:
13267:
13263:
13262:
13257:
13251:
13243:
13241:0-471-16433-X
13237:
13233:
13229:
13223:
13215:
13211:
13207:
13203:
13198:
13193:
13189:
13185:
13182:(2): 025705.
13181:
13177:
13176:
13171:
13167:
13160:
13152:
13148:
13144:
13140:
13136:
13132:
13127:
13122:
13118:
13114:
13113:
13105:
13098:
13094:
13090:
13086:
13082:
13078:
13074:
13069:
13064:
13060:
13056:
13055:
13050:
13044:
13036:
13032:
13028:
13022:
13018:
13017:
13012:
13006:
12998:
12994:
12990:
12984:
12980:
12979:
12974:
12968:
12960:
12956:
12952:
12948:
12943:
12938:
12933:
12928:
12924:
12920:
12917:(3): 035008.
12916:
12912:
12911:
12906:
12899:
12891:
12885:
12881:
12880:
12875:
12869:
12867:
12858:
12854:
12850:
12844:
12840:
12839:
12831:
12824:
12820:
12816:
12812:
12808:
12804:
12800:
12796:
12792:
12791:
12786:
12779:
12771:
12769:0-393-09804-4
12765:
12761:
12757:
12756:French, A. P.
12751:
12743:
12739:
12735:
12733:0-19-850657-0
12729:
12725:
12724:
12719:
12715:
12709:
12701:
12697:
12693:
12687:
12683:
12682:
12677:
12671:
12669:
12660:
12656:
12652:
12648:
12644:
12640:
12636:
12632:
12628:
12624:
12623:
12615:
12607:
12603:
12599:
12597:0-201-31611-0
12593:
12589:
12588:
12583:
12577:
12575:
12566:
12562:
12558:
12554:
12550:
12546:
12542:
12538:
12533:
12528:
12524:
12520:
12519:
12514:
12507:
12499:
12495:
12491:
12489:0-486-43924-0
12485:
12481:
12480:
12475:
12471:
12465:
12463:
12447:
12441:
12437:
12433:
12429:
12428:
12420:
12412:
12408:
12404:
12402:90-277-0107-5
12398:
12394:
12393:
12388:
12382:
12374:
12370:
12366:
12362:
12358:
12354:
12350:
12346:
12343:(6): 065201.
12342:
12338:
12337:
12332:
12325:
12317:
12313:
12309:
12305:
12301:
12297:
12293:
12289:
12288:
12283:
12279:
12273:
12265:
12261:
12257:
12251:
12247:
12246:
12241:
12235:
12233:
12224:
12220:
12216:
12212:
12208:
12204:
12200:
12196:
12195:
12190:
12183:
12175:
12171:
12167:
12163:
12159:
12155:
12151:
12147:
12146:
12141:
12137:
12136:Rosen, Nathan
12131:
12123:
12119:
12115:
12111:
12107:
12103:
12099:
12095:
12090:
12085:
12081:
12077:
12076:
12071:
12064:
12056:
12052:
12048:
12044:
12040:
12036:
12032:
12028:
12027:
12022:
12018:
12012:
12004:
12000:
11996:
11992:
11987:
11982:
11977:
11972:
11968:
11964:
11961:(2): 020126.
11960:
11956:
11955:
11950:
11943:
11935:
11931:
11927:
11921:
11916:
11915:
11909:
11903:
11895:
11891:
11887:
11881:
11877:
11873:
11872:
11867:
11861:
11859:
11850:
11846:
11842:
11840:0-486-66250-0
11836:
11832:
11831:
11826:
11822:
11816:
11808:
11804:
11800:
11794:
11787:
11786:
11781:
11780:Wiles, Andrew
11777:
11776:Jaffe, Arthur
11773:
11767:
11759:
11755:
11751:
11745:
11740:
11735:
11731:
11727:
11726:Baez, John C.
11721:
11713:
11709:
11708:
11700:
11696:
11692:
11686:
11678:
11674:
11670:
11666:
11661:
11656:
11651:
11646:
11642:
11638:
11637:
11632:
11625:
11617:
11613:
11609:
11603:
11599:
11595:
11589:
11587:
11578:
11574:
11570:
11566:
11562:
11558:
11554:
11550:
11549:
11544:
11540:
11534:
11526:
11522:
11518:
11514:
11510:
11506:
11502:
11498:
11493:
11488:
11484:
11480:
11479:
11474:
11467:
11465:
11456:
11452:
11448:
11444:
11440:
11436:
11435:
11430:
11423:
11415:
11411:
11407:
11403:
11399:
11395:
11391:
11387:
11386:
11381:
11374:
11366:
11362:
11358:
11352:
11348:
11347:
11342:
11338:
11334:
11330:
11324:
11322:
11313:
11307:
11303:
11299:
11295:
11294:
11289:
11283:
11275:
11271:
11267:
11263:
11259:
11255:
11251:
11247:
11243:
11239:
11238:
11233:
11226:
11218:
11214:
11210:
11206:
11202:
11198:
11194:
11190:
11189:
11184:
11177:
11169:
11165:
11161:
11157:
11153:
11149:
11145:
11141:
11140:
11135:
11128:
11120:
11116:
11112:
11108:
11104:
11100:
11096:
11092:
11091:
11086:
11079:
11071:
11067:
11063:
11057:
11053:
11052:
11047:
11043:
11039:
11033:
11025:
11021:
11017:
11013:
11008:
11003:
10999:
10995:
10991:
10987:
10986:
10981:
10977:
10971:
10963:
10959:
10955:
10951:
10947:
10943:
10939:
10935:
10934:
10926:
10919:
10911:
10907:
10903:
10901:0-521-57327-0
10897:
10893:
10892:
10884:
10882:
10873:
10869:
10865:
10861:
10857:
10853:
10849:
10845:
10841:
10837:
10836:
10831:
10824:
10816:
10812:
10808:
10802:
10798:
10797:
10792:
10786:
10778:
10774:
10770:
10764:
10760:
10759:
10754:
10753:Boas, Mary L.
10748:
10746:
10744:
10735:
10731:
10727:
10723:
10718:
10717:11577/3340932
10713:
10708:
10703:
10699:
10695:
10692:(1): 010111.
10691:
10687:
10686:
10681:
10674:
10659:
10655:
10651:
10645:
10637:
10633:
10629:
10625:
10621:
10617:
10613:
10609:
10608:
10603:
10599:
10593:
10585:
10581:
10577:
10573:
10568:
10563:
10559:
10555:
10552:(1870): 429.
10551:
10547:
10546:
10541:
10537:
10531:
10523:
10522:
10517:
10513:
10507:
10499:
10493:
10489:
10482:
10474:
10468:
10464:
10463:
10455:
10447:
10443:
10439:
10435:
10431:
10427:
10423:
10419:
10418:
10413:
10409:
10403:
10388:
10381:
10377:
10371:
10363:
10359:
10352:
10344:
10340:
10336:
10332:
10328:
10324:
10320:
10316:
10312:
10308:
10307:
10302:
10295:
10287:
10283:
10279:
10275:
10271:
10267:
10263:
10259:
10258:
10253:
10249:
10243:
10235:
10231:
10227:
10223:
10219:
10215:
10211:
10207:
10206:
10201:
10194:
10186:
10184:0-06-273100-9
10180:
10176:
10172:
10171:Gonick, Larry
10166:
10158:
10152:
10148:
10144:
10137:
10130:
10125:
10121:
10117:
10111:
10107:
10103:
10099:
10095:
10091:
10087:
10081:
10079:
10070:
10066:
10062:
10060:0-201-02010-6
10056:
10052:
10051:
10046:
10042:
10038:
10032:
10030:
10021:
10017:
10013:
10009:
10008:
10003:
9997:
9989:
9985:
9981:
9975:
9971:
9970:
9962:
9960:
9958:
9956:
9947:
9943:
9938:
9933:
9929:
9925:
9922:(1): 010108.
9921:
9917:
9916:
9911:
9907:
9900:
9892:
9888:
9884:
9877:
9869:
9862:
9854:
9850:
9846:
9842:
9838:
9834:
9830:
9826:
9825:
9820:
9813:
9805:
9801:
9797:
9791:
9787:
9786:
9781:
9775:
9773:
9771:
9769:
9767:
9765:
9763:
9761:
9759:
9757:
9755:
9753:
9751:
9742:
9738:
9734:
9730:
9724:
9716:
9712:
9705:
9697:
9693:
9688:
9683:
9679:
9675:
9668:
9660:
9656:
9652:
9646:
9642:
9641:
9636:
9632:
9628:
9622:
9620:
9618:
9616:
9614:
9612:
9610:
9608:
9606:
9604:
9595:
9588:
9580:
9576:
9572:
9566:
9562:
9558:
9557:
9549:
9541:
9537:
9532:
9527:
9523:
9519:
9516:(1): 010110.
9515:
9511:
9510:
9505:
9498:
9490:
9486:
9482:
9478:
9474:
9470:
9466:
9462:
9461:
9456:
9449:
9441:
9437:
9433:
9427:
9423:
9422:
9417:
9411:
9409:
9407:
9405:
9403:
9394:
9390:
9386:
9382:
9378:
9374:
9370:
9366:
9365:
9360:
9356:
9350:
9342:
9338:
9334:
9328:
9324:
9323:
9318:
9314:
9308:
9306:
9297:
9293:
9289:
9283:
9279:
9275:
9271:
9267:
9261:
9259:
9243:
9236:
9232:
9226:
9218:
9214:
9210:
9204:
9200:
9199:
9191:
9183:
9182:
9174:
9166:
9159:
9157:
9148:
9146:0-534-40896-6
9142:
9138:
9137:
9129:
9125:
9111:
9106:
9102:
9098:
9092:
9085:
9080:
9071:
9063:
9057:
9048:
9039:
9030:
9021:
9012:
9003:
8994:
8985:
8960:
8957:
8944:
8940:
8934:
8924:
8917:
8913:
8907:
8897:
8890:
8884:
8880:
8870:
8869:Norton's dome
8867:
8865:
8862:
8860:
8857:
8855:
8852:
8850:
8847:
8845:
8842:
8840:
8837:
8836:
8830:
8828:
8824:
8820:
8816:
8811:
8808:
8804:
8798:
8796:
8792:
8788:
8787:
8782:
8778:
8774:
8773:Jakob Hermann
8758:
8755:
8752:
8749:
8741:
8737:
8733:
8729:
8725:
8717:
8713:
8709:
8705:
8700:
8694:
8688:
8686:
8682:
8678:
8673:
8671:
8667:
8663:
8659:
8654:
8652:
8648:
8647:
8641:
8631:
8622:
8620:
8616:
8612:
8608:
8604:
8600:
8599:
8593:
8588:
8586:
8585:
8573:
8564:
8560:
8556:
8554:
8550:
8546:
8540:
8535:
8527:
8523:
8521:
8517:
8516:
8511:
8507:
8495:
8490:
8485:
8483:
8471:
8467:
8465:
8461:
8457:
8453:
8449:
8445:
8441:
8440:
8435:
8429:
8419:
8417:
8413:
8409:
8405:
8401:
8397:
8392:
8388:
8379:
8377:
8373:
8369:
8361:
8354:
8340:
8330:
8329:
8321:
8316:
8313:
8309:
8305:
8304:
8296:
8291:
8288:
8281:
8276:
8275:
8266:
8263:
8259:
8254:
8249:
8247:
8243:
8239:
8235:
8231:
8226:
8217:
8214:
8212:
8208:
8203:
8199:
8195:
8186:
8183:
8179:
8177:
8173:
8157:
8149:
8133:
8108:
8105:
8102:
8086:
8082:
8072:
8070:
8066:
8061:
8056:
8051:
8049:
8043:
8041:
8037:
8021:
8017:
8013:
8010:
8007:
8004:
7997:
7993:
7977:
7974:
7956:
7952:
7939:
7931:
7923:
7920:
7912:
7909:
7896:
7895:cross product
7892:
7876:
7867:
7863:
7858:
7842:
7838:
7815:
7811:
7788:
7784:
7761:
7757:
7747:
7743:
7742:Coulomb's law
7739:
7737:
7733:
7723:
7721:
7704:
7695:
7679:
7657:
7653:
7645:
7642:
7639:
7631:
7623:
7618:
7616:
7612:
7608:
7604:
7597:
7592:
7578:
7565:
7559:
7556:
7552:
7547:
7543:
7534:
7526:
7520:
7507:
7503:
7499:
7494:
7485:
7482:
7473:
7467:
7464:
7459:
7453:
7440:
7430:
7428:
7424:
7407:
7404:
7396:
7393:
7390:
7381:
7376:
7367:
7364:
7355:
7349:
7346:
7341:
7335:
7322:
7301:
7281:
7278:
7270:
7267:
7258:
7249:
7246:
7237:
7231:
7228:
7223:
7220:
7209:
7197:
7189:
7185:
7169:
7166:
7158:
7153:
7148:
7144:
7135:
7122:
7119:
7115:
7110:
7104:
7096:
7082:
7062:
7048:
7045:
7040:
7035:
7031:
7022:
7014:
7011:
7007:
7002:
6996:
6988:
6979:
6948:
6928:
6924:
6920:
6917:
6914:
6906:
6897:
6893:
6890:
6884:
6876:
6867:
6847:
6844:
6834:
6831:
6826:
6801:
6793:
6777:
6754:
6751:
6740:
6720:
6700:
6680:
6672:
6656:
6634:
6620:of positions
6604:
6601:
6598:
6595:
6590:
6580:
6575:
6562:
6554:
6550:
6540:
6537:
6534:
6520:
6514:
6511:
6506:
6503:
6497:
6494:
6488:
6485:
6480:
6477:
6454:
6449:
6446:
6441:
6435:
6432:
6427:
6424:
6401:
6395:
6374:
6371:
6365:
6362:
6357:
6354:
6328:
6307:
6301:
6298:
6293:
6290:
6267:
6261:
6255:
6252:
6246:
6243:
6237:
6233:
6227:
6221:
6218:
6215:
6185:
6165:
6145:
6137:
6133:
6125:
6121:
6117:
6108:
6106:
6101:
6097:
6083:
6077:
6074:
6069:
6066:
6060:
6057:
6048:
6045:
6039:
6030:
6027:
6023:
6013:
5997:
5991:
5983:
5974:
5970:
5961:
5958:
5947:
5938:
5931:
5928:
5924:
5914:
5910:
5891:
5887:
5864:
5860:
5836:
5830:
5808:
5801:
5798:
5791:
5786:
5783:
5778:
5775:
5755:
5752:
5749:
5746:
5743:
5734:
5731:
5725:
5722:
5716:
5693:
5690:
5667:
5658:
5649:
5647:
5643:
5639:
5634:
5623:
5621:
5617:
5612:
5610:
5602:Singularities
5599:
5597:
5581:
5561:
5553:
5543:
5535:
5532:
5529:
5519:
5516:
5511:
5508:
5492:
5481:
5475:
5467:
5453:
5449:
5411:
5391:
5371:
5363:
5360:
5350:
5347:
5342:
5339:
5323:
5312:
5306:
5298:
5272:
5268:
5259:
5246:
5242:
5240:
5236:
5193:
5190:
5169:
5165:
5160:
5158:
5154:
5150:
5146:
5137:
5132:
5117:
5115:
5110:
5106:
5102:
5097:
5094:
5090:
5086:
5082:
5078:
5074:
5070:
5060:
5055:
5051:
5041:
5037:
4979:
4976:
4950:
4942:
4934:
4930:
4904:
4862:
4854:
4846:
4838:
4835:
4827:
4821:
4818:
4808:
4802:
4794:
4786:
4782:
4776:
4773:
4763:
4757:
4753:
4747:
4744:
4734:
4711:
4703:
4695:
4682:
4681:cross product
4633:
4631:
4627:
4623:
4613:
4599:
4578:
4558:
4553:
4547:
4535:
4531:
4522:
4517:
4514:
4511:
4507:
4503:
4476:
4466:
4463:
4460:
4455:
4441:at positions
4426:
4422:
4418:
4415:
4412:
4407:
4403:
4389:
4385:
4381:
4376:
4371:
4361:
4359:
4348:
4346:
4329:
4325:
4317:
4314:
4301:
4297:
4292:
4288:
4284:
4280:
4276:
4272:
4262:
4222:
4219:
4214:
4211:
4200:
4194:
4191:
4181:
4175:
4172:
4122:
4091:
4085:
4072:
4071:
4064:
4059:
4049:
4047:
4043:
4039:
4034:
4018:
4014:
4010:
4005:
4002:
3994:
3993:Taylor series
3978:
3958:
3950:
3934:
3914:
3894:
3874:
3871:
3868:
3865:
3860:
3857:
3852:
3849:
3841:
3837:
3833:
3828:
3823:
3819:
3806:
3801:
3787:
3784:
3781:
3761:
3741:
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3711:
3689:
3668:
3665:
3662:
3659:
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3647:
3644:
3641:
3638:
3635:
3629:
3623:
3603:
3599:
3596:
3593:
3590:
3582:
3578:
3574:
3569:
3564:
3560:
3553:
3533:
3530:
3527:
3524:
3521:
3513:
3497:
3494:
3491:
3471:
3468:
3465:
3445:
3425:
3413:
3408:
3403:
3393:
3390:
3386:
3382:
3368:
3346:
3342:
3337:
3333:
3330:
3327:
3319:
3303:
3299:
3293:
3289:
3285:
3277:
3259:
3254:
3250:
3244:
3241:
3221:
3201:
3189:
3184:
3179:
3169:
3155:
3147:
3143:
3138:
3125:
3119:
3110:
3100:
3096:
3089:
3085:
3080:
3077:
3071:
3068:
3048:
3028:
3008:
2988:
2968:
2948:
2928:
2925:
2905:
2885:
2865:
2845:
2825:
2818:
2814:
2809:
2806:
2803:
2797:
2794:
2786:
2782:
2774:
2770:
2766:
2765:bouncing ball
2761:
2756:
2752:
2742:
2733:
2731:
2726:
2725:Frank Wilczek
2715:
2656:
2650:
2647:
2640:
2630:
2624:
2618:
2615:
2608:
2598:
2592:
2586:
2583:
2573:
2526:
2516:
2511:
2501:
2474:
2445:
2430:
2426:
2422:
2417:
2415:
2411:
2403:
2399:
2395:
2391:
2387:
2381:
2378:
2377:
2371:
2346:
2342:
2338:
2333:
2331:
2327:
2323:
2318:
2317:
2313:
2309:
2305:
2297:
2293:
2289:
2285:
2281:
2276:
2272:
2259:
2251:
2247:
2243:
2231:
2227:
2220:
2217:
2192:
2183:
2180:
2174:
2171:
2161:
2155:
2152:
2127:
2107:
2100:
2097:
2087:
2081:
2056:
2047:
2044:
2031:
2024:
2021:
2020:
2014:
2012:
2007:
2002:
1997:
1995:
1988:
1985:
1984:
1983:
1977:
1973:
1968:
1954:
1951:
1947:
1943:
1939:
1935:
1931:
1927:
1922:
1920:
1896:
1886:
1882:
1874:
1864:
1857:
1798:
1793:
1774:
1770:
1766:
1761:
1756:
1752:
1740:
1724:
1718:
1707:
1701:
1698:
1692:
1686:
1683:
1677:
1669:
1663:
1652:
1646:
1643:
1638:
1635:
1629:
1626:
1618:
1603:
1597:
1586:
1580:
1577:
1571:
1565:
1562:
1556:
1548:
1542:
1531:
1525:
1522:
1517:
1514:
1491:
1488:
1485:
1479:
1473:
1466:
1462:
1455:
1428:
1424:
1403:
1383:
1361:
1357:
1336:
1313:
1307:
1300:. A function
1299:
1283:
1280:
1260:
1257:
1249:
1233:
1227:
1224:
1219:
1216:
1210:
1207:
1187:
1159:
1158:instantaneous
1155:
1138:
1130:
1094:
1086:
1082:
1078:
1073:
1069:
1058:
1054:
1047:
1044:
1036:
1032:
1025:
1019:
1013:
1005:
977:
973:
950:
946:
922:
916:
908:
904:
899:
896:
892:
885:Prerequisites
882:
880:
876:
872:
868:
864:
860:
859:
854:
846:
843:
839:
835:
832:
831:
830:
828:
824:
820:
816:
815:physical laws
812:
801:
796:
794:
789:
787:
782:
781:
779:
778:
772:
762:
759:
754:
748:
747:
746:
745:
737:
734:
732:
729:
727:
724:
722:
719:
717:
714:
712:
709:
707:
704:
702:
699:
697:
694:
692:
689:
687:
684:
682:
679:
677:
674:
672:
669:
667:
664:
662:
659:
657:
654:
652:
649:
647:
644:
642:
639:
637:
634:
632:
629:
627:
624:
622:
619:
618:
611:
610:
603:
599:
595:
591:
588:
587:
583:
580:
578:
575:
573:
570:
568:
565:
561:
558:
557:
556:
553:
551:
548:
546:
543:
541:
538:
537:
533:
528:
527:
519:
516:
514:
511:
507:
504:
502:
499:
498:
497:
494:
492:
489:
487:
484:
482:
477:
474:
470:
467:
466:
462:
459:
456:
452:
448:
447:
443:
440:
438:
435:
433:
430:
428:
423:
421:
418:
416:
413:
411:
408:
407:
400:
399:
388:
385:
383:
380:
378:
375:
373:
370:
368:
365:
363:
360:
359:
357:
356:
351:
348:
347:
342:
341:
335:
334:
326:
323:
321:
318:
316:
313:
311:
308:
306:
303:
301:
298:
296:
293:
291:
287:
285:
282:
280:
276:
274:
271:
268:
264:
260:
258:
255:
253:
250:
248:
245:
243:
240:
236:
233:
231:
228:
227:
226:
223:
221:
218:
216:
213:
211:
208:
206:
203:
202:
195:
194:
186:
183:
181:
178:
176:
173:
171:
168:
166:
163:
161:
158:
156:
153:
151:
148:
147:
140:
139:
133:
130:
128:
125:
123:
120:
119:
117:
116:
112:
93:
90:
80:
74:
60:
59:
56:
53:
52:
48:
47:
44:
40:
33:
19:
16071:Isaac Newton
16050:Solar System
15961:Isaac Newton
15873:
15866:
15858:
15849:
15782:Isaac Barrow
15720: (home)
15515:
15461:Newtonianism
15436:Newton scale
15399:Impact depth
15372: (1754)
15367:
15364: (1728)
15359:
15349:
15336:
15321:
15307: (1711)
15302:
15299: (1707)
15294:
15291: (1704)
15286:
15283: (1704)
15278:
15275: (1687)
15270:
15267: (1684)
15262:
15259: (1671)
15254:
15248:Publications
15199:. Retrieved
15193:
15186:Frebel, Anna
15143:
15140:Reich, Karin
15134:
15101:
15095:
15085:
15073:. Retrieved
15059:. Retrieved
15045:. Retrieved
15041:
15028:
14987:
14981:
14971:
14930:
14924:
14914:
14904:
14900:
14898:
14891:. Retrieved
14885:
14875:
14847:
14837:
14796:
14790:
14780:
14768:. Retrieved
14762:
14756:
14748:
14715:
14709:
14699:
14671:
14661:
14652:
14624:
14618:
14608:
14573:
14567:
14526:
14520:
14510:
14477:
14471:
14461:
14428:
14422:
14412:
14400:. Retrieved
14394:
14384:
14357:
14348:
14307:
14301:
14288:
14260:
14253:
14220:
14214:
14201:
14174:
14133:
14127:
14100:
14091:
14063:
14056:
14023:
14017:
14004:
13971:
13965:
13955:
13922:
13918:
13892:
13885:
13857:
13850:
13817:
13811:
13798:
13788:
13781:
13771:
13764:
13731:
13727:
13669:
13663:
13622:
13616:
13565:
13559:
13546:
13519:
13510:
13475:
13469:
13458:
13456:
13421:(1): 32β36.
13418:
13412:
13402:
13377:
13373:
13363:
13332:
13326:
13299:
13292:
13260:
13256:Peres, Asher
13250:
13231:
13222:
13179:
13173:
13159:
13116:
13110:
13104:
13096:
13058:
13052:
13043:
13015:
13005:
12977:
12967:
12914:
12908:
12898:
12878:
12837:
12830:
12822:
12794:
12788:
12778:
12759:
12750:
12722:
12708:
12680:
12626:
12620:
12614:
12586:
12522:
12516:
12506:
12478:
12449:. Retrieved
12426:
12419:
12391:
12381:
12340:
12334:
12324:
12291:
12285:
12272:
12244:
12198:
12192:
12182:
12149:
12143:
12130:
12079:
12073:
12063:
12030:
12024:
12017:Ball, Philip
12011:
11958:
11952:
11942:
11913:
11902:
11870:
11829:
11815:
11784:
11766:
11729:
11720:
11711:
11705:
11697:(May 1995).
11695:Xia, Zhihong
11685:
11640:
11634:
11624:
11597:
11594:Zee, Anthony
11552:
11546:
11533:
11482:
11476:
11438:
11432:
11422:
11389:
11383:
11373:
11345:
11341:Leader, Imre
11292:
11282:
11241:
11235:
11225:
11195:(2): L7βL9.
11192:
11186:
11176:
11143:
11137:
11127:
11097:(1): 18β19.
11094:
11088:
11078:
11050:
11032:
10989:
10983:
10976:Chabay, Ruth
10970:
10937:
10931:
10918:
10890:
10842:(1): 59β66.
10839:
10833:
10823:
10795:
10785:
10757:
10689:
10683:
10673:
10661:. Retrieved
10657:
10644:
10614:(1): 24β32.
10611:
10605:
10592:
10549:
10543:
10530:
10520:
10506:
10487:
10481:
10461:
10454:
10424:(1): 41β45.
10421:
10415:
10402:
10390:. Retrieved
10386:
10370:
10361:
10351:
10310:
10304:
10294:
10261:
10255:
10242:
10212:(1): 54β65.
10209:
10203:
10193:
10174:
10165:
10146:
10136:
10127:
10093:
10049:
10011:
10005:
9996:
9968:
9919:
9913:
9899:
9882:
9876:
9867:
9861:
9828:
9822:
9812:
9784:
9732:
9723:
9714:
9704:
9680:(1): 60β73.
9677:
9673:
9667:
9639:
9593:
9587:
9555:
9548:
9513:
9507:
9497:
9464:
9458:
9448:
9420:
9368:
9362:
9349:
9321:
9277:
9245:. Retrieved
9241:
9225:
9197:
9190:
9180:
9173:
9164:
9135:
9128:
9105:protoscience
9091:
9079:
9070:
9061:
9056:
9047:
9038:
9029:
9020:
9011:
9002:
8993:
8984:
8933:
8923:
8915:
8911:
8906:
8896:
8883:
8825:invented by
8812:
8807:living force
8799:
8790:
8784:
8739:
8731:
8723:
8721:
8711:
8703:
8692:
8684:
8674:
8655:
8644:
8638:
8614:
8606:
8596:
8589:
8582:
8580:
8562:
8558:
8552:
8542:
8538:
8533:
8519:
8513:
8502:
8487:
8481:
8478:
8463:
8452:heliocentric
8450:purported a
8447:
8443:
8437:
8431:
8412:John Buridan
8385:
8365:
8337:
8326:
8308:Wren Library
8301:
8250:
8237:
8233:
8223:
8215:
8213:to express.
8192:
8184:
8180:
8176:four-vectors
8088:
8068:
8064:
8052:
8044:
7961:
7890:
7861:
7859:
7830:exerts upon
7740:
7729:
7619:
7600:
7426:
7422:
6546:
6538:
6535:
6129:
6120:Emmy Noether
6098:
5655:
5629:
5613:
5605:
5238:
5234:
5161:
5142:
5131:Chaos theory
5098:
5093:eccentricity
5065:
5038:
4634:
4619:
4395:with masses
4393:
4354:
4290:
4268:
4076:
4069:
4041:
4037:
4035:
3802:
3702:is equal to
3417:
3410:An undamped
3383:
3193:
3139:
2778:
2739:
2721:
2425:force fields
2418:
2413:
2407:
2379:
2336:
2334:
2319:
2315:
2311:
2301:
2295:
2291:
2287:
2284:normal force
2120:If the mass
2027:
2022:
2005:
1998:
1991:
1986:
1981:
1949:
1945:
1941:
1937:
1933:
1929:
1925:
1923:
1794:
1738:
1617:Acceleration
1616:
1157:
900:
894:
890:
888:
862:
856:
853:Isaac Newton
850:
838:acceleration
826:
810:
809:
600: /
596: /
594:displacement
592: /
485:
453: /
415:Displacement
353:
345:
344:
338:Formulations
325:Virtual work
265: /
205:Acceleration
198:Fundamentals
43:
32:Newton's law
15990:Mathematics
15861:by Paolozzi
15800:Roger Cotes
15409:Newton disc
15323:Quaestiones
15296:Arithmetica
14354:Jammer, Max
13444:2158/530056
12942:10852/74677
11908:Byers, Nina
10791:Brown, Mike
10658:Physics 361
10516:"Mechanics"
10102:Bell, J. S.
10014:: 144β159.
9831:: 160β166.
9247:12 February
9231:Tong, David
8914:instead of
8823:quaternions
8666:John Wallis
8635:(1571β1630)
8577:(1629β1695)
8499:(1596β1650)
8475:(1564β1642)
8242:measurement
7732:electricity
7188:chain rules
6553:wave optics
6111:Hamiltonian
5101:closed form
5079:, that is,
736:von Neumann
403:Core topics
16060:Categories
15948:Categories
15924:XMM-Newton
15841:Depictions
15812:John Keill
15734:Apple tree
15729:Later life
15724:Early life
15304:De Analysi
15201:17 January
15034:Gbur, Greg
14755:"Newton's
14280:1144105192
14119:1058581988
13126:1908.07936
13068:1802.10119
13035:1020305599
12997:1164503847
12857:1202475208
12532:1805.01372
12089:1910.09414
11986:1808/29610
11934:1150964892
11758:1195899886
11739:1609.01421
11714:: 538β546.
11650:2006.14924
11616:1288147292
10663:16 January
10392:13 January
10129:mechanics.
9741:1120819093
9687:2112.02339
9416:Gbur, Greg
9217:1084752471
9120:References
8889:David Tong
8724:Principia,
8691:After the
8685:Principia,
8607:immaterial
8426:See also:
8356:Aristotle
8260:, and the
7429:derivative
5652:Lagrangian
5241:derivative
5155:, and the
5089:hyperbolas
3188:barycenter
2402:atmosphere
2337:definition
2017:Second law
1248:derivative
903:kinematics
813:are three
671:d'Alembert
651:Maupertuis
614:Scientists
496:Rigid body
170:Kinematics
16026:Astronomy
15763:Relations
15272:Principia
15162:799299609
15126:0002-9505
15020:122097990
15012:0031-9120
14905:Principia
14845:(2005) .
14829:125948408
14821:0143-0807
14732:0039-7857
14691:892067655
14649:246612625
14641:0007-0874
14600:972369868
14559:145120248
14543:0007-0874
14502:0031-9228
14453:0002-9505
14356:(1999) .
14340:144575106
14324:0021-1753
14245:243203703
14237:0021-1753
14193:953450997
14083:934741893
14048:170120455
14040:0036-8075
13996:0002-9505
13947:144406041
13877:182818133
13834:0277-903X
13756:144278075
13704:243143427
13696:2469-9896
13647:233803836
13639:0031-921X
13600:149482566
13592:2469-9896
13538:495305340
13502:878730683
13453:0002-9505
13386:0392-095X
13355:874097920
13318:759812415
13214:126311599
13206:0143-0807
13151:182656563
13143:1233-1821
13093:119546199
12959:127471222
12951:0031-9120
12819:0034-6861
12700:317496332
12659:122180759
12651:1751-8113
12557:0002-9505
12476:(2005) .
12373:126380404
12365:0143-0807
12316:0002-9505
12264:966177746
12223:0002-9505
12174:0002-9505
12122:204800598
12114:0002-9505
12055:204188746
12003:203484310
11995:2469-9896
11894:860391091
11827:(1990) .
11807:466500872
11677:220127889
11669:0002-9939
11577:0002-9505
11517:0143-0807
11492:1012.4384
11455:0002-9505
11414:0002-9505
11365:682200048
11274:119949261
11266:0143-0807
11217:121740340
11209:0143-0807
11168:0002-9505
11119:0031-921X
11070:794034942
11024:197512796
11016:0002-9505
10962:0002-9505
10872:250883796
10864:0143-0807
10815:495271396
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3663:
3648:ω
3645:
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1595:Δ
1578:−
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1079:−
1045:−
1011:Δ
1003:Δ
716:Liouville
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518:Vibration
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15886:Namesake
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14963:46923474
14955:29857796
14933:: 1β11.
14867:57579169
14740:11794836
14711:Synthese
14669:(1969).
14551:25592244
14376:40964671
14296:(1962).
14099:(1975).
13806:(1955).
13494:44216227
13394:43915795
13284:28854083
13258:(1993).
13119:: 7β26.
13013:(2018).
12975:(2021).
12758:(1968).
12742:44694623
12720:(2000).
12678:(2009).
12606:47056311
12565:53625857
12498:56526974
12451:24 March
12389:(1966).
12242:(2016).
11868:(2007).
11849:20934820
11782:(eds.).
11596:(2020).
11525:58892714
11343:(eds.).
11290:(1997).
10910:37903527
10793:(2010).
10777:61332593
10755:(2006).
10652:(2020).
10514:(1889).
10378:(2003).
10092:(1969).
9891:66-11527
9731:(1968).
9637:(2007).
9561:OpenStax
9418:(2011).
9319:(1998).
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8706:(1831),
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15061:7 March
15047:7 March
14992:Bibcode
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12033:: 100.
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15160:
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13316:
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13238:
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10494:
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