2937:. According to Galileo's concept of gravitation, a dropped stone falls with constant acceleration down towards the Earth. However, Newton explains that when a stone is thrown horizontally (meaning sideways or perpendicular to Earth's gravity) it follows a curved path. "For a stone projected is by the pressure of its own weight forced out of the rectilinear path, which by the projection alone it should have pursued, and made to describe a curve line in the air; and through that crooked way is at last brought down to the ground. And the greater the velocity is with which it is projected, the farther it goes before it falls to the Earth." Newton further reasons that if an object were "projected in an horizontal direction from the top of a high mountain" with sufficient velocity, "it would reach at last quite beyond the circumference of the Earth, and return to the mountain from which it was projected."
807:
3243:
remains in use in basic education, if the priority is to teach the difference between mass from weight.) This traditional "amount of matter" belief was contradicted by the fact that different atoms (and, later, different elementary particles) can have different masses, and was further contradicted by
Einstein's theory of relativity (1905), which showed that the measurable mass of an object increases when energy is added to it (for example, by increasing its temperature or forcing it near an object that electrically repels it.) This motivates a search for a different definition of mass that is more accurate than the traditional definition of "the amount of matter in an object".
1590:. This force keeps the object from going into free fall. Weight is the opposing force in such circumstances and is thus determined by the acceleration of free fall. On the surface of the Earth, for example, an object with a mass of 50 kilograms weighs 491 newtons, which means that 491 newtons is being applied to keep the object from going into free fall. By contrast, on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 newtons, because only 81.5 newtons is required to keep this object from going into a free fall on the moon. Restated in mathematical terms, on the surface of the Earth, the weight
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and "gravitational mass", although these quantities are identical; the conceptual distinction between these two fundamental definitions of mass is maintained for teaching purposes because they involve two distinct methods of measurement. It was long considered anomalous that the two distinct measurements of mass (inertial and gravitational) gave an identical result. The property, observed by
Galileo, that objects of different mass fall with the same rate of acceleration (ignoring air resistance), shows that inertial and gravitational mass are the same.
2961:: every object has gravitational mass, and therefore, every object generates a gravitational field. Newton further assumed that the strength of each object's gravitational field would decrease according to the square of the distance to that object. If a large collection of small objects were formed into a giant spherical body such as the Earth or Sun, Newton calculated the collection would create a gravitational field proportional to the total mass of the body, and inversely proportional to the square of the distance to the body's center.
42:
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1927:. Einstein's equivalence principle states that within sufficiently small regions of spacetime, it is impossible to distinguish between a uniform acceleration and a uniform gravitational field. Thus, the theory postulates that the force acting on a massive object caused by a gravitational field is a result of the object's tendency to move in a straight line (in other words its inertia) and should therefore be a function of its inertial mass and the strength of the gravitational field.
1900:, in which there is no air resistance, the hammer and the feather should hit the ground at exactly the same time (assuming the acceleration of both objects towards each other, and of the ground towards both objects, for its own part, is negligible). This can easily be done in a high school laboratory by dropping the objects in transparent tubes that have the air removed with a vacuum pump. It is even more dramatic when done in an environment that naturally has a vacuum, as
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820:
2377:, who had some of the most precise astronomical data available. Using Brahe's precise observations of the planet Mars, Kepler spent the next five years developing his own method for characterizing planetary motion. In 1609, Johannes Kepler published his three laws of planetary motion, explaining how the planets orbit the Sun. In Kepler's final planetary model, he described planetary orbits as following elliptical paths with the Sun at a focal point of the
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Galileo's reliance on scientific experimentation to establish physical principles would have a profound effect on future generations of scientists. It is unclear if these were just hypothetical experiments used to illustrate a concept, or if they were real experiments performed by
Galileo, but the results obtained from these experiments were both realistic and compelling. A biography by Galileo's pupil
3247:
3960:, which is that the measurement of instantaneous acceleration is impossible: unlike the measurement of time or distance, there is no way to measure acceleration with a single measurement; one must make multiple measurements (of position, time, etc.) and perform a computation to obtain the acceleration. Poincaré termed this to be an "insurmountable flaw" in the Mach definition of mass.
5712:, and can safely be ignored for many purposes. In most practical applications, Newtonian gravity is assumed because it is usually sufficiently accurate, and is simpler than General Relativity; for example, NASA uses primarily Newtonian gravity to design space missions, although "accuracies are routinely enhanced by accounting for tiny relativistic effects".
2775:, to work through the mathematical details of Keplerian orbits to determine if Hooke's hypothesis was correct. Newton's own investigations verified that Hooke was correct, but due to personal differences between the two men, Newton chose not to reveal this to Hooke. Isaac Newton kept quiet about his discoveries until 1684, at which time he told a friend,
1430:. Passive gravitational mass is determined by dividing an object's weight by its free-fall acceleration. Two objects within the same gravitational field will experience the same acceleration; however, the object with a smaller passive gravitational mass will experience a smaller force (less weight) than the object with a larger passive gravitational mass.
2217:, which balances the force of one object's weight against the force of another object's weight. The two sides of a balance scale are close enough that the objects experience similar gravitational fields. Hence, if they have similar masses then their weights will also be similar. This allows the scale, by comparing weights, to also compare masses.
2779:, that he had solved the problem of gravitational orbits, but had misplaced the solution in his office. After being encouraged by Halley, Newton decided to develop his ideas about gravity and publish all of his findings. In November 1684, Isaac Newton sent a document to Edmund Halley, now lost but presumed to have been titled
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enormous gravitating sphere. However, from a practical standpoint, the gravitational fields of small objects are extremely weak and difficult to measure. Newton's books on universal gravitation were published in the 1680s, but the first successful measurement of the Earth's mass in terms of traditional mass units, the
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water thus collected was weighed, after each descent, on a very accurate balance; the differences and ratios of these weights gave us the differences and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results.
5022:
1550:" are often used interchangeably. For instance, a person's weight may be stated as 75 kg. In a constant gravitational field, the weight of an object is proportional to its mass, and it is unproblematic to use the same unit for both concepts. But because of slight differences in the strength of the
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speeds. Instead, the imaginary mass creates an instability in the configuration:- any configuration in which one or more field excitations are tachyonic will spontaneously decay, and the resulting configuration contains no physical tachyons. This process is known as tachyon condensation. Well known
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to demonstrate that their time of descent was independent of their mass. In support of this conclusion, Galileo had advanced the following theoretical argument: He asked if two bodies of different masses and different rates of fall are tied by a string, does the combined system fall faster because it
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The distinction between "active" and "passive" is very abstract, and applies to post-graduate level applications of
General Relativity to certain problems in cosmology, and is otherwise not used. There is, nevertheless, an important conceptual distinction in Newtonian physics between "inertial mass"
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must often be subtracted from the mass of the unbound system, because binding energy commonly leaves the system at the time it is bound. The mass of the system changes in this process merely because the system was not closed during the binding process, so the energy escaped. For example, the binding
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For example, according to Newton's theory of universal gravitation, each carob seed produces a gravitational field. Therefore, if one were to gather an immense number of carob seeds and form them into an enormous sphere, then the gravitational field of the sphere would be proportional to the number
1165:
of ice. However, because precise measurement of a cubic decimetre of water at the specified temperature and pressure was difficult, in 1889 the kilogram was redefined as the mass of a metal object, and thus became independent of the metre and the properties of water, this being a copper prototype of
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For example, a nuclear bomb in an idealized super-strong box, sitting on a scale, would in theory show no change in mass when detonated (although the inside of the box would become much hotter). In such a system, the mass of the box would change only if energy were allowed to escape from the box as
5885:
It is possible to make a slight distinction between "rest mass" and "invariant mass". For a system of two or more particles, none of the particles are required be at rest with respect to the observer for the system as a whole to be at rest with respect to the observer. To avoid this confusion, some
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have an attraction or gravitating power towards their own centers, and also attract all the other celestial bodies that are within the sphere of their activity. He further stated that gravitational attraction increases by how much nearer the body wrought upon is to its own center. In correspondence
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demonstrated his first telescope to a group of
Venetian merchants, and in early January 1610, Galileo observed four dim objects near Jupiter, which he mistook for stars. However, after a few days of observation, Galileo realized that these "stars" were in fact orbiting Jupiter. These four objects
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is applied. It is determined by applying a force to an object and measuring the acceleration that results from that force. An object with small inertial mass will accelerate more than an object with large inertial mass when acted upon by the same force. One says the body of greater mass has greater
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By finding the exact relationship between a body's gravitational mass and its gravitational field, Newton provided a second method for measuring gravitational mass. The mass of the Earth can be determined using Kepler's method (from the orbit of Earth's Moon), or it can be determined by measuring
2027:
What we now know as mass was until the time of Newton called âweight.â ... A goldsmith believed that an ounce of gold was a quantity of gold. ... But the ancients believed that a beam balance also measured âheavinessâ which they recognized through their muscular senses. ... Mass and its associated
4369:
with respect to mass and energy, both kinds of mass are conserved in any given frame of reference. The conservation of mass holds even as some types of particles are converted to others. Matter particles (such as atoms) may be converted to non-matter particles (such as photons of light), but this
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Measuring gravitational mass in terms of traditional mass units is simple in principle, but extremely difficult in practice. According to Newton's theory, all objects produce gravitational fields and it is theoretically possible to collect an immense number of small objects and form them into an
2535:
Galileo had shown that objects in free fall under the influence of the Earth's gravitational field have a constant acceleration, and
Galileo's contemporary, Johannes Kepler, had shown that the planets follow elliptical paths under the influence of the Sun's gravitational mass. However, Galileo's
958:
comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.
3242:
argued in 1851 that every object contains a number of "points" (basically, interchangeable elementary particles), and that mass is proportional to the number of points the object contains. (In practice, this "amount of matter" definition is adequate for most of classical mechanics, and sometimes
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a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water, which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for a part of its length; the
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Sometime prior to 1638, Galileo turned his attention to the phenomenon of objects in free fall, attempting to characterize these motions. Galileo was not the first to investigate Earth's gravitational field, nor was he the first to accurately describe its fundamental characteristics. However,
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drives a physical system that has reached a local limit and might naively be expected to produce physical tachyons, to an alternate stable state where no physical tachyons exist. Once the tachyonic field reaches the minimum of the potential, its quanta are not tachyons any more but rather are
7179:, p.286: "People initially thought of tachyons as particles travelling faster than the speed of light...But we now know that a tachyon indicates an instability in a theory that contains it. Regrettably for science fiction fans, tachyons are not real physical particles that appear in nature."
3974:
Typically, the mass of objects is measured in terms of the kilogram, which since 2019 is defined in terms of fundamental constants of nature. The mass of an atom or other particle can be compared more precisely and more conveniently to that of another atom, and thus scientists developed the
3357:
of a body. Consider two objects with different masses. If we apply an identical force to each, the object with a bigger mass will experience a smaller acceleration, and the object with a smaller mass will experience a bigger acceleration. We might say that the larger mass exerts a greater
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does not affect the total amount of mass or energy. Although things like heat may not be matter, all types of energy still continue to exhibit mass. Thus, mass and energy do not change into one another in relativity; rather, both are names for the same thing, and neither mass nor energy
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in modern physics and are discussed in popular books on physics. Under no circumstances do any excitations ever propagate faster than light in such theoriesâthe presence or absence of a tachyonic mass has no effect whatsoever on the maximum velocity of signals (there is no violation of
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is a state which is only approximately constant over time; If it exists long enough to be measured, it can be formally described as having a complex mass, with the real part of the mass greater than its imaginary part. If both parts are of the same magnitude, this is interpreted as a
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2421:
in honor of their discoverer) were the first celestial bodies observed to orbit something other than the Earth or Sun. Galileo continued to observe these moons over the next eighteen months, and by the middle of 1611, he had obtained remarkably accurate estimates for their periods.
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the gravitational acceleration on the Earth's surface, and multiplying that by the square of the Earth's radius. The mass of the Earth is approximately three-millionths of the mass of the Sun. To date, no other accurate method for measuring gravitational mass has been discovered.
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1870:
1625:
For other situations, such as when objects are subjected to mechanical accelerations from forces other than the resistance of a planetary surface, the weight force is proportional to the mass of an object multiplied by the total acceleration away from free fall, which is called the
3539:
2240:
then the object was said to weigh one Roman ounce (uncia). The Roman pound and ounce were both defined in terms of different sized collections of the same common mass standard, the carob seed. The ratio of a Roman ounce (144 carob seeds) to a Roman pound (1728 carob seeds) was:
5395:
appearing in a scattering process rather than a particle, as it is considered not to exist long enough to be measured independently of the scattering process. In the case of a tachyon, the real part of the mass is zero, and hence no concept of a particle can be attributed to it.
1670:, Newton's third law implies that active and passive gravitational mass must always be identical (or at least proportional), but the classical theory offers no compelling reason why the gravitational mass has to equal the inertial mass. That it does is merely an empirical fact.
1630:. Through such mechanisms, objects in elevators, vehicles, centrifuges, and the like, may experience weight forces many times those caused by resistance to the effects of gravity on objects, resulting from planetary surfaces. In such cases, the generalized equation for weight
2480:
to slow the acceleration enough so that the elapsed time could be measured. The ball was allowed to roll a known distance down the ramp, and the time taken for the ball to move the known distance was measured. The time was measured using a water clock described as follows:
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Vertical section drawing of
Cavendish's torsion balance instrument including the building in which it was housed. The large balls were hung from a frame so they could be rotated into position next to the small balls by a pulley from outside. Figure 1 of Cavendish's
2556:
The quantity of matter is the measure of the same, arising from its density and bulk conjunctly. ... It is this quantity that I mean hereafter everywhere under the name of body or mass. And the same is known by the weight of each body; for it is proportional to the
986:
There are several distinct phenomena that can be used to measure mass. Although some theorists have speculated that some of these phenomena could be independent of each other, current experiments have found no difference in results regardless of how it is measured:
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light or heat. However, in that case, the removed energy would take its associated mass with it. Letting heat or radiation out of such a system is simply a way to remove mass. Thus, mass, like energy, cannot be destroyed, but only moved from one place to another.
5817:
1868:
2467:
published in 1638. One of
Galileo's fictional characters, Salviati, describes an experiment using a bronze ball and a wooden ramp. The wooden ramp was "12 cubits long, half a cubit wide and three finger-breadths thick" with a straight, smooth, polished
1581:
in all situations where the mass is accelerated away from free fall. For example, when a body is at rest in a gravitational field (rather than in free fall), it must be accelerated by a force from a scale or the surface of a planetary body such as the
3572:, respectively. Suppose that these accelerations are non-zero, so that the forces between the two objects are non-zero. This occurs, for example, if the two objects are in the process of colliding with one another. Newton's third law then states that
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1422:
is subject to a smaller gravitational field, and hence accelerates more slowly, than the same object would if it were in free-fall near the Earth. The gravitational field near the Moon is weaker because the Moon has less active gravitational
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found that the Earth's density was 5.448 ± 0.033 times that of water. As of 2009, the Earth's mass in kilograms is only known to around five digits of accuracy, whereas its gravitational mass is known to over nine significant figures.
1022:
The mass of an object determines its acceleration in the presence of an applied force. The inertia and the inertial mass describe this property of physical bodies at the qualitative and quantitative level respectively. According to
2799:). The first was received by the Royal Society on 28 April 1685â86; the second on 2 March 1686â87; and the third on 6 April 1686â87. The Royal Society published Newton's entire collection at their own expense in May 1686â87.
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of carob seeds in the sphere. Hence, it should be theoretically possible to determine the exact number of carob seeds that would be required to produce a gravitational field similar to that of the Earth or Sun. In fact, by
4575:
The "relativistic" mass and energy concepts are related to their "rest" counterparts, but they do not have the same value as their rest counterparts in systems where there is a net momentum. Because the relativistic mass is
1892:, must be absent or at least negligible. For example, if a hammer and a feather are dropped from the same height through the air on Earth, the feather will take much longer to reach the ground; the feather is not really in
3727:
1113:". This is sometimes referred to as gravitational mass. Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are identical; since 1915, this observation has been incorporated
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At the time when
Viviani asserts that the experiment took place, Galileo had not yet formulated the final version of his law of free fall. He had, however, formulated an earlier version that predicted that bodies
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1860:
pendulum, in 1889. As of 2008, no deviation from universality, and thus from
Galilean equivalence, has ever been found, at least to the precision 10. More precise experimental efforts are still being carried out.
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also holds in macroscopic systems. For example, if one takes exactly one kilogram of ice, and applies heat, the mass of the resulting melt-water will be more than a kilogram: it will include the mass from the
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4472:
5590:
This equation shows that the total energy of a particle (bradyon or tachyon) contains a contribution from its rest mass (the "rest massâenergy") and a contribution from its motion, the kinetic energy. When
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from 1679 and 1680, Hooke conjectured that gravitational forces might decrease according to the double of the distance between the two bodies. Hooke urged Newton, who was a pioneer in the development of
2530:
1953:. To date, a number of different models have been proposed which advocate different views of the origin of mass. The problem is complicated by the fact that the notion of mass is strongly related to the
5106:
2949:
An apple experiences gravitational fields directed towards every part of the Earth; however, the sum total of these many fields produces a single gravitational field directed towards the Earth's center.
4207:
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becomes important for measurements with a precision better than a few percent, and for places far from the surface of the Earth, such as in space or on other planets. Conceptually, "mass" (measured in
161:
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However, this notion of applying "identical" forces to different objects brings us back to the fact that we have not really defined what a force is. We can sidestep this difficulty with the help of
2802:
Isaac Newton had bridged the gap between Kepler's gravitational mass and Galileo's gravitational acceleration, resulting in the discovery of the following relationship which governed both of these:
1652:
is the proper acceleration of the object caused by all influences other than gravity. (Again, if gravity is the only influence, such as occurs when an object falls freely, its weight will be zero).
5188:
2208:
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1867:
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4217:. In order to formulate the equations of physics such that mass values do not change between observers, it is convenient to use rest mass. The rest mass of a body is also related to its energy
6371:
1666:
Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them. In
1484:
on the surface of the Earth, for example, are found to measure less time (run slower) when compared to similar clocks in space. This difference in elapsed time is a form of curvature called
2460:
is now more massive, or does the lighter body in its slower fall hold back the heavier body? The only convincing resolution to this question is that all bodies must fall at the same rate.
5486:
3365:, which states that if one object exerts a force on a second object, it will experience an equal and opposite force. To be precise, suppose we have two objects of constant inertial masses
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is taken to be the mass of the neutron in free space, and the relative accelerations for the proton and neutron in deuterium are computed, then the above formula over-estimates the mass
3329:
5750:
3811:
1480:
is extremely weak and difficult to measure. For this reason, curvature was not discovered until after it was predicted by Einstein's theory of general relativity. Extremely precise
5350:, thus preserving causality. Therefore, information still does not propagate faster than light, and solutions grow exponentially, but not superluminally (there is no violation of
3250:
Massmeter, a device for measuring the inertial mass of an astronaut in weightlessness. The mass is calculated via the oscillation period for a spring with the astronaut attached (
1820:
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185:
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7519:
1896:-fall because the force of air resistance upwards against the feather is comparable to the downward force of gravity. On the other hand, if the experiment is performed in a
4236:
8625:
7213:... so existence of particles v > c ... Called tachyons ... would present relativity with serious ... problems of infinite creation energies and causality paradoxes.
5740:
This constant ratio was later shown to be a direct measure of the Sun's active gravitational mass; it has units of distance cubed per time squared, and is known as the
3910:, to the mass of the proton in free space (which is greater by about 0.239%âthis is due to the binding energy of deuterium). Thus, for example, if the reference weight
5267:
may have imaginary mass, any physical particles do not; the "imaginary mass" shows that the system becomes unstable, and sheds the instability by undergoing a type of
5017:{\displaystyle i\hbar {\frac {\partial }{\partial t}}\Psi (\mathbf {r} ,\,t)=\left(-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}+V(\mathbf {r} )\right)\Psi (\mathbf {r} ,\,t).}
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3759:
as (say) 1 kilogram. Then we can measure the mass of any other object in the universe by colliding it with the reference object and measuring the accelerations.
1774:
1736:
3188:
3902:) needed to bring two masses sufficiently close to one another to perform the measurement of mass. This is most vividly demonstrated by comparing the mass of the
3251:
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1833:
all objects fall at the same rate in a given gravitational field. This phenomenon is referred to as the "universality of free-fall". In addition, the constant
8715:
2911:
A cannon on top of a very high mountain shoots a cannonball horizontally. If the speed is low, the cannonball quickly falls back to Earth (A, B). At
1414:
of gravitational field over an enclosing surface). Gravitational field can be measured by allowing a small "test object" to fall freely and measuring its
3238:
Mass was traditionally believed to be a measure of the quantity of matter in a physical body, equal to the "amount of matter" in an object. For example,
2808:
2476:, also smooth and polished as possible". And into this groove was placed "a hard, smooth and very round bronze ball". The ramp was inclined at various
6789:
6259:"The pre-Newtonian meaning of the word "weight"; a comment on "Kepler and the origins of pre-Newtonian mass" [Am. J. Phys. 85, 115â123 (2017)]"
6689:
2548:)), but called it 'weight' as did everyone at that time." Finally, in 1686, Newton gave this distinct concept its own name. In the first paragraph of
5918:
3636:
7077:
6391:
1386:, and in some cases equal, and this proportionality gives rise to the abstract concept of mass. There are a number of ways mass can be measured or
5029:
2957:) which stated that the heavens were made of entirely different material, Newton's theory of mass was groundbreaking partly because it introduced
6342:
5977:
2490:
Galileo found that for an object in free fall, the distance that the object has fallen is always proportional to the square of the elapsed time:
3131:{\displaystyle \mathbf {F} _{\text{AB}}=-GM_{\text{A}}M_{\text{B}}{\frac {{\hat {\mathbf {R} }}_{\text{AB}}}{|\mathbf {R} _{\text{AB}}|^{2}}}\ }
3239:
2791:
4845:{\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\ \left(\,{\frac {\partial L}{\partial {\dot {x}}_{i}}}\,\right)\ =\ m\,{\ddot {x}}_{i}.}
851:
4034:
2721:{\displaystyle 1.2\pi ^{2}\cdot 10^{-5}{\frac {{\text{AU}}^{3}}{{\text{y}}^{2}}}=3.986\cdot 10^{14}{\frac {{\text{m}}^{3}}{{\text{s}}^{2}}}}
7657:
5513:
4480:
3534:{\displaystyle {\begin{aligned}\mathbf {F_{12}} &=m_{1}\mathbf {a} _{1},\\\mathbf {F_{21}} &=m_{2}\mathbf {a} _{2},\end{aligned}}}
5867:
These two properties are very useful, as they allow spherical collections of objects to be treated exactly like large individual objects.
4703:
440:
2969:
it is a simple matter of abstraction to realize that any traditional mass unit can theoretically be used to measure gravitational mass.
8010:
2933:
used to bridge the gap between Galileo's gravitational acceleration and Kepler's elliptical orbits. It appeared in Newton's 1728 book
559:
6579:
4398:
4213:
The invariant mass of systems is the same for observers in all inertial frames, while the relativistic mass depends on the observer's
1852:
to slow the motion and increase the timing accuracy. Increasingly precise experiments have been performed, such as those performed by
5330:
mass might seem troubling because there is no classical interpretation of an imaginary mass, the mass is not quantized. Rather, the
7225:
Kutasov, David; Marino, Marcos & Moore, Gregory W. (2000). "Some exact results on tachyon condensation in string field theory".
1570:, which can be influenced by the nearby gravitational field. No matter how strong the gravitational field, objects in free fall are
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532:
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of London, with a promise that a fuller presentation would follow. Newton later recorded his ideas in a three-book set, entitled
2496:
1848:. This is most likely apocryphal: he is more likely to have performed his experiments with balls rolling down nearly frictionless
5641:
5047:
4673:
idea that the gravitational force as experienced locally while standing on a massive body (such as the Earth) is the same as the
3154:
is the magnitude at a given location in a gravitational field, then the gravitational force on an object with gravitational mass
1175:
4149:
3350:
of the body's centre of mass. For the moment, we will put aside the question of what "force acting on the body" actually means.
117:
5708:
The distinction between "active" and "passive" gravitational mass does not exist in the Newtonian view of gravity as found in
1884:
The universality of free-fall only applies to systems in which gravity is the only acting force. All other forces, especially
8003:
7206:
7155:
6873:
6637:
Coelho, Ricardo Lopes (January 2010). "On the Concept of Force: How Understanding its History can Improve Physics Teaching".
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4226:
2348:{\displaystyle {\frac {\mathrm {ounce} }{\mathrm {pound} }}={\frac {W_{144}}{W_{1728}}}={\frac {144}{1728}}={\frac {1}{12}}.}
975:
5150:
2156:
1161:(kg). The kilogram is 1000 grams (g), and was first defined in 1795 as the mass of one cubic decimetre of water at the
5939:
Mass can be understood as a measurement of inertia, the resistance of an object to be set in motion or stopped from motion.
5646:
4018:(which increases with velocity). Rest mass is the Newtonian mass as measured by an observer moving along with the object.
3924:(by 0.239%) for the proton in deuterium. At best, Mach's formula can only be used to obtain ratios of masses, that is, as
3579:
2364:
2102:
2023:. The concept of "weight" would incorporate "amount" and acquire a double meaning that was not clearly recognized as such.
3832:
3379:. We isolate the two objects from all other physical influences, so that the only forces present are the force exerted on
1691:" has the most important consequence for freely falling objects. Suppose an object has inertial and gravitational masses
514:
6190:
Voisin, G.; Cognard, I.; Freire, P. C. C.; Wex, N.; Guillemot, L.; Desvignes, G.; Kramer, M.; Theureau, G. (June 2020).
7947:
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1840:
The first experiments demonstrating the universality of free-fall wereâaccording to scientific 'folklore'âconducted by
895:, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple
868:
77:
4580:, it has gradually fallen into disuse among physicists. There is disagreement over whether the concept remains useful
6562:
2220:
Consequently, historical weight standards were often defined in terms of amounts. The Romans, for example, used the
844:
7586:
2092:
is the number of objects in the collection. Proportionality, by definition, implies that two values have a constant
1680:
starting with the assumption that the inertial and passive gravitational masses are the same. This is known as the
8751:
8726:
8687:
7650:
5812:{\displaystyle \mu =4\pi ^{2}{\frac {{\text{distance}}^{3}}{{\text{time}}^{2}}}\propto {\text{gravitational mass}}}
5741:
5417:
2888:
2236:, then the object was said to weigh one Roman pound. If, on the other hand, the object's weight was equivalent to
1024:
806:
6191:
5699:
These are used mainly in the United States except in scientific contexts where SI units are usually used instead.
5383:
3298:
1511:. In relativistic quantum mechanics, mass is one of the irreducible representation labels of the Poincaré group.
180:
5362:
This is a special case of the general rule, where unstable massive particles are formally described as having a
3783:
2883:
is the apparent acceleration of a body as it passes through a region of space where gravitational fields exist,
5347:
435:
175:
4010:, physicists have used different definitions of the term. In these frameworks, two kinds of mass are defined:
3018:, Newton's law of gravitation states that each object exerts a gravitational force on the other, of magnitude
19:
This article is about the scientific concept. For the main liturgical service in some Christian churches, see
9037:
8029:
6820:
2390:
2039:
1383:
1154:
47:
7610:
3261:
is the mass of an object measured by its resistance to acceleration. This definition has been championed by
9022:
7983:
7942:
5408:
5135:
as developed in the 1960s, this term arises from the coupling of the field Ï to an additional field Ί, the
1677:
837:
824:
585:
508:
430:
273:
5926:
5378:, a particle (a "one-particle state") is roughly defined as a state which is constant over time; i.e., an
9027:
7643:
7014:
6757:
Ori Belkind, "Physical Systems: Conceptual Pathways between Flat Space-time and Matter" (2012) Springer (
6116:
5626:
must be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number.
4719:
4680:
4607:
4577:
4378:
1997:
1485:
1450:
1232:
504:
305:
1786:
1465:. Pair production and nuclear fusion are processes in which measurable amounts of mass are converted to
283:
6613:
4686:
However, it turns out that it is impossible to find an objective general definition for the concept of
4648:
4001:
1688:
1539:
1136:
995:
896:
724:
613:
539:
399:
332:
4377:
Both rest and relativistic mass can be expressed as an energy by applying the well-known relationship
4354:{\displaystyle (m_{\mathrm {rest} })c^{2}={\sqrt {E_{\mathrm {total} }^{2}-(|\mathbf {p} |c)^{2}}}.\!}
9032:
8658:
8463:
8317:
7840:
2781:
2552:, Newton defined quantity of matter as âdensity and bulk conjunctlyâ, and mass as quantity of matter.
2048:
1984:
1954:
1946:
1936:
1407:
1115:
478:
899:
which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a
8430:
7407:
Aharonov, Y.; Komar, A.; Susskind, L. (1969). "Superluminal Behavior, Causality, and Instability".
6063:
5320:
4699:
4695:
1826:
This says that the ratio of gravitational to inertial mass of any object is equal to some constant
754:
598:
6494:
5681:
When a distinction is necessary, the active and passive gravitational masses may be distinguished.
3741:| is non-zero, the fraction is well-defined, which allows us to measure the inertial mass of
8441:
7952:
6554:
5651:
2588:
1182:
1171:
994:
measures an object's resistance to being accelerated by a force (represented by the relationship
704:
468:
8601:
8501:
7598:
6865:
6859:
6004:
5403:
theory, the same formulas that apply to ordinary slower-than-light particles (sometimes called "
5045:
4702:
in a way that is invariant for all observers. For a given observer, this can be achieved by the
4396:
4234:
3894:
The primary difficulty with Mach's definition of mass is that it fails to take into account the
744:
7976:
6845:
5366:
mass, with the real part being their mass in the usual sense, and the imaginary part being the
4620:
3577:
3285:
3226:
to be read off. Assuming the gravitational field is equivalent on both sides of the balance, a
3147:
2924:
1661:
1110:
749:
566:
7198:
6192:"An improved test of the strong equivalence principle with the pulsar in a triple star system"
5748:
4877:
4731:
4147:
2536:
free fall motions and Kepler's planetary motions remained distinct during Galileo's lifetime.
955:
8576:
8446:
8184:
7957:
6442:
6089:
5886:
sources will use "rest mass" only for individual particles, and "invariant mass" for systems.
4658:
4478:
4121:
3830:
3781:
3362:
3009:
2785:(Latin for "On the motion of bodies in an orbit"). Halley presented Newton's findings to the
2608:
2456:
2442:
Distance traveled by a freely falling ball is proportional to the square of the elapsed time.
1845:
1784:
1687:
The particular equivalence often referred to as the "Galilean equivalence principle" or the "
1681:
1181:
However, the mass of the IPK and its national copies have been found to drift over time. The
1120:
900:
759:
734:
420:
238:
24:
7190:
7139:
6650:
6459:
6217:
1853:
8898:
8823:
8451:
8223:
7700:
7554:
7457:
7416:
7388:
7350:
7297:
7244:
7112:
7058:
7023:
6979:
6928:
6720:
6646:
6587:
6315:
6270:
6213:
6164:
6029:
5375:
5355:
5335:
5272:
2983:
2469:
2038:
Humans, at some early era, realized that the weight of a collection of similar objects was
2020:
1957:
but a theory of the latter has not been yet reconciled with the currently popular model of
1949:
is a theory which attempts to explain the origin of mass from the most fundamental laws of
1747:
1741:
Given this force, the acceleration of the object can be determined by Newton's second law:
1709:
1434:
1347:
779:
739:
647:
643:
635:
625:
415:
408:
164:
7147:
7050:
6417:
6407:
5844:
5838:
5367:
5298:
in a 1967 paper, but it was soon realized that Feinberg's model in fact did not allow for
3164:
1426:
Passive gravitational mass is a measure of the strength of an object's interaction with a
774:
8:
8629:
8358:
8306:
8026:
7867:
5709:
4715:
3274:
1942:
1667:
1627:
1427:
1220:
1048:
967:
892:
554:
495:
473:
218:
213:
208:
108:
7558:
7461:
7420:
7354:
7309:
7301:
7256:
7248:
7116:
7062:
7027:
6995:
6983:
6944:
6932:
6724:
6548:
6319:
6274:
6168:
6033:
1699:, respectively. If the only force acting on the object comes from a gravitational field
1313:, primarily used in astronomy to compare large masses such as stars or galaxies (â
7892:
7570:
7544:
7366:
7340:
7313:
7287:
7260:
7234:
6961:
Rindler, W.; Vandyck, M.A.; Murugesan, P.; Ruschin, S.; Sauter, C.; Okun, L.B. (1990).
6890:
6848:". Chapter 6 in Science and Hypothesis. London: Walter Scott Publishing (1905): 89-110.
6812:
6662:
6377:
6288:
6229:
6203:
6155:
6045:
6019:
5636:
4662:
4654:
4214:
4007:
3278:
3266:
2930:
1993:
1924:
1619:
1555:
1526:
1521:
1504:
1387:
1325:
1276:(lb), a unit of mass (about 0.45 kg), which is used alongside the similarly named
1124:
943:
684:
425:
300:
268:
228:
88:
7566:
7362:
7097:
6327:
1047:. A body's mass also determines the degree to which it generates and is affected by a
8648:
8566:
8402:
8161:
7625:
7370:
7202:
7191:
7151:
6869:
6816:
6666:
6558:
6520:
6421:
6381:
6292:
6233:
6095:
6049:
5848:
5400:
5276:
5247:
5195:
4015:
3270:
2954:
2596:
2394:
1202:
1018:
measures the gravitational force exerted on an object in a known gravitational field.
876:
694:
651:
608:
603:
544:
320:
310:
203:
7574:
7317:
7264:
6778:, Open Court, La Salle, Ill., Cambridge University Press, 1982, Vol. 2, pp. 335â354.
5876:
In its original form, Newton's second law is valid only for bodies of constant mass.
3957:
1453:. This equivalence is exemplified in a large number of physical processes including
8735:
8705:
8671:
8390:
8346:
8301:
7805:
7562:
7465:
7424:
7358:
7305:
7252:
7120:
7066:
7031:
6987:
6936:
6804:
6728:
6654:
6363:
6323:
6278:
6221:
6172:
6037:
5600:
5327:
5312:
5284:
5268:
5235:
5132:
4691:
4675:
4623:. This number is small but not negligible: about 3.7 nanograms. It is given by the
3895:
2869:{\displaystyle \mathbf {g} =-\mu {\frac {\hat {\mathbf {R} }}{|\mathbf {R} |^{2}}}}
2762:
2448:
2382:
1958:
1551:
1411:
1371:
1194:
1189:
in November 2018. The new definition uses only invariant quantities of nature: the
888:
789:
769:
714:
709:
655:
630:
485:
343:
288:
263:
6225:
5194:
of the value for the mass of each elementary particle to the value of the unknown
2750:
2544:
According to K. M. Browne: "Kepler formed a concept of mass ('amount of matter' (
2233:
1880:
Astronaut David Scott performs the feather and hammer drop experiment on the Moon.
8980:
8940:
7445:
6514:
5507:) should still apply, along with the formula for the total energy of a particle:
5343:
5304:
5295:
5251:
5223:
5213:
5140:
4670:
3207:
2987:
2966:
2916:
2915:, it will revolve around Earth along an elliptical orbit (C, D). Beyond the
2583:
2413:
2398:
2370:
1857:
1841:
1673:
1489:
1454:
1449:. Mass can be converted into other forms of energy according to the principle of
1442:
1198:
784:
729:
679:
674:
593:
8743:
8679:
7140:
5951:
950:, even though mass is often determined by measuring the object's weight using a
41:
8924:
8888:
8813:
8594:
8481:
8371:
8272:
7995:
7055:
Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften, Berlin
5387:
5363:
5339:
5316:
5280:
5128:
5113:
5033:
4869:
4687:
4612:
4588:
4139:
4023:
3899:
3819:
3230:
measures relative weight, giving the relative gravitation mass of each object.
3211:
2945:
2895:
is the radial coordinate (the distance between the centers of the two bodies).
2418:
2386:
1989:
1962:
1889:
1849:
1830:
1571:
1466:
1462:
1438:
1374:, one may distinguish conceptually between at least seven different aspects of
1266:
1190:
963:
811:
719:
620:
337:
20:
7621:
6658:
4698:, making it impossible to write the gravitational field energy as part of the
3722:{\displaystyle m_{1}=m_{2}{\frac {|\mathbf {a} _{2}|}{|\mathbf {a} _{1}|}}\!.}
1562:) refers to an intrinsic property of an object, whereas "weight" (measured in
9017:
9011:
8798:
8666:
8380:
7582:
7506:
7469:
7428:
7224:
7177:
Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions
7070:
6970:
6919:
6465:
6413:
6176:
6143:
5714:
5407:" in discussions of tachyons) must also apply to tachyons. In particular the
5371:
5231:
5037:
4861:
4666:
4593:
4366:
3980:
3976:
3969:
3199:
2912:
2786:
2776:
2602:
2214:
1481:
1277:
1238:
1162:
1146:
872:
699:
526:
6711:
Hecht, Eugene (January 2006). "There Is No Really Good Definition of Mass".
6041:
4596:
is often lost in the form of gamma rays when the nuclei are formed, leaving
3979:(also known as the unified atomic mass unit). By definition, 1 Da (one
2761:
had published his concept of gravitational forces in 1674, stating that all
1394:
Inertial mass is a measure of an object's resistance to acceleration when a
8873:
8859:
8759:
8695:
8420:
8203:
8114:
7666:
7384:
6609:
5331:
5299:
3347:
3227:
2767:
2758:
2406:
2225:
1578:
1508:
1273:
1167:
951:
931:
908:
764:
689:
378:
258:
5690:
The dalton is convenient for expressing the masses of atoms and molecules.
2562:
Isaac Newton, Mathematical principles of natural philosophy, Definition I.
1566:) measures an object's resistance to deviating from its current course of
1495:
Quantum mass manifests itself as a difference between an object's quantum
1012:
determines the strength of the gravitational field generated by an object.
8241:
7882:
7617:
5612:
5604:
5308:
5255:
5191:
5136:
4624:
4616:
4388:
3277:
definition of mass differs slightly from the definition in the theory of
3215:
2374:
1901:
1500:
1284:
1262:
971:
924:
7549:
6895:
6373:
Mathematical Discourses and Demonstrations, Relating to Two New Sciences
2016:
1622:, (expressed as the acceleration experienced by a free-falling object).
7345:
7331:
Gibbons, G.W. (2002). "Cosmological evolution of the rolling tachyon".
7292:
7239:
6808:
5379:
3358:"resistance" to changing its state of motion in response to the force.
3262:
2972:
1458:
1343:
1299:
549:
223:
7535:
L.B. Okun (2002). "Photons, Clocks, Gravity and the Concept of Mass".
7124:
6991:
6732:
6283:
6258:
5217:
4108:{\displaystyle m_{\mathrm {relative} }=\gamma (m_{\mathrm {rest} })\!}
2232:) as a measurement standard. If an object's weight was equivalent to
1406:
Active gravitational mass is a measure of the strength of an object's
8334:
8261:
8249:
7823:
7635:
7606:
7594:
6940:
6682:"Teachers Learn the Difference Between Mass and Weight Even in Space"
6550:
Newton's Principia: The mathematical principles of natural philosophy
5620:
5580:{\displaystyle E={\frac {mc^{2}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}.}
5504:
5392:
5351:
5260:
5250:) are a purely hypothetical concept not generally believed to exist,
4564:{\displaystyle E_{\mathrm {total} }=(m_{\mathrm {relative} })c^{2}\!}
4011:
3984:
3907:
2473:
2430:
1909:
1567:
1559:
1496:
1477:
1473:
1415:
1242:
916:
571:
7035:
5275:(closely related to second order phase transitions) that results in
1779:
Putting these together, the gravitational acceleration is given by:
8638:
8537:
8291:
8150:
8104:
7795:
6447:. Translated by Motte, A. Printed for Benjamin Motte. pp. 1â2.
6208:
6024:
5496:
5243:
5207:
4581:
3987:
atom, and thus, a carbon-12 atom has a mass of exactly 12 Da.
3770:
3763:
3195:
3150:. The above statement may be reformulated in the following way: if
2772:
1885:
1446:
1158:
935:
912:
490:
373:
348:
70:
6146:
BeitrÀge zum Gesetz der ProportionalitÀt von TrÀgheit und GravitÀt
5835:
falling through the same medium would fall at the same speed. See
4627:
of melting ice (334 kJ/kg) divided by the speed of light squared (
8964:
7912:
7687:
7629:
6360:
Discorsi e Dimostrazioni Matematiche, Intorno Ă Due Nuove Scienze
6306:
Drake, S. (1979). "Galileo's Discovery of the Law of Free Fall".
5404:
5291:
5239:
5227:
5121:
4601:
4597:
3354:
2378:
2229:
1950:
1563:
1441:
of a system of particles, meaning the energy of that system in a
1400:
939:
904:
463:
316:
233:
65:
4467:{\displaystyle E_{\mathrm {rest} }=(m_{\mathrm {rest} })c^{2}\!}
2907:
1503:. The quantum mass of a particle is proportional to the inverse
8878:
8847:
8803:
8781:
8235:
8134:
8099:
7857:
7830:
7746:
7736:
6546:
5608:
4022:
is the total quantity of energy in a body or system divided by
3903:
2438:
2008:
1979:
1897:
1547:
1476:
is a relativistic manifestation of the existence of mass. Such
1224:
1185:
came into effect on 20 May 2019, following a final vote by the
1141:
947:
880:
522:
368:
278:
6960:
6580:"Curious About Astronomy: How do you measure a planet's mass?"
6516:
The Mathematical Papers of Isaac Newton, Volume VI (1684â1691)
5978:"New Quantum Theory Separates Gravitational and Inertial Mass"
4391:
and "relativistic energy" (total system energy) respectively:
1915:
A stronger version of the equivalence principle, known as the
1382:. Every experiment to date has shown these seven values to be
1062:(center of mass to center of mass) from a second body of mass
8912:
8837:
8771:
8375:
8281:
8276:
8213:
8188:
7770:
6461:
An attempt to prove the motion of the earth from observations
3339:
2477:
2402:
2221:
2093:
1583:
1531:
1395:
1213:
920:
358:
353:
295:
6889:
G. Oas (2005). "On the Abuse and Use of Relativistic Mass".
3292:
if, at any instant of time, it obeys the equation of motion
3246:
2525:{\displaystyle {\text{Distance}}\propto {{\text{Time}}^{2}}}
2033:
K. M. Browne, The pre-Newtonian meaning of the word âweightâ
8994:
8954:
8193:
8124:
8089:
7810:
7721:
5101:{\displaystyle (-i\gamma ^{\mu }\partial _{\mu }+m)\psi =0}
2452:
1905:
1587:
1535:
1419:
1418:
acceleration. For example, an object in free-fall near the
1186:
884:
363:
4202:{\displaystyle \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}
7197:(5th ed.). New York: W.H. Freeman & Co. p.
4690:
in general relativity. At the core of the problem is the
1310:
156:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
7012:
Sandin, T.R. (1991). "In Defense of Relativistic Mass".
2986:, did not occur until 1797, over a hundred years later.
1577:
The force known as "weight" is proportional to mass and
1488:. Other forms of curvature have been measured using the
1378:, or seven physical notions that involve the concept of
3252:
Tsiolkovsky State Museum of the History of Cosmonautics
2405:
of these two values is constant for all planets in the
2088:
is the weight of the collection of similar objects and
1837:
can be taken as 1 by defining our units appropriately.
1324:
the mass of a particle, as identified with its inverse
7448:(1967). "Possibility of Faster-Than-Light Particles".
6189:
5183:{\displaystyle G_{\psi }{\overline {\psi }}\phi \psi }
3755:
is our "reference" object, and we can define its mass
2203:{\displaystyle {\frac {W_{n}}{W_{m}}}={\frac {n}{m}}.}
970:
is believed to be a result of their coupling with the
8604:
7406:
6772:
Einstein's Theories and the Operational Point of View
5753:
5516:
5420:
5153:
5050:
4882:
4736:
4483:
4401:
4239:
4152:
4124:
4037:
3956:|. An additional difficulty was pointed out by
3843:
3835:
3786:
3639:
3619:{\displaystyle \mathbf {F} _{12}=-\mathbf {F} _{21};}
3582:
3430:
3301:
3167:
3027:
2811:
2613:
2499:
2455:
of the same material, but different masses, from the
2250:
2159:
2146:{\displaystyle {\frac {W_{n}}{n}}={\frac {W_{m}}{m}}}
2105:
2051:
1789:
1750:
1712:
1208:
Non-SI units accepted for use with SI units include:
1183:
re-definition of the kilogram and several other units
875:. It was traditionally believed to be related to the
120:
6481:
Correspondence of Isaac Newton, Volume 2 (1676â1687)
5599:, the denominator in the equation for the energy is
3882:{\displaystyle K={\dfrac {1}{2}}m|\mathbf {v} |^{2}}
3194:
This is the basis by which masses are determined by
1257:
Outside the SI system, other units of mass include:
46:
A 2 kg (4.4 lb) cast iron weight used for
7137:
5254:with imaginary mass have come to play an important
8619:
7850:
7587:"The Origin of Mass and the Feebleness of Gravity"
7138:Misner, C.W.; Thorne, K.S.; Wheeler, J.A. (1973).
5811:
5579:
5480:
5182:
5100:
5016:
4856:After quantization, replacing the position vector
4844:
4563:
4466:
4353:
4201:
4130:
4107:
3881:
3805:
3721:
3618:
3533:
3353:This equation illustrates how mass relates to the
3323:
3182:
3130:
2868:
2720:
2524:
2347:
2202:
2145:
2073:
2028:downward force were believed to be the same thing.
1814:
1768:
1730:
1655:
919:is applied. The object's mass also determines the
891:. It was found that different atoms and different
155:
6444:The mathematical principles of natural philosophy
6141:
5359:ordinary particles with a positive mass-squared.
4560:
4463:
4350:
4104:
4028:. The two are related by the following equation:
3715:
9009:
8025:
7504:
5208:Tachyonic particles and imaginary (complex) mass
3265:and has since been developed into the notion of
2919:, it will leave the Earth without returning (E).
2891:) of the body causing gravitational fields, and
1295:), a quantity derived from fundamental constants
7485:
7188:
6344:Dialogue Concerning the Two Chief World Systems
2940:
2539:
1507:and can be determined through various forms of
6091:Relativity: Special, General, And Cosmological
4718:, the inert mass of a particle appears in the
4619:) used to melt the ice; this follows from the
4600:which have less mass than the free particles (
2463:A later experiment was described in Galileo's
1069:, each body is subject to an attractive force
8011:
7651:
7581:
7440:
7438:
7189:Tipler, Paul A.; Llewellyn, Ralph A. (2008).
6857:
6369:
6056:
5481:{\displaystyle E^{2}=p^{2}c^{2}+m^{2}c^{4}\;}
5120:is now simply a constant associated with the
2797:Mathematical Principles of Natural Philosophy
845:
7098:"There Is No Really Good Definition of Mass"
6542:
6540:
6538:
6536:
6142:Eötvös, R.V.; Pekår, D.; Fekete, E. (1922).
6002:
2042:to the number of objects in the collection:
1216:(t) (or "metric ton"), equal to 1000 kg
7517:
7402:
7400:
7048:
6094:. Oxford University Press. pp. 16â18.
3324:{\displaystyle \mathbf {F} =m\mathbf {a} ,}
3206:is proportional to the displacement of the
2792:PhilosophiĂŠ Naturalis Principia Mathematica
1538:. Weight varies due to different amount of
8018:
8004:
7658:
7644:
7537:Nuclear Physics B: Proceedings Supplements
7435:
7171:
7169:
7167:
6753:
6751:
6547:Sir Isaac Newton; N.W. Chittenden (1848).
6483:. Cambridge University Press. p. 297.
6087:
5477:
3983:) is exactly one-twelfth of the mass of a
3806:{\displaystyle \mathbf {p} =m\mathbf {v} }
1241:(Da), equal to 1/12 of the mass of a free
852:
838:
40:
7605:
7593:
7548:
7534:
7481:
7479:
7344:
7291:
7238:
6894:
6745:Ernst Mach, "Science of Mechanics" (1919)
6533:
6512:
6282:
6207:
6023:
5004:
4918:
4819:
4801:
4764:
3281:, but the essential meaning is the same.
1968:
7444:
7397:
6478:
5843:. University of Chicago Press. pp.
3245:
2971:
2944:
2906:
2749:
2437:
2429:
2401:of its orbit, or equivalently, that the
1983:
1863:
1525:
1140:
7488:An Introduction to Quantum Field Theory
7330:
7324:
7278:Sen, Ashoke (2002). "Rolling Tachyon".
7218:
7164:
6787:
6748:
6405:
6357:
6340:
6081:
5143:results in the replacement of the term
4683:(i.e. accelerated) frame of reference.
2213:An early use of this relationship is a
1176:International Prototype of the Kilogram
9010:
7665:
7486:Peskin, M.E.; Schroeder, D.V. (1995).
7476:
7383:
7377:
7182:
7011:
6888:
6776:Albert Einstein: Philosopher-Scientist
6636:
6608:
6440:
6370:Crew, H.; de Salvio, A., eds. (1954).
6256:
6069:. BIPM. 10 November 2016. pp. 2â9
2953:In contrast to earlier theories (e.g.
2902:
1973:
1844:obtained by dropping objects from the
1227:, used to express mass in units of eV/
883:in a body, until the discovery of the
7999:
7639:
7095:
7089:
6963:"Putting to Rest Mass Misconceptions"
6710:
6679:
6615:A Treatise of the System of the World
6457:
6305:
6252:
6250:
6123:. Nature America, Inc. pp. 32â39
6003:von Klitzing, Klaus (February 2017).
5836:
4709:
4642:
4227:relativistic energy-momentum equation
3995:
3284:In classical mechanics, according to
2994:Given two objects A and B, of masses
2935:A Treatise of the System of the World
2425:
1530:Mass and weight of a given object on
534:Newton's law of universal gravitation
16:Amount of matter present in an object
7507:"The Equivalence of Mass and Energy"
7505:Francisco Flores (6 February 2012).
6909:
6903:
6858:Taylor, E.F.; Wheeler, J.A. (1992).
6114:
5916:
5647:Effective mass (solid-state physics)
5044:
4679:experienced by an observer in a non-
4395:
4233:
3762:Additionally, mass relates a body's
1634:of an object is related to its mass
1594:of an object is related to its mass
1410:(gravitational flux is equal to the
7511:Stanford Encyclopedia of Philosophy
7277:
7271:
6577:
5642:Effective mass (springâmass system)
5326:Although the notion of a tachyonic
4704:stressâenergyâmomentum pseudotensor
4669:. At the core of this assertion is
3576:
2358:
1280:(about 4.5 N), a unit of force
515:Mechanics of planar particle motion
123:
13:
7948:International System of Quantities
6247:
5747:
5657:International System of Quantities
5124:described by the wave function Ï.
5071:
4990:
4959:
4904:
4895:
4891:
4876:
4776:
4768:
4746:
4740:
4730:
4541:
4538:
4535:
4532:
4529:
4526:
4523:
4520:
4502:
4499:
4496:
4493:
4490:
4444:
4441:
4438:
4435:
4417:
4414:
4411:
4408:
4300:
4297:
4294:
4291:
4288:
4258:
4255:
4252:
4249:
4221:and the magnitude of its momentum
4146:
4095:
4092:
4089:
4086:
4065:
4062:
4059:
4056:
4053:
4050:
4047:
4044:
3421:. Newton's second law states that
2283:
2280:
2277:
2274:
2271:
2266:
2263:
2260:
2257:
2254:
1815:{\displaystyle a={\frac {M}{m}}g.}
1515:
1174:in 1799, and the platinumâiridium
14:
9049:
7599:"Does mass change with velocity?"
7498:
7078:On the Dynamics of Moving Systems
7057:, Erster Halbband (29): 542â570,
6328:10.1038/scientificamerican0573-84
6115:Kane, Gordon (4 September 2008).
4886:
4477:
3829:
3780:
3210:beneath the weighing pan, as per
2607:
2567:
2365:Kepler's laws of planetary motion
1783:
1145:The kilogram is one of the seven
7972:
7971:
7926:
7076:English Wikisource translation:
6064:"Draft of the ninth SI Brochure"
5742:standard gravitational parameter
4997:
4978:
4911:
4323:
3990:
3963:
3863:
3799:
3788:
3697:
3673:
3603:
3585:
3514:
3489:
3485:
3466:
3441:
3437:
3314:
3303:
3288:, we say that a body has a mass
3233:
3222:into account, allowing the mass
3100:
3076:
3030:
2889:standard gravitational parameter
2847:
2831:
2813:
2451:stated that Galileo had dropped
1437:, mass is nothing else than the
1130:
819:
818:
805:
138:
8042:Linear/translational quantities
7611:"What is the mass of a photon?"
7131:
7042:
7005:
6954:
6882:
6851:
6838:
6781:
6764:
6739:
6704:
6680:Gibbs, Yvonne (31 March 2017).
6673:
6630:
6602:
6571:
6506:
6487:
6472:
6451:
6434:
6351:
6334:
6299:
6183:
6135:
6108:
5889:
5879:
5870:
5861:
5824:
5734:
5702:
5607:is negative. Because the total
5139:. In the case of fermions, the
2074:{\displaystyle W_{n}\propto n,}
1656:Inertial vs. gravitational mass
1574:, though they still have mass.
1031:is subjected to a single force
7280:Journal of High Energy Physics
7227:Journal of High Energy Physics
7051:"Zur Dynamik bewegter Systeme"
6618:. London: F. Fayram. p. 6
6519:. Cambridge University Press.
5996:
5970:
5944:
5910:
5693:
5684:
5675:
5086:
5051:
5008:
4993:
4982:
4974:
4922:
4907:
4604:) of which they are composed.
4547:
4511:
4450:
4426:
4336:
4328:
4318:
4314:
4264:
4240:
4101:
4077:
3869:
3858:
3708:
3691:
3684:
3667:
3112:
3094:
3080:
2853:
2842:
2835:
2472:. The groove was lined with "
2011:weighing the heart of Hunefer.
1917:Einstein equivalence principle
1703:, the force on the object is:
1365:
1309:), defined as the mass of the
1:
8047:Angular/rotational quantities
7567:10.1016/S0920-5632(02)01472-X
7363:10.1016/s0370-2693(02)01881-6
7310:10.1088/1126-6708/2002/04/048
7257:10.1088/1126-6708/2000/10/045
6513:Whiteside, D.T., ed. (2008).
5917:Bray, Nancy (28 April 2015).
5903:
5032:(relativistically invariant)
2381:. Kepler discovered that the
2001:
1546:In everyday usage, mass and "
1155:International System of Units
1025:Newton's second law of motion
976:BroutâEnglertâHiggs mechanism
441:Koopmanâvon Neumann mechanics
7943:History of the metric system
7518:Gordon Kane (27 June 2005).
6479:Turnbull, H.W., ed. (1960).
6196:Astronomy & Astrophysics
5662:2019 revision of the SI base
5169:
2959:universal gravitational mass
2941:Universal gravitational mass
2540:Mass as distinct from weight
1925:general theory of relativity
1921:strong equivalence principle
1678:general theory of relativity
1542:whereas mass stays the same.
1269:of mass (about 14.6 kg)
981:
927:attraction to other bodies.
907:, meaning the resistance to
509:Non-inertial reference frame
7:
7015:American Journal of Physics
6263:American Journal of Physics
6226:10.1051/0004-6361/202038104
5629:
3400:, and the force exerted on
2887:is the gravitational mass (
2389:of each planet is directly
1923:, lies at the heart of the
1620:Earth's gravitational field
1618:is the acceleration due to
1552:Earth's gravitational field
1486:gravitational time dilation
1195:caesium hyperfine frequency
436:Appell's equation of motion
306:Inertial frame of reference
10:
9054:
8620:{\displaystyle {\dot {m}}}
8044:
6409:On the Shoulders of Giants
5211:
4649:Mass in general relativity
4646:
4578:proportional to the energy
4002:Mass in special relativity
3999:
3967:
2929:Newton's cannonball was a
2922:
2362:
1977:
1934:
1904:did on the surface of the
1689:weak equivalence principle
1659:
1540:gravitational acceleration
1519:
1137:Orders of magnitude (mass)
1134:
1051:. If a first body of mass
1027:, if a body of fixed mass
1016:Passive gravitational mass
18:
8318:specific angular momentum
8046:
8041:
8036:
7966:
7935:
7924:
7841:thermodynamic temperature
7686:
7681:
7673:
7624:(video) published by the
6864:. W.H. Freeman. pp.
6774:, in: P.A. Schilpp, ed.,
6659:10.1007/s11191-008-9183-1
6406:Hawking, S., ed. (2002).
5603:, as the value under the
5147:Ï in the Lagrangian with
4365:So long as the system is
3947:| / |
3558:are the accelerations of
3202:, for example, the force
2782:De motu corporum in gyrum
2606:
2577:
2574:
2021:predates recorded history
1955:gravitational interaction
1947:mass generation mechanism
1937:Mass generation mechanism
1930:
1554:at different places, the
1346:, as identified with its
1157:(SI) unit of mass is the
1010:Active gravitational mass
87:
76:
64:
54:
39:
34:
7470:10.1103/PhysRev.159.1089
7429:10.1103/PhysRev.182.1400
7146:. W.H. Freeman. p.
7071:10.1002/andp.19083310602
6578:Cuk, M. (January 2003).
6177:10.1002/andp.19223730903
5668:
5619:be imaginary: i.e. the
5409:energyâmomentum relation
5348:commute (or anticommute)
5321:condensed matter physics
4696:Einstein field equations
1058:is placed at a distance
974:in what is known as the
966:of physics, the mass of
599:Rotating reference frame
431:HamiltonâJacobi equation
8442:rotational acceleration
7520:"The Mysteries of Mass"
6651:2010Sc&Ed..19...91C
6639:Science & Education
6218:2020A&A...638A..24V
6117:"The Mysteries of Mass"
6042:10.1360/SSPMA2017-00044
5652:Extension (metaphysics)
5346:separated points still
5334:is; even for tachyonic
4720:EulerâLagrange equation
4608:Massâenergy equivalence
4131:{\displaystyle \gamma }
3342:acting on the body and
2589:Sidereal orbital period
2373:sought employment with
1451:massâenergy equivalence
1233:massâenergy equivalence
1172:Kilogramme des Archives
540:Newton's laws of motion
400:Newton's laws of motion
8621:
7958:Systems of measurement
7609:; et al. (2008).
7597:; et al. (2012).
7096:Hecht, Eugene (2006).
6978:(5): 13â14, 115, 117.
6788:Gillies, D.A. (1972).
6404:and also available in
6257:Browne, K. M. (2018).
5813:
5581:
5482:
5184:
5102:
5018:
4846:
4661:is the equivalence of
4621:conservation of energy
4587:In bound systems, the
4565:
4468:
4355:
4203:
4132:
4109:
4014:(invariant mass), and
4006:In some frameworks of
3883:
3807:
3723:
3620:
3535:
3325:
3255:
3240:BarreÂŽ de Saint-Venant
3184:
3148:gravitational constant
3132:
2978:
2950:
2920:
2870:
2755:
2722:
2565:
2526:
2443:
2435:
2434:Galileo Galilei (1636)
2349:
2204:
2147:
2075:
2036:
2012:
1969:Pre-Newtonian concepts
1881:
1816:
1770:
1732:
1543:
1342:the mass of a star or
1170:in 1793, the platinum
1150:
1111:gravitational constant
567:Simple harmonic motion
480:Euler's laws of motion
274:D'Alembert's principle
157:
23:. For other uses, see
8622:
7620:(27 September 2017).
6912:"The Concept of Mass"
5982:MIT Technology Review
5814:
5615:, the numerator must
5582:
5483:
5303:examples include the
5185:
5103:
5019:
4847:
4659:equivalence principle
4566:
4469:
4356:
4204:
4133:
4110:
3884:
3808:
3724:
3621:
3536:
3326:
3249:
3214:, and the scales are
3185:
3133:
2975:
2948:
2910:
2871:
2753:
2723:
2554:
2527:
2457:Leaning Tower of Pisa
2441:
2433:
2350:
2205:
2148:
2076:
2040:directly proportional
2025:
1987:
1879:
1846:Leaning Tower of Pisa
1817:
1771:
1769:{\displaystyle F=ma.}
1733:
1731:{\displaystyle F=Mg.}
1682:equivalence principle
1529:
1388:operationally defined
1144:
1135:Further information:
1121:equivalence principle
421:Hamiltonian mechanics
239:Statistical mechanics
158:
25:Mass (disambiguation)
9038:Extensive quantities
8602:
8452:angular acceleration
8224:angular displacement
7390:The Elegant Universe
7049:Planck, Max (1907),
6441:Newton, I. (1729) .
6358:Galileo, G. (1638).
6341:Galileo, G. (1632).
5833:of the same material
5751:
5514:
5495:is the relativistic
5418:
5376:quantum field theory
5356:Tachyon condensation
5273:tachyon condensation
5151:
5048:
4880:
4734:
4700:stressâenergy tensor
4481:
4399:
4237:
4150:
4122:
4035:
3833:
3784:
3637:
3580:
3428:
3299:
3183:{\displaystyle F=Mg}
3165:
3025:
2984:Cavendish experiment
2809:
2611:
2497:
2248:
2157:
2103:
2049:
1787:
1748:
1710:
1348:Schwarzschild radius
1245:atom, approximately
968:elementary particles
893:elementary particles
644:Angular acceleration
636:Rotational frequency
416:Lagrangian mechanics
409:Analytical mechanics
165:Second law of motion
118:
9023:Physical quantities
8542:weighted position:
8359:rotational velocity
8307:kinematic viscosity
8027:Classical mechanics
7868:amount of substance
7622:The Concept of Mass
7589:(video). MIT Video.
7559:2002NuPhS.110..151O
7530:on 10 October 2007.
7524:Scientific American
7462:1967PhRv..159.1089F
7421:1969PhRv..182.1400A
7355:2002PhLB..537....1G
7302:2002JHEP...04..048S
7249:2000JHEP...10..045K
7117:2006PhTea..44...40H
7105:The Physics Teacher
7063:1908AnP...331....1P
7028:1991AmJPh..59.1032S
6984:1990PhT....43e..13R
6933:1989PhT....42f..31O
6910:Okun, L.B. (1989).
6846:Classical Mechanics
6725:2006PhTea..44...40H
6713:The Physics Teacher
6553:. D. Adee. p.
6320:1973SciAm.228e..84D
6308:Scientific American
6275:2018AmJPh..86..471B
6169:1922AnP...373...11E
6121:Scientific American
6088:W. Rindler (2006).
6034:2017SSPMA..47l9503L
6005:"Metrology in 2019"
5710:classical mechanics
5499:of the bradyon and
5218:Tachyon § Mass
4716:classical mechanics
4374:without the other.
4310:
3286:Newton's second law
3275:classical mechanics
2925:Newton's cannonball
2913:intermediate speeds
2903:Newton's cannonball
2412:On 25 August 1609,
2007:). The scene shows
1988:Depiction of early
1974:Weight as an amount
1943:theoretical physics
1668:classical mechanics
1628:proper acceleration
1428:gravitational field
1049:gravitational field
1035:, its acceleration
496:Harmonic oscillator
474:Equations of motion
109:Classical mechanics
103:Part of a series on
9028:SI base quantities
8617:
7893:luminous intensity
7667:SI base quantities
6809:10.1007/BF00484997
6458:Hooke, R. (1674).
6378:Dover Publications
6156:Annalen der Physik
5837:Drake, S. (1978).
5809:
5806:gravitational mass
5637:Mass versus weight
5577:
5478:
5190:. This shifts the
5180:
5098:
5028:In the ostensibly
5014:
4842:
4710:In quantum physics
4655:general relativity
4643:General relativity
4561:
4464:
4351:
4282:
4215:frame of reference
4199:
4128:
4105:
4008:special relativity
3996:Special relativity
3906:in the nucleus of
3879:
3852:
3803:
3719:
3616:
3531:
3529:
3414:, which we denote
3393:, which we denote
3363:Newton's third law
3321:
3279:special relativity
3256:
3180:
3128:
2979:
2951:
2931:thought experiment
2921:
2866:
2756:
2754:Isaac Newton, 1689
2718:
2522:
2444:
2436:
2426:Galilean free fall
2345:
2200:
2153:, or equivalently
2143:
2071:
2013:
1994:Papyrus of Hunefer
1882:
1812:
1766:
1728:
1544:
1522:Mass versus weight
1505:Compton wavelength
1445:where it has zero
1408:gravitational flux
1326:Compton wavelength
1151:
1125:general relativity
1109:is the "universal
869:intrinsic property
812:Physics portal
426:Routhian mechanics
301:Frame of reference
153:
9005:
9004:
9000:
8999:
8614:
8567:moment of inertia
7993:
7992:
7921:
7920:
7626:Royal Institution
7208:978-0-7167-7550-8
7157:978-0-7167-0344-0
7125:10.1119/1.2150758
7082:See paragraph 16.
6992:10.1063/1.2810555
6875:978-0-7167-2327-1
6861:Spacetime Physics
6844:Henri Poincaré. "
6733:10.1119/1.2150758
6584:Ask an Astronomer
6526:978-0-521-04585-8
6427:978-0-7624-1348-5
6394:on 1 October 2013
6387:978-1-275-10057-2
6362:. Vol. 213.
6284:10.1119/1.5027490
6101:978-0-19-856731-8
5952:"The Higgs boson"
5854:978-0-226-16226-3
5807:
5799:
5791:
5779:
5572:
5571:
5569:
5401:Lorentz invariant
5388:unstable particle
5277:symmetry breaking
5248:faster than light
5196:coupling constant
5172:
4956:
4902:
4830:
4815:
4809:
4799:
4789:
4758:
4754:
4671:Albert Einstein's
4345:
4197:
4196:
4020:Relativistic mass
4016:relativistic mass
3851:
3825:to its velocity:
3713:
3338:is the resultant
3271:Percy W. Bridgman
3146:is the universal
3127:
3123:
3107:
3089:
3083:
3066:
3056:
3037:
3008:, separated by a
2955:celestial spheres
2864:
2838:
2748:
2747:
2741:9.806 65 m/s
2716:
2708:
2696:
2669:
2661:
2649:
2513:
2503:
2417:(later named the
2340:
2327:
2314:
2287:
2195:
2182:
2141:
2121:
1877:
1804:
1662:Eötvös experiment
1203:elementary charge
862:
861:
609:Centrifugal force
604:Centripetal force
560:Euler's equations
545:Relative velocity
321:Moment of inertia
151:
125:
98:
97:
9045:
9033:Moment (physics)
8992:
8988:
8976:
8972:
8952:
8948:
8936:
8932:
8910:
8906:
8896:
8886:
8871:
8867:
8857:
8835:
8831:
8821:
8811:
8796:
8792:
8779:
8755:
8749:
8741:
8730:
8724:
8713:
8706:angular momentum
8691:
8685:
8677:
8662:
8656:
8646:
8633:
8627:
8626:
8624:
8623:
8618:
8616:
8615:
8607:
8580:
8574:
8558:
8535:
8516:
8511:
8489:
8467:
8461:
8444:
8428:
8406:
8400:
8391:angular velocity
8388:
8369:
8368:
8355:
8354:
8347:rotational speed
8343:
8342:
8325:
8314:
8299:
8289:
8270:
8269:
8252:
8247:
8233:
8221:
8201:
8182:
8181:
8175:
8169:
8158:
8132:
8112:
8097:
8081:
8074:
8039:
8038:
8020:
8013:
8006:
7997:
7996:
7975:
7974:
7930:
7929:
7904:
7874:
7852:
7847:
7825:
7820:
7816:
7814:
7806:electric current
7787:
7761:
7757:
7753:
7728:
7679:
7678:
7660:
7653:
7646:
7637:
7636:
7614:
7602:
7590:
7578:
7552:
7531:
7526:. Archived from
7514:
7492:
7491:
7490:. Perseus Books.
7483:
7474:
7473:
7456:(5): 1089â1105.
7446:Feinberg, Gerald
7442:
7433:
7432:
7415:(5): 1400â1403.
7404:
7395:
7394:
7393:. Vintage Books.
7381:
7375:
7374:
7348:
7328:
7322:
7321:
7295:
7275:
7269:
7268:
7242:
7222:
7216:
7215:
7196:
7186:
7180:
7173:
7162:
7161:
7145:
7135:
7129:
7128:
7102:
7093:
7087:
7073:
7046:
7040:
7039:
7009:
7003:
7002:
7001:on 22 July 2011.
7000:
6994:. Archived from
6967:
6958:
6952:
6951:
6950:on 22 July 2011.
6949:
6943:. Archived from
6941:10.1063/1.881171
6916:
6907:
6901:
6900:
6898:
6886:
6880:
6879:
6855:
6849:
6842:
6836:
6835:
6833:
6831:
6826:on 26 April 2016
6825:
6819:. Archived from
6794:
6785:
6779:
6768:
6762:
6755:
6746:
6743:
6737:
6736:
6708:
6702:
6701:
6699:
6697:
6692:on 20 March 2023
6688:. Archived from
6677:
6671:
6670:
6634:
6628:
6627:
6625:
6623:
6606:
6600:
6599:
6597:
6595:
6590:on 20 March 2003
6586:. Archived from
6575:
6569:
6568:
6544:
6531:
6530:
6510:
6504:
6503:
6501:
6491:
6485:
6484:
6476:
6470:
6469:
6455:
6449:
6448:
6438:
6432:
6431:
6403:
6401:
6399:
6390:. Archived from
6368:, translated in
6367:
6355:
6349:
6348:
6338:
6332:
6331:
6303:
6297:
6296:
6286:
6254:
6245:
6244:
6242:
6240:
6211:
6187:
6181:
6180:
6152:
6139:
6133:
6132:
6130:
6128:
6112:
6106:
6105:
6085:
6079:
6078:
6076:
6074:
6068:
6060:
6054:
6053:
6027:
6009:
6000:
5994:
5993:
5991:
5989:
5974:
5968:
5967:
5965:
5963:
5948:
5942:
5941:
5936:
5934:
5925:. Archived from
5914:
5897:
5893:
5887:
5883:
5877:
5874:
5868:
5865:
5859:
5858:
5828:
5822:
5819:
5816:
5815:
5810:
5808:
5805:
5800:
5798:
5797:
5792:
5789:
5786:
5785:
5780:
5777:
5774:
5772:
5771:
5738:
5732:
5729:
5726:
5724:
5722:
5720:
5718:
5716:
5706:
5700:
5697:
5691:
5688:
5682:
5679:
5586:
5584:
5583:
5578:
5573:
5570:
5568:
5567:
5558:
5557:
5548:
5540:
5539:
5538:
5537:
5524:
5487:
5485:
5484:
5479:
5476:
5475:
5466:
5465:
5453:
5452:
5443:
5442:
5430:
5429:
5313:particle physics
5294:" was coined by
5285:particle physics
5269:phase transition
5189:
5187:
5186:
5181:
5173:
5165:
5163:
5162:
5133:particle physics
5108:
5105:
5104:
5099:
5079:
5078:
5069:
5068:
5040:, this becomes:
5024:
5021:
5020:
5015:
5000:
4989:
4985:
4981:
4967:
4966:
4957:
4955:
4947:
4946:
4937:
4914:
4903:
4901:
4890:
4864:, the parameter
4852:
4849:
4848:
4843:
4838:
4837:
4832:
4831:
4823:
4813:
4807:
4806:
4802:
4800:
4798:
4797:
4796:
4791:
4790:
4782:
4774:
4766:
4756:
4755:
4753:
4749:
4743:
4738:
4638:
4636:
4571:
4568:
4567:
4562:
4559:
4558:
4546:
4545:
4544:
4507:
4506:
4505:
4474:
4471:
4470:
4465:
4462:
4461:
4449:
4448:
4447:
4422:
4421:
4420:
4361:
4358:
4357:
4352:
4346:
4344:
4343:
4331:
4326:
4321:
4309:
4304:
4303:
4281:
4276:
4275:
4263:
4262:
4261:
4209:
4206:
4205:
4200:
4198:
4195:
4194:
4185:
4180:
4179:
4164:
4160:
4137:
4135:
4134:
4129:
4114:
4112:
4111:
4106:
4100:
4099:
4098:
4070:
4069:
4068:
3955:
3946:
3896:potential energy
3889:
3886:
3885:
3880:
3878:
3877:
3872:
3866:
3861:
3853:
3844:
3813:
3810:
3809:
3804:
3802:
3791:
3748:. In this case,
3740:
3728:
3726:
3725:
3720:
3714:
3712:
3711:
3706:
3705:
3700:
3694:
3688:
3687:
3682:
3681:
3676:
3670:
3664:
3662:
3661:
3649:
3648:
3626:
3623:
3622:
3617:
3612:
3611:
3606:
3594:
3593:
3588:
3540:
3538:
3537:
3532:
3530:
3523:
3522:
3517:
3511:
3510:
3494:
3493:
3492:
3475:
3474:
3469:
3463:
3462:
3446:
3445:
3444:
3330:
3328:
3327:
3322:
3317:
3306:
3189:
3187:
3186:
3181:
3137:
3135:
3134:
3129:
3125:
3124:
3122:
3121:
3120:
3115:
3109:
3108:
3105:
3103:
3097:
3091:
3090:
3087:
3085:
3084:
3079:
3074:
3070:
3068:
3067:
3064:
3058:
3057:
3054:
3039:
3038:
3035:
3033:
2875:
2873:
2872:
2867:
2865:
2863:
2862:
2861:
2856:
2850:
2845:
2839:
2834:
2829:
2827:
2816:
2763:celestial bodies
2728:
2725:
2724:
2719:
2717:
2715:
2714:
2709:
2706:
2703:
2702:
2697:
2694:
2691:
2689:
2688:
2670:
2668:
2667:
2662:
2659:
2656:
2655:
2650:
2647:
2644:
2642:
2641:
2626:
2625:
2572:
2571:
2563:
2531:
2529:
2528:
2523:
2521:
2520:
2519:
2514:
2511:
2504:
2501:
2465:Two New Sciences
2449:Vincenzo Viviani
2359:Planetary motion
2354:
2352:
2351:
2346:
2341:
2333:
2328:
2320:
2315:
2313:
2312:
2303:
2302:
2293:
2288:
2286:
2269:
2252:
2234:1728 carob seeds
2209:
2207:
2206:
2201:
2196:
2188:
2183:
2181:
2180:
2171:
2170:
2161:
2152:
2150:
2149:
2144:
2142:
2137:
2136:
2127:
2122:
2117:
2116:
2107:
2080:
2078:
2077:
2072:
2061:
2060:
2034:
2019:is very old and
2006:
2003:
1959:particle physics
1878:
1822:
1819:
1818:
1813:
1805:
1797:
1775:
1773:
1772:
1767:
1737:
1735:
1734:
1729:
1647:
1638:by the equation
1617:
1616:
1615:9.80665 m/s
1607:
1412:surface integral
1372:physical science
1360:
1359:
1357:
1338:
1337:
1335:
1320:
1318:
1294:
1292:
1252:
1250:
1223:(eV), a unit of
1108:
1107:
1105:
1094:
1004:
889:particle physics
854:
847:
840:
827:
822:
821:
814:
810:
809:
715:Johann Bernoulli
710:Daniel Bernoulli
631:Tangential speed
535:
511:
486:Fictitious force
481:
333:Mechanical power
323:
264:Angular momentum
162:
160:
159:
154:
152:
150:
142:
141:
132:
127:
126:
100:
99:
44:
32:
31:
9053:
9052:
9048:
9047:
9046:
9044:
9043:
9042:
9008:
9007:
9006:
9001:
8990:
8989:
8984:
8974:
8973:
8968:
8950:
8949:
8944:
8934:
8933:
8928:
8908:
8907:
8902:
8892:
8882:
8869:
8868:
8863:
8851:
8833:
8832:
8827:
8817:
8807:
8794:
8793:
8791:
8785:
8775:
8753:
8750:
8747:
8739:
8728:
8725:
8719:
8716:angular impulse
8709:
8689:
8686:
8683:
8675:
8660:
8657:
8652:
8642:
8631:
8628:
8606:
8605:
8603:
8600:
8599:
8598:
8578:
8575:
8570:
8543:
8536:
8531:
8514:
8512:
8505:
8490:
8485:
8465:
8462:
8455:
8445:
8440:
8429:
8424:
8404:
8401:
8394:
8384:
8370:
8362:
8357:
8350:
8345:
8338:
8333:
8326:
8321:
8316:
8310:
8300:
8295:
8285:
8271:
8265:
8260:
8248:
8245:
8240:
8234:
8227:
8217:
8202:
8197:
8187:
8177:
8171:
8165:
8160:
8154:
8133:
8128:
8113:
8108:
8098:
8093:
8077:
8070:
8032:
8024:
7994:
7989:
7962:
7931:
7927:
7922:
7903:
7897:
7872:
7845:
7824: I
7818:
7812:
7785:
7759:
7755:
7751:
7726:
7715:
7710:
7702:
7674:Base quantities
7669:
7664:
7585:(13 May 2001).
7550:physics/0111134
7501:
7496:
7495:
7484:
7477:
7450:Physical Review
7443:
7436:
7405:
7398:
7382:
7378:
7329:
7325:
7276:
7272:
7223:
7219:
7209:
7187:
7183:
7174:
7165:
7158:
7136:
7132:
7100:
7094:
7090:
7047:
7043:
7036:10.1119/1.16642
7010:
7006:
6998:
6965:
6959:
6955:
6947:
6914:
6908:
6904:
6896:physics/0504110
6887:
6883:
6876:
6856:
6852:
6843:
6839:
6829:
6827:
6823:
6792:
6786:
6782:
6770:P.W. Bridgman,
6769:
6765:
6756:
6749:
6744:
6740:
6709:
6705:
6695:
6693:
6678:
6674:
6635:
6631:
6621:
6619:
6607:
6603:
6593:
6591:
6576:
6572:
6565:
6545:
6534:
6527:
6511:
6507:
6499:
6493:
6492:
6488:
6477:
6473:
6456:
6452:
6439:
6435:
6428:
6397:
6395:
6388:
6356:
6352:
6339:
6335:
6304:
6300:
6255:
6248:
6238:
6236:
6188:
6184:
6150:
6140:
6136:
6126:
6124:
6113:
6109:
6102:
6086:
6082:
6072:
6070:
6066:
6062:
6061:
6057:
6007:
6001:
5997:
5987:
5985:
5976:
5975:
5971:
5961:
5959:
5950:
5949:
5945:
5932:
5930:
5915:
5911:
5906:
5901:
5900:
5894:
5890:
5884:
5880:
5875:
5871:
5866:
5862:
5855:
5840:Galileo at Work
5829:
5825:
5804:
5793:
5788:
5787:
5781:
5776:
5775:
5773:
5767:
5763:
5752:
5749:
5739:
5735:
5713:
5707:
5703:
5698:
5694:
5689:
5685:
5680:
5676:
5671:
5666:
5632:
5595:is larger than
5563:
5559:
5553:
5549:
5547:
5533:
5529:
5525:
5523:
5515:
5512:
5511:
5471:
5467:
5461:
5457:
5448:
5444:
5438:
5434:
5425:
5421:
5419:
5416:
5415:
5340:field operators
5296:Gerald Feinberg
5238:mass. Although
5224:tachyonic field
5220:
5214:Tachyonic field
5212:Main articles:
5210:
5203:
5164:
5158:
5154:
5152:
5149:
5148:
5141:Higgs mechanism
5074:
5070:
5064:
5060:
5049:
5046:
4996:
4977:
4962:
4958:
4948:
4942:
4938:
4936:
4932:
4928:
4910:
4894:
4889:
4881:
4878:
4868:appears in the
4833:
4822:
4821:
4820:
4792:
4781:
4780:
4779:
4775:
4767:
4765:
4763:
4759:
4745:
4744:
4739:
4737:
4735:
4732:
4722:as a parameter
4712:
4651:
4645:
4634:
4632:
4554:
4550:
4519:
4518:
4514:
4489:
4488:
4484:
4482:
4479:
4457:
4453:
4434:
4433:
4429:
4407:
4406:
4402:
4400:
4397:
4339:
4335:
4327:
4322:
4317:
4305:
4287:
4286:
4280:
4271:
4267:
4248:
4247:
4243:
4238:
4235:
4190:
4186:
4181:
4175:
4171:
4159:
4151:
4148:
4123:
4120:
4119:
4085:
4084:
4080:
4043:
4042:
4038:
4036:
4033:
4032:
4004:
3998:
3993:
3972:
3966:
3954:
3948:
3945:
3939:
3937:
3930:
3923:
3916:
3873:
3868:
3867:
3862:
3857:
3842:
3834:
3831:
3818:and the body's
3798:
3787:
3785:
3782:
3754:
3747:
3739:
3733:
3707:
3701:
3696:
3695:
3690:
3689:
3683:
3677:
3672:
3671:
3666:
3665:
3663:
3657:
3653:
3644:
3640:
3638:
3635:
3634:
3607:
3602:
3601:
3589:
3584:
3583:
3581:
3578:
3571:
3564:
3557:
3550:
3528:
3527:
3518:
3513:
3512:
3506:
3502:
3495:
3488:
3484:
3483:
3480:
3479:
3470:
3465:
3464:
3458:
3454:
3447:
3440:
3436:
3435:
3431:
3429:
3426:
3425:
3420:
3413:
3406:
3399:
3392:
3385:
3378:
3371:
3313:
3302:
3300:
3297:
3296:
3236:
3166:
3163:
3162:
3116:
3111:
3110:
3104:
3099:
3098:
3093:
3092:
3086:
3075:
3073:
3072:
3071:
3069:
3063:
3059:
3053:
3049:
3034:
3029:
3028:
3026:
3023:
3022:
3017:
3007:
3000:
2988:Henry Cavendish
2967:unit conversion
2943:
2927:
2917:escape velocity
2905:
2857:
2852:
2851:
2846:
2841:
2840:
2830:
2828:
2826:
2812:
2810:
2807:
2806:
2736:Earth's radius
2733:Earth's gravity
2710:
2705:
2704:
2698:
2693:
2692:
2690:
2684:
2680:
2663:
2658:
2657:
2651:
2646:
2645:
2643:
2634:
2630:
2621:
2617:
2612:
2609:
2584:Semi-major axis
2570:
2564:
2561:
2542:
2515:
2510:
2509:
2508:
2500:
2498:
2495:
2494:
2428:
2414:Galileo Galilei
2399:semi-major axis
2371:Johannes Kepler
2367:
2361:
2332:
2319:
2308:
2304:
2298:
2294:
2292:
2270:
2253:
2251:
2249:
2246:
2245:
2238:144 carob seeds
2187:
2176:
2172:
2166:
2162:
2160:
2158:
2155:
2154:
2132:
2128:
2126:
2112:
2108:
2106:
2104:
2101:
2100:
2056:
2052:
2050:
2047:
2046:
2035:
2032:
2015:The concept of
2005: 1285 BCE
2004:
1982:
1976:
1971:
1961:, known as the
1939:
1933:
1864:
1858:torsion balance
1850:inclined planes
1796:
1788:
1785:
1749:
1746:
1745:
1711:
1708:
1707:
1674:Albert Einstein
1664:
1658:
1639:
1614:
1609:
1599:
1524:
1518:
1516:Weight vs. mass
1490:Gravity Probe B
1455:pair production
1443:reference frame
1368:
1355:
1353:
1351:
1333:
1331:
1329:
1316:
1314:
1308:
1305:
1290:
1288:
1248:
1246:
1199:Planck constant
1178:(IPK) in 1889.
1139:
1133:
1103:
1101:
1096:
1089:
1083:
1076:
1070:
1068:
1057:
996:
984:
934:of mass is the
858:
817:
804:
803:
796:
795:
794:
669:
661:
660:
640:
594:Circular motion
588:
578:
577:
576:
533:
503:
500:
479:
458:
450:
449:
446:
445:
403:
393:
385:
384:
383:
342:
338:Mechanical work
331:
315:
253:
245:
244:
243:
198:
190:
167:
143:
137:
133:
131:
122:
121:
119:
116:
115:
57:
50:
28:
17:
12:
11:
5:
9051:
9041:
9040:
9035:
9030:
9025:
9020:
9003:
9002:
8998:
8997:
8978:
8962:
8960:
8957:
8938:
8922:
8920:
8916:
8915:
8876:
8845:
8843:
8840:
8801:
8789:
8769:
8767:
8763:
8762:
8733:
8703:
8701:
8698:
8669:
8636:
8613:
8610:
8595:Mass flow rate
8592:
8588:
8587:
8585:
8583:
8564:
8561:
8559:
8540:
8525:
8521:
8520:
8518:
8499:
8497:
8494:
8492:
8479:
8477:
8473:
8472:
8470:
8449:
8438:
8435:
8433:
8418:
8416:
8412:
8411:
8409:
8378:
8331:
8328:
8304:
8279:
8258:
8254:
8253:
8238:
8211:
8209:
8206:
8191:
8148:
8146:
8142:
8141:
8139:
8137:
8122:
8119:
8117:
8102:
8087:
8083:
8082:
8075:
8068:
8065:
8062:
8059:
8056:
8053:
8049:
8048:
8045:
8043:
8037:
8034:
8033:
8023:
8022:
8015:
8008:
8000:
7991:
7990:
7988:
7987:
7980:
7967:
7964:
7963:
7961:
7960:
7955:
7950:
7945:
7939:
7937:
7933:
7932:
7925:
7923:
7919:
7918:
7915:
7910:
7908:
7905:
7901:
7895:
7889:
7888:
7885:
7880:
7878:
7875:
7870:
7864:
7863:
7860:
7855:
7853:
7848:
7843:
7837:
7836:
7833:
7828:
7826:
7821:
7808:
7802:
7801:
7798:
7793:
7791:
7788:
7783:
7777:
7776:
7773:
7768:
7766:
7763:
7749:
7743:
7742:
7739:
7734:
7732:
7729:
7724:
7722:time, duration
7718:
7717:
7712:
7707:
7705:
7698:
7695:
7691:
7690:
7685:
7683:
7677:
7675:
7671:
7670:
7663:
7662:
7655:
7648:
7640:
7634:
7633:
7615:
7603:
7591:
7579:
7532:
7515:
7500:
7499:External links
7497:
7494:
7493:
7475:
7434:
7396:
7376:
7346:hep-th/0204008
7323:
7293:hep-th/0203211
7270:
7240:hep-th/0009148
7217:
7207:
7193:Modern Physics
7181:
7175:Lisa Randall,
7163:
7156:
7130:
7088:
7086:
7085:
7041:
7004:
6953:
6902:
6881:
6874:
6850:
6837:
6780:
6763:
6747:
6738:
6703:
6672:
6629:
6601:
6570:
6563:
6532:
6525:
6505:
6486:
6471:
6450:
6433:
6426:
6386:
6364:Louis Elsevier
6350:
6333:
6298:
6246:
6182:
6134:
6107:
6100:
6080:
6055:
6012:Nature Physics
5995:
5984:. 14 June 2010
5969:
5958:. 3 April 2024
5943:
5929:on 30 May 2023
5908:
5907:
5905:
5902:
5899:
5898:
5888:
5878:
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5853:
5823:
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5820:
5803:
5796:
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5733:
5701:
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5683:
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5644:
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5556:
5552:
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5536:
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5528:
5522:
5519:
5489:
5488:
5474:
5470:
5464:
5460:
5456:
5451:
5447:
5441:
5437:
5433:
5428:
5424:
5374:. However, in
5336:quantum fields
5317:ferromagnetism
5281:current models
5209:
5206:
5201:
5179:
5176:
5171:
5168:
5161:
5157:
5129:Standard Model
5110:
5109:
5097:
5094:
5091:
5088:
5085:
5082:
5077:
5073:
5067:
5063:
5059:
5056:
5053:
5034:Dirac equation
5026:
5025:
5013:
5010:
5007:
5003:
4999:
4995:
4992:
4988:
4984:
4980:
4976:
4973:
4970:
4965:
4961:
4954:
4951:
4945:
4941:
4935:
4931:
4927:
4924:
4921:
4917:
4913:
4909:
4906:
4900:
4897:
4893:
4888:
4885:
4870:kinetic energy
4854:
4853:
4841:
4836:
4829:
4826:
4818:
4812:
4805:
4795:
4788:
4785:
4778:
4773:
4770:
4762:
4752:
4748:
4742:
4711:
4708:
4688:invariant mass
4647:Main article:
4644:
4641:
4613:thermal energy
4589:binding energy
4573:
4572:
4557:
4553:
4549:
4543:
4540:
4537:
4534:
4531:
4528:
4525:
4522:
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4504:
4501:
4498:
4495:
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4487:
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4456:
4452:
4446:
4443:
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4428:
4425:
4419:
4416:
4413:
4410:
4405:
4363:
4362:
4349:
4342:
4338:
4334:
4330:
4325:
4320:
4316:
4313:
4308:
4302:
4299:
4296:
4293:
4290:
4285:
4279:
4274:
4270:
4266:
4260:
4257:
4254:
4251:
4246:
4242:
4211:
4210:
4193:
4189:
4184:
4178:
4174:
4170:
4167:
4163:
4158:
4155:
4140:Lorentz factor
4127:
4116:
4115:
4103:
4097:
4094:
4091:
4088:
4083:
4079:
4076:
4073:
4067:
4064:
4061:
4058:
4055:
4052:
4049:
4046:
4041:
4000:Main article:
3997:
3994:
3992:
3989:
3968:Main article:
3965:
3962:
3958:Henri Poincaré
3952:
3943:
3935:
3928:
3921:
3914:
3900:binding energy
3892:
3891:
3876:
3871:
3865:
3860:
3856:
3850:
3847:
3841:
3838:
3820:kinetic energy
3816:
3815:
3801:
3797:
3794:
3790:
3769:to its linear
3752:
3745:
3737:
3730:
3729:
3718:
3710:
3704:
3699:
3693:
3686:
3680:
3675:
3669:
3660:
3656:
3652:
3647:
3643:
3628:
3627:
3615:
3610:
3605:
3600:
3597:
3592:
3587:
3569:
3562:
3555:
3548:
3542:
3541:
3526:
3521:
3516:
3509:
3505:
3501:
3498:
3496:
3491:
3487:
3482:
3481:
3478:
3473:
3468:
3461:
3457:
3453:
3450:
3448:
3443:
3439:
3434:
3433:
3418:
3411:
3404:
3397:
3390:
3383:
3376:
3369:
3332:
3331:
3320:
3316:
3312:
3309:
3305:
3267:operationalism
3235:
3232:
3192:
3191:
3179:
3176:
3173:
3170:
3140:
3139:
3119:
3114:
3102:
3096:
3082:
3078:
3062:
3052:
3048:
3045:
3042:
3032:
3015:
3005:
2998:
2942:
2939:
2923:Main article:
2904:
2901:
2877:
2876:
2860:
2855:
2849:
2844:
2837:
2833:
2825:
2822:
2819:
2815:
2746:
2745:
2744:6 375 km
2742:
2738:
2737:
2734:
2730:
2729:
2713:
2701:
2687:
2683:
2679:
2676:
2673:
2666:
2654:
2640:
2637:
2633:
2629:
2624:
2620:
2616:
2605:
2599:
2592:
2591:
2586:
2580:
2579:
2578:Mass of Earth
2576:
2569:
2568:Newtonian mass
2566:
2559:
2546:copia materiae
2541:
2538:
2533:
2532:
2518:
2507:
2488:
2487:
2427:
2424:
2419:Galilean moons
2387:orbital period
2360:
2357:
2356:
2355:
2344:
2339:
2336:
2331:
2326:
2323:
2318:
2311:
2307:
2301:
2297:
2291:
2285:
2282:
2279:
2276:
2273:
2268:
2265:
2262:
2259:
2256:
2211:
2210:
2199:
2194:
2191:
2186:
2179:
2175:
2169:
2165:
2140:
2135:
2131:
2125:
2120:
2115:
2111:
2082:
2081:
2070:
2067:
2064:
2059:
2055:
2030:
1996:(dated to the
1990:balance scales
1978:Main article:
1975:
1972:
1970:
1967:
1963:Standard Model
1935:Main article:
1932:
1929:
1890:air resistance
1831:if and only if
1824:
1823:
1811:
1808:
1803:
1800:
1795:
1792:
1777:
1776:
1765:
1762:
1759:
1756:
1753:
1739:
1738:
1727:
1724:
1721:
1718:
1715:
1676:developed his
1657:
1654:
1520:Main article:
1517:
1514:
1513:
1512:
1493:
1470:
1469:or vice versa.
1467:kinetic energy
1463:nuclear fusion
1431:
1424:
1404:
1367:
1364:
1363:
1362:
1340:
1322:
1306:
1303:
1296:
1281:
1270:
1255:
1254:
1235:
1217:
1191:speed of light
1132:
1129:
1106:10 Nâ
kgâ
m
1087:
1081:
1074:
1066:
1055:
1020:
1019:
1013:
1007:
983:
980:
964:Standard Model
954:, rather than
903:of the body's
860:
859:
857:
856:
849:
842:
834:
831:
830:
829:
828:
815:
798:
797:
793:
792:
787:
782:
777:
772:
767:
762:
757:
752:
747:
742:
737:
732:
727:
722:
717:
712:
707:
702:
697:
692:
687:
682:
677:
671:
670:
667:
666:
663:
662:
659:
658:
639:
638:
633:
628:
623:
621:Coriolis force
618:
617:
616:
606:
601:
596:
590:
589:
584:
583:
580:
579:
575:
574:
569:
564:
563:
562:
557:
547:
542:
537:
530:
519:
518:
517:
512:
499:
498:
493:
488:
483:
476:
471:
466:
460:
459:
456:
455:
452:
451:
448:
447:
444:
443:
438:
433:
428:
423:
418:
412:
406:
404:
397:
394:
391:
390:
387:
386:
382:
381:
376:
371:
366:
361:
356:
351:
346:
340:
335:
329:
324:
313:
308:
303:
298:
293:
292:
291:
286:
276:
271:
266:
261:
255:
254:
251:
250:
247:
246:
242:
241:
236:
231:
226:
221:
216:
211:
206:
200:
199:
196:
195:
192:
191:
189:
188:
183:
178:
172:
169:
168:
163:
149:
146:
140:
136:
130:
112:
111:
105:
104:
96:
95:
92:
85:
84:
81:
74:
73:
68:
62:
61:
58:
56:Common symbols
55:
52:
51:
45:
37:
36:
21:Mass (liturgy)
15:
9:
6:
4:
3:
2:
9050:
9039:
9036:
9034:
9031:
9029:
9026:
9024:
9021:
9019:
9016:
9015:
9013:
8996:
8987:
8982:
8979:
8971:
8966:
8963:
8961:
8958:
8956:
8947:
8942:
8939:
8931:
8926:
8923:
8921:
8918:
8917:
8914:
8905:
8900:
8895:
8890:
8885:
8880:
8877:
8875:
8866:
8861:
8856:
8855:
8849:
8846:
8844:
8841:
8839:
8830:
8825:
8820:
8815:
8810:
8805:
8802:
8800:
8788:
8783:
8778:
8773:
8770:
8768:
8765:
8764:
8761:
8757:
8745:
8737:
8734:
8732:
8723:
8717:
8712:
8707:
8704:
8702:
8699:
8697:
8693:
8681:
8673:
8670:
8668:
8664:
8655:
8650:
8645:
8640:
8637:
8635:
8611:
8608:
8596:
8593:
8590:
8589:
8586:
8584:
8582:
8573:
8568:
8565:
8562:
8560:
8557:
8554:
8550:
8546:
8541:
8539:
8534:
8529:
8526:
8523:
8522:
8519:
8510:
8509:
8503:
8500:
8498:
8495:
8493:
8488:
8483:
8480:
8478:
8475:
8474:
8471:
8469:
8460:
8459:
8453:
8450:
8448:
8443:
8439:
8436:
8434:
8432:
8427:
8422:
8419:
8417:
8414:
8413:
8410:
8408:
8399:
8398:
8392:
8387:
8382:
8381:angular speed
8379:
8377:
8373:
8367:
8366:
8360:
8353:
8348:
8341:
8336:
8332:
8329:
8324:
8319:
8313:
8308:
8305:
8303:
8298:
8293:
8288:
8283:
8280:
8278:
8274:
8268:
8263:
8259:
8256:
8255:
8251:
8243:
8239:
8237:
8232:
8231:
8225:
8220:
8215:
8212:
8210:
8207:
8205:
8200:
8195:
8192:
8190:
8186:
8180:
8174:
8168:
8163:
8157:
8152:
8149:
8147:
8144:
8143:
8140:
8138:
8136:
8131:
8126:
8123:
8120:
8118:
8116:
8111:
8106:
8103:
8101:
8096:
8091:
8088:
8085:
8084:
8080:
8076:
8073:
8069:
8066:
8063:
8060:
8057:
8054:
8051:
8050:
8040:
8035:
8031:
8028:
8021:
8016:
8014:
8009:
8007:
8002:
8001:
7998:
7986:
7985:
7981:
7979:
7978:
7969:
7968:
7965:
7959:
7956:
7954:
7953:2019 revision
7951:
7949:
7946:
7944:
7941:
7940:
7938:
7934:
7916:
7914:
7911:
7909:
7906:
7900:
7896:
7894:
7891:
7890:
7886:
7884:
7881:
7879:
7876:
7871:
7869:
7866:
7865:
7861:
7859:
7856:
7854:
7849:
7844:
7842:
7839:
7838:
7834:
7832:
7829:
7827:
7822:
7809:
7807:
7804:
7803:
7799:
7797:
7794:
7792:
7789:
7784:
7782:
7779:
7778:
7774:
7772:
7769:
7767:
7764:
7750:
7748:
7745:
7744:
7740:
7738:
7735:
7733:
7730:
7725:
7723:
7720:
7719:
7713:
7708:
7706:
7704:
7699:
7696:
7693:
7692:
7689:
7684:
7680:
7676:
7672:
7668:
7661:
7656:
7654:
7649:
7647:
7642:
7641:
7638:
7631:
7627:
7623:
7619:
7616:
7612:
7608:
7604:
7600:
7596:
7592:
7588:
7584:
7583:Frank Wilczek
7580:
7576:
7572:
7568:
7564:
7560:
7556:
7551:
7546:
7542:
7538:
7533:
7529:
7525:
7521:
7516:
7512:
7508:
7503:
7502:
7489:
7482:
7480:
7471:
7467:
7463:
7459:
7455:
7451:
7447:
7441:
7439:
7430:
7426:
7422:
7418:
7414:
7410:
7403:
7401:
7392:
7391:
7386:
7385:Greene, Brian
7380:
7372:
7368:
7364:
7360:
7356:
7352:
7347:
7342:
7338:
7334:
7333:Phys. Lett. B
7327:
7319:
7315:
7311:
7307:
7303:
7299:
7294:
7289:
7285:
7281:
7274:
7266:
7262:
7258:
7254:
7250:
7246:
7241:
7236:
7232:
7228:
7221:
7214:
7210:
7204:
7200:
7195:
7194:
7185:
7178:
7172:
7170:
7168:
7159:
7153:
7149:
7144:
7143:
7134:
7126:
7122:
7118:
7114:
7110:
7106:
7099:
7092:
7083:
7079:
7075:
7074:
7072:
7068:
7064:
7060:
7056:
7052:
7045:
7037:
7033:
7029:
7025:
7021:
7017:
7016:
7008:
6997:
6993:
6989:
6985:
6981:
6977:
6973:
6972:
6971:Physics Today
6964:
6957:
6946:
6942:
6938:
6934:
6930:
6926:
6922:
6921:
6920:Physics Today
6913:
6906:
6897:
6892:
6885:
6877:
6871:
6867:
6863:
6862:
6854:
6847:
6841:
6822:
6818:
6814:
6810:
6806:
6802:
6798:
6791:
6784:
6777:
6773:
6767:
6760:
6754:
6752:
6742:
6734:
6730:
6726:
6722:
6718:
6714:
6707:
6691:
6687:
6683:
6676:
6668:
6664:
6660:
6656:
6652:
6648:
6645:(1): 91â113.
6644:
6640:
6633:
6617:
6616:
6611:
6610:Newton, Isaac
6605:
6589:
6585:
6581:
6574:
6566:
6564:9780520009295
6560:
6556:
6552:
6551:
6543:
6541:
6539:
6537:
6528:
6522:
6518:
6517:
6509:
6502:. p. 16.
6498:
6497:
6490:
6482:
6475:
6467:
6466:Royal Society
6463:
6462:
6454:
6446:
6445:
6437:
6429:
6423:
6419:
6415:
6414:Running Press
6411:
6410:
6393:
6389:
6383:
6379:
6375:
6374:
6365:
6361:
6354:
6346:
6345:
6337:
6329:
6325:
6321:
6317:
6313:
6309:
6302:
6294:
6290:
6285:
6280:
6276:
6272:
6269:(6): 471â74.
6268:
6264:
6260:
6253:
6251:
6235:
6231:
6227:
6223:
6219:
6215:
6210:
6205:
6201:
6197:
6193:
6186:
6178:
6174:
6170:
6166:
6162:
6158:
6157:
6149:
6147:
6138:
6122:
6118:
6111:
6103:
6097:
6093:
6092:
6084:
6065:
6059:
6051:
6047:
6043:
6039:
6035:
6031:
6026:
6021:
6017:
6013:
6006:
5999:
5983:
5979:
5973:
5957:
5953:
5947:
5940:
5928:
5924:
5920:
5913:
5909:
5892:
5882:
5873:
5864:
5856:
5850:
5846:
5842:
5841:
5834:
5827:
5818:
5801:
5794:
5782:
5768:
5764:
5760:
5757:
5754:
5746:
5745:
5743:
5737:
5728:
5711:
5705:
5696:
5687:
5678:
5674:
5663:
5660:
5658:
5655:
5653:
5650:
5648:
5645:
5643:
5640:
5638:
5635:
5634:
5627:
5625:
5622:
5618:
5614:
5610:
5606:
5602:
5598:
5594:
5574:
5564:
5560:
5554:
5550:
5544:
5541:
5534:
5530:
5526:
5520:
5517:
5510:
5509:
5508:
5506:
5502:
5498:
5494:
5472:
5468:
5462:
5458:
5454:
5449:
5445:
5439:
5435:
5431:
5426:
5422:
5414:
5413:
5412:
5410:
5406:
5402:
5397:
5394:
5389:
5385:
5381:
5377:
5373:
5372:natural units
5369:
5365:
5360:
5357:
5353:
5349:
5345:
5341:
5337:
5333:
5329:
5324:
5322:
5318:
5314:
5310:
5306:
5301:
5297:
5293:
5288:
5286:
5282:
5278:
5274:
5270:
5266:
5263:). While the
5262:
5257:
5253:
5249:
5245:
5241:
5237:
5233:
5232:quantum field
5229:
5225:
5219:
5215:
5205:
5200:
5197:
5193:
5177:
5174:
5166:
5159:
5155:
5146:
5142:
5138:
5134:
5130:
5125:
5123:
5119:
5115:
5107:
5095:
5092:
5089:
5083:
5080:
5075:
5065:
5061:
5057:
5054:
5043:
5042:
5041:
5039:
5038:natural units
5035:
5031:
5023:
5011:
5005:
5001:
4986:
4971:
4968:
4963:
4952:
4949:
4943:
4939:
4933:
4929:
4925:
4919:
4915:
4898:
4883:
4875:
4874:
4873:
4871:
4867:
4863:
4862:wave function
4859:
4851:
4839:
4834:
4827:
4824:
4816:
4810:
4803:
4793:
4786:
4783:
4771:
4760:
4750:
4729:
4728:
4727:
4725:
4721:
4717:
4707:
4705:
4701:
4697:
4693:
4692:non-linearity
4689:
4684:
4682:
4678:
4677:
4672:
4668:
4667:inertial mass
4664:
4663:gravitational
4660:
4656:
4650:
4640:
4630:
4626:
4622:
4618:
4614:
4609:
4605:
4603:
4599:
4595:
4594:atomic nuclei
4590:
4585:
4583:
4582:pedagogically
4579:
4570:
4555:
4551:
4515:
4508:
4485:
4476:
4473:
4458:
4454:
4430:
4423:
4403:
4394:
4393:
4392:
4390:
4386:
4385:
4381:
4375:
4373:
4368:
4360:
4347:
4340:
4332:
4311:
4306:
4283:
4277:
4272:
4268:
4244:
4232:
4231:
4230:
4228:
4224:
4220:
4216:
4208:
4191:
4187:
4182:
4176:
4172:
4168:
4165:
4161:
4156:
4153:
4145:
4144:
4143:
4141:
4125:
4081:
4074:
4071:
4039:
4031:
4030:
4029:
4027:
4026:
4021:
4017:
4013:
4009:
4003:
3991:In relativity
3988:
3986:
3982:
3978:
3971:
3970:Dalton (unit)
3964:Atomic masses
3961:
3959:
3951:
3942:
3934:
3931: /
3927:
3920:
3913:
3909:
3905:
3901:
3897:
3888:
3874:
3854:
3848:
3845:
3839:
3836:
3828:
3827:
3826:
3824:
3821:
3812:
3795:
3792:
3779:
3778:
3777:
3775:
3772:
3768:
3765:
3760:
3758:
3751:
3744:
3736:
3716:
3702:
3678:
3658:
3654:
3650:
3645:
3641:
3633:
3632:
3631:
3625:
3613:
3608:
3598:
3595:
3590:
3575:
3574:
3573:
3568:
3561:
3554:
3547:
3524:
3519:
3507:
3503:
3499:
3497:
3476:
3471:
3459:
3455:
3451:
3449:
3424:
3423:
3422:
3417:
3410:
3403:
3396:
3389:
3382:
3375:
3368:
3364:
3359:
3356:
3351:
3349:
3345:
3341:
3337:
3318:
3310:
3307:
3295:
3294:
3293:
3291:
3287:
3282:
3280:
3276:
3273:. The simple
3272:
3268:
3264:
3260:
3259:Inertial mass
3253:
3248:
3244:
3241:
3234:Inertial mass
3231:
3229:
3225:
3221:
3217:
3213:
3209:
3205:
3201:
3200:spring scales
3197:
3177:
3174:
3171:
3168:
3161:
3160:
3159:
3157:
3153:
3149:
3145:
3117:
3060:
3050:
3046:
3043:
3040:
3021:
3020:
3019:
3014:
3011:
3004:
2997:
2992:
2989:
2985:
2974:
2970:
2968:
2962:
2960:
2956:
2947:
2938:
2936:
2932:
2926:
2918:
2914:
2909:
2900:
2896:
2894:
2890:
2886:
2882:
2858:
2823:
2820:
2817:
2805:
2804:
2803:
2800:
2798:
2794:
2793:
2788:
2787:Royal Society
2784:
2783:
2778:
2777:Edmond Halley
2774:
2769:
2764:
2760:
2752:
2743:
2740:
2739:
2735:
2732:
2731:
2727:
2711:
2699:
2685:
2681:
2677:
2674:
2671:
2664:
2652:
2638:
2635:
2631:
2627:
2622:
2618:
2614:
2604:
2603:sidereal year
2600:
2598:
2594:
2593:
2590:
2587:
2585:
2582:
2581:
2573:
2558:
2553:
2551:
2547:
2537:
2516:
2505:
2493:
2492:
2491:
2484:
2483:
2482:
2479:
2475:
2471:
2466:
2461:
2458:
2454:
2450:
2440:
2432:
2423:
2420:
2415:
2410:
2408:
2404:
2400:
2396:
2392:
2388:
2384:
2380:
2376:
2372:
2366:
2342:
2337:
2334:
2329:
2324:
2321:
2316:
2309:
2305:
2299:
2295:
2289:
2244:
2243:
2242:
2239:
2235:
2231:
2227:
2223:
2218:
2216:
2215:balance scale
2197:
2192:
2189:
2184:
2177:
2173:
2167:
2163:
2138:
2133:
2129:
2123:
2118:
2113:
2109:
2099:
2098:
2097:
2095:
2091:
2087:
2068:
2065:
2062:
2057:
2053:
2045:
2044:
2043:
2041:
2029:
2024:
2022:
2018:
2010:
1999:
1995:
1991:
1986:
1981:
1966:
1964:
1960:
1956:
1952:
1948:
1944:
1938:
1928:
1926:
1922:
1918:
1913:
1911:
1907:
1903:
1899:
1895:
1891:
1887:
1862:
1859:
1855:
1854:Lorånd Eötvös
1851:
1847:
1843:
1838:
1836:
1832:
1829:
1821:
1809:
1806:
1801:
1798:
1793:
1790:
1782:
1781:
1780:
1763:
1760:
1757:
1754:
1751:
1744:
1743:
1742:
1725:
1722:
1719:
1716:
1713:
1706:
1705:
1704:
1702:
1698:
1694:
1690:
1685:
1683:
1679:
1675:
1671:
1669:
1663:
1653:
1651:
1646:
1642:
1637:
1633:
1629:
1623:
1621:
1612:
1606:
1602:
1597:
1593:
1589:
1585:
1580:
1575:
1573:
1569:
1565:
1561:
1557:
1553:
1549:
1541:
1537:
1533:
1528:
1523:
1510:
1506:
1502:
1498:
1494:
1491:
1487:
1483:
1482:atomic clocks
1479:
1475:
1472:Curvature of
1471:
1468:
1464:
1460:
1456:
1452:
1448:
1444:
1440:
1436:
1433:According to
1432:
1429:
1425:
1421:
1417:
1413:
1409:
1405:
1402:
1397:
1393:
1392:
1391:
1389:
1385:
1381:
1377:
1373:
1349:
1345:
1341:
1327:
1323:
1312:
1301:
1297:
1286:
1282:
1279:
1278:pound (force)
1275:
1271:
1268:
1267:Imperial unit
1264:
1260:
1259:
1258:
1244:
1240:
1236:
1234:
1230:
1226:
1222:
1218:
1215:
1211:
1210:
1209:
1206:
1204:
1200:
1196:
1192:
1188:
1184:
1179:
1177:
1173:
1169:
1164:
1163:melting point
1160:
1156:
1148:
1147:SI base units
1143:
1138:
1131:Units of mass
1128:
1126:
1122:
1118:
1117:
1112:
1099:
1093:
1086:
1080:
1073:
1065:
1061:
1054:
1050:
1046:
1042:
1038:
1034:
1030:
1026:
1017:
1014:
1011:
1008:
1005:
1003:
999:
993:
992:Inertial mass
990:
989:
988:
979:
977:
973:
969:
965:
960:
957:
956:balance scale
953:
949:
945:
941:
937:
933:
928:
926:
925:gravitational
922:
918:
914:
910:
906:
902:
898:
894:
890:
886:
882:
878:
874:
870:
866:
855:
850:
848:
843:
841:
836:
835:
833:
832:
826:
816:
813:
808:
802:
801:
800:
799:
791:
788:
786:
783:
781:
778:
776:
773:
771:
768:
766:
763:
761:
758:
756:
753:
751:
748:
746:
743:
741:
738:
736:
733:
731:
728:
726:
723:
721:
718:
716:
713:
711:
708:
706:
703:
701:
698:
696:
693:
691:
688:
686:
683:
681:
678:
676:
673:
672:
665:
664:
657:
653:
649:
645:
642:
641:
637:
634:
632:
629:
627:
624:
622:
619:
615:
612:
611:
610:
607:
605:
602:
600:
597:
595:
592:
591:
587:
582:
581:
573:
570:
568:
565:
561:
558:
556:
553:
552:
551:
548:
546:
543:
541:
538:
536:
531:
528:
524:
521:
520:
516:
513:
510:
506:
502:
501:
497:
494:
492:
489:
487:
484:
482:
477:
475:
472:
470:
467:
465:
462:
461:
454:
453:
442:
439:
437:
434:
432:
429:
427:
424:
422:
419:
417:
414:
413:
411:
410:
405:
402:
401:
396:
395:
389:
388:
380:
377:
375:
372:
370:
367:
365:
362:
360:
357:
355:
352:
350:
347:
345:
341:
339:
336:
334:
330:
328:
325:
322:
318:
314:
312:
309:
307:
304:
302:
299:
297:
294:
290:
287:
285:
282:
281:
280:
277:
275:
272:
270:
267:
265:
262:
260:
257:
256:
249:
248:
240:
237:
235:
232:
230:
227:
225:
222:
220:
217:
215:
212:
210:
207:
205:
202:
201:
194:
193:
187:
184:
182:
179:
177:
174:
173:
171:
170:
166:
147:
144:
134:
128:
114:
113:
110:
107:
106:
102:
101:
93:
90:
86:
82:
79:
75:
72:
69:
67:
63:
59:
53:
49:
43:
38:
33:
30:
26:
22:
8985:
8969:
8945:
8929:
8903:
8893:
8883:
8864:
8853:
8852:
8828:
8818:
8808:
8786:
8776:
8721:
8710:
8653:
8643:
8571:
8555:
8552:
8548:
8544:
8532:
8527:
8507:
8506:
8502:angular jerk
8486:
8457:
8456:
8425:
8421:acceleration
8396:
8395:
8385:
8364:
8363:
8351:
8339:
8322:
8311:
8296:
8286:
8266:
8229:
8228:
8218:
8198:
8185:displacement
8178:
8172:
8166:
8155:
8129:
8109:
8094:
8078:
8071:
7982:
7970:
7898:
7780:
7540:
7536:
7528:the original
7523:
7510:
7487:
7453:
7449:
7412:
7408:
7389:
7379:
7339:(1â2): 1â4.
7336:
7332:
7326:
7283:
7279:
7273:
7230:
7226:
7220:
7212:
7192:
7184:
7176:
7141:
7133:
7111:(1): 40â45.
7108:
7104:
7091:
7081:
7054:
7044:
7022:(11): 1032.
7019:
7013:
7007:
6996:the original
6975:
6969:
6956:
6945:the original
6927:(6): 31â36.
6924:
6918:
6905:
6884:
6860:
6853:
6840:
6828:. Retrieved
6821:the original
6800:
6796:
6783:
6775:
6771:
6766:
6758:
6741:
6719:(1): 40â45.
6716:
6712:
6706:
6694:. Retrieved
6690:the original
6685:
6675:
6642:
6638:
6632:
6620:. Retrieved
6614:
6604:
6592:. Retrieved
6588:the original
6583:
6573:
6549:
6515:
6508:
6495:
6489:
6480:
6474:
6460:
6453:
6443:
6436:
6408:
6396:. Retrieved
6392:the original
6372:
6359:
6353:
6343:
6336:
6314:(5): 84â92.
6311:
6307:
6301:
6266:
6262:
6237:. Retrieved
6199:
6195:
6185:
6163:(9): 11â66.
6160:
6154:
6145:
6137:
6125:. Retrieved
6120:
6110:
6090:
6083:
6073:10 September
6071:. Retrieved
6058:
6015:
6011:
5998:
5988:25 September
5986:. Retrieved
5981:
5972:
5960:. Retrieved
5955:
5946:
5938:
5931:. Retrieved
5927:the original
5922:
5912:
5891:
5881:
5872:
5863:
5839:
5832:
5826:
5736:
5704:
5695:
5686:
5677:
5623:
5616:
5596:
5592:
5589:
5500:
5492:
5490:
5398:
5361:
5332:scalar field
5325:
5305:condensation
5300:superluminal
5289:
5264:
5226:, or simply
5221:
5198:
5144:
5126:
5117:
5116:" parameter
5111:
5027:
4865:
4857:
4855:
4723:
4713:
4685:
4676:pseudo-force
4674:
4652:
4628:
4606:
4586:
4574:
4383:
4379:
4376:
4371:
4364:
4222:
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2768:Isaac Newton
2759:Robert Hooke
2757:
2575:Earth's Moon
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2407:Solar System
2391:proportional
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1998:19th dynasty
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1509:spectroscopy
1384:proportional
1379:
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1352:1 cm â
1330:1 cm â
1256:
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1221:electronvolt
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648:displacement
646: /
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469:Displacement
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398:
392:Formulations
379:Virtual work
326:
319: /
259:Acceleration
252:Fundamentals
66:SI unit
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7618:Jim Baggott
7543:: 151â155.
7233:(10): 045.
7142:Gravitation
6759:Chapter 5.3
6416:. pp.
5601:"imaginary"
5384:Hamiltonian
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5192:explanandum
5137:Higgs field
5112:where the "
4637:10 m/s
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4617:latent heat
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3212:Hooke's law
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1902:David Scott
1556:distinction
1501:wave number
1439:rest energy
1366:Definitions
1285:Planck mass
972:Higgs boson
911:(change of
897:definitions
790:von Neumann
457:Core topics
9012:Categories
8977:m s, N m s
8953:m s,
8899:Lagrangian
8824:Lagrangian
8064:Dimensions
8052:Dimensions
7286:(4): 048.
6209:2005.01388
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5904:References
5380:eigenvalue
5368:decay rate
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1660:See also:
1572:weightless
1492:satellite.
1459:beta decay
1435:relativity
1358:10 kg
1344:black hole
1336:10 kg
1319:10 kg
1300:solar mass
1293:10 kg
1251:10 kg
942:, mass is
725:d'Alembert
705:Maupertuis
668:Scientists
550:Rigid body
224:Kinematics
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8612:˙
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8262:frequency
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7595:John Baez
7409:Phys. Rev
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5919:"Science"
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1568:free fall
1560:kilograms
1497:frequency
1478:curvature
1474:spacetime
1416:free-fall
1265:(sl), an
1243:carbon-12
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917:net force
915:) when a
770:Liouville
652:frequency
572:Vibration
289:potential
214:Continuum
209:Celestial
186:Textbooks
89:Conserved
78:Extensive
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8760:J s
8756:m s
8731:m s
8692:m s
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8639:momentum
8292:velocity
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8030:SI units
7977:Category
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7265:15664546
6830:10 April
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6398:11 April
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5234:with an
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1159:kilogram
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921:strength
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877:quantity
825:Category
750:Hamilton
735:Lagrange
730:Clairaut
695:Horrocks
656:velocity
626:Pendulum
614:reactive
586:Rotation
555:dynamics
505:Inertial
491:Friction
374:Velocity
349:Momentum
229:Kinetics
219:Dynamics
197:Branches
181:Timeline
71:kilogram
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8965:rotatum
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7630:YouTube
7555:Bibcode
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7417:Bibcode
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7024:Bibcode
6980:Bibcode
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6866:248â149
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6647:Bibcode
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2397:of the
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2230:siliqua
1992:in the
1951:physics
1919:or the
1908:during
1842:Galileo
1586:or the
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1401:inertia
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940:physics
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901:measure
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745:Poisson
740:Laplace
685:Huygens
680:Galileo
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464:Damping
317:Inertia
311:Impulse
284:kinetic
234:Statics
204:Applied
176:History
8879:energy
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760:Cauchy
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700:Halley
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527:linear
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279:Energy
269:Couple
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5463:2
5459:m
5455:+
5450:2
5446:c
5440:2
5436:p
5432:=
5427:2
5423:E
5242:(
5202:Ï
5199:G
5156:G
5145:m
5118:m
5096:0
5093:=
5087:)
5084:m
5081:+
5058:i
5052:(
5012:.
5009:)
5006:t
5002:,
4998:r
4994:(
4987:)
4983:)
4979:r
4975:(
4972:V
4969:+
4964:2
4953:m
4950:2
4944:2
4930:(
4926:=
4923:)
4920:t
4916:,
4912:r
4908:(
4899:t
4884:i
4866:m
4858:x
4840:.
4835:i
4825:x
4817:m
4811:=
4804:)
4794:i
4784:x
4772:L
4761:(
4751:t
4747:d
4741:d
4724:m
4635:Ă
4633:9
4629:c
4615:(
4556:2
4552:c
4548:)
4542:e
4539:v
4536:i
4533:t
4530:a
4527:l
4524:e
4521:r
4516:m
4512:(
4509:=
4503:l
4500:a
4497:t
4494:o
4491:t
4486:E
4459:2
4455:c
4451:)
4445:t
4442:s
4439:e
4436:r
4431:m
4427:(
4424:=
4418:t
4415:s
4412:e
4409:r
4404:E
4380:E
4348:.
4341:2
4337:)
4333:c
4329:|
4324:p
4319:|
4315:(
4307:2
4301:l
4298:a
4295:t
4292:o
4289:t
4284:E
4278:=
4273:2
4269:c
4265:)
4259:t
4256:s
4253:e
4250:r
4245:m
4241:(
4223:p
4219:E
4192:2
4188:c
4183:/
4177:2
4173:v
4166:1
4162:1
4157:=
4102:)
4096:t
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4090:e
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4082:m
4078:(
4072:=
4066:e
4063:v
4060:i
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4054:a
4051:l
4048:e
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4040:m
4025:c
3953:1
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3941:a
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3929:1
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3922:1
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3915:2
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3890:.
3875:2
3870:|
3864:v
3859:|
3855:m
3849:2
3846:1
3840:=
3837:K
3823:K
3814:,
3800:v
3796:m
3793:=
3789:p
3774:v
3767:p
3757:m
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3746:1
3743:m
3738:1
3735:a
3717:.
3709:|
3703:1
3698:a
3692:|
3685:|
3679:2
3674:a
3668:|
3659:2
3655:m
3651:=
3646:1
3642:m
3614:;
3604:F
3596:=
3586:F
3570:2
3567:m
3563:1
3560:m
3556:2
3553:a
3549:1
3546:a
3525:,
3520:2
3515:a
3508:2
3504:m
3500:=
3486:F
3477:,
3472:1
3467:a
3460:1
3456:m
3452:=
3438:F
3416:F
3412:1
3409:m
3405:2
3402:m
3395:F
3391:2
3388:m
3384:1
3381:m
3377:2
3374:m
3370:1
3367:m
3344:a
3336:F
3319:,
3315:a
3311:m
3308:=
3304:F
3290:m
3224:M
3220:g
3204:F
3190:.
3178:g
3175:M
3172:=
3169:F
3156:M
3152:g
3144:G
3138:,
3118:2
3113:|
3101:R
3095:|
3077:R
3065:B
3061:M
3055:A
3051:M
3047:G
3041:=
3031:F
3013:R
3006:B
3003:M
2999:A
2996:M
2893:R
2885:Ό
2881:g
2859:2
2854:|
2848:R
2843:|
2832:R
2818:=
2814:g
2712:2
2707:s
2700:3
2695:m
2672:=
2665:2
2660:y
2653:3
2639:5
2623:2
2517:2
2343:.
2335:1
2330:=
2317:=
2306:W
2296:W
2290:=
2284:d
2281:n
2278:u
2275:o
2272:p
2267:e
2264:c
2261:n
2258:u
2255:o
2198:.
2193:m
2190:n
2185:=
2178:m
2174:W
2168:n
2164:W
2139:m
2134:m
2130:W
2124:=
2119:n
2114:n
2110:W
2090:n
2086:W
2069:,
2066:n
2058:n
2054:W
1835:K
1828:K
1810:.
1807:g
1802:m
1799:M
1794:=
1791:a
1764:.
1761:a
1758:m
1755:=
1752:F
1726:.
1723:g
1720:M
1717:=
1714:F
1701:g
1697:M
1693:m
1650:a
1641:W
1636:m
1632:W
1611:g
1601:W
1596:m
1592:W
1403:.
1356:Ă
1350:(
1339:)
1334:Ă
1328:(
1321:)
1317:Ă
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1302:(
1291:Ă
1253:.
1249:Ă
1229:c
1149:.
1104:Ă
1098:G
1092:r
1090:/
1088:B
1085:m
1082:A
1075:g
1072:F
1067:B
1064:m
1060:r
1056:A
1053:m
1045:m
1043:/
1041:F
1037:a
1033:F
1029:m
998:F
853:e
846:t
839:v
529:)
148:t
145:d
139:p
135:d
129:=
124:F
91:?
80:?
60:m
27:.
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