922:
2159:
1754:
1175:
5174:
2154:{\displaystyle {\boldsymbol {\tau }}_{\mathrm {net} }=I_{1}{\dot {\omega _{1}}}{\hat {\boldsymbol {e_{1}}}}+I_{2}{\dot {\omega _{2}}}{\hat {\boldsymbol {e_{2}}}}+I_{3}{\dot {\omega _{3}}}{\hat {\boldsymbol {e_{3}}}}+I_{1}\omega _{1}{\frac {d{\hat {\boldsymbol {e_{1}}}}}{dt}}+I_{2}\omega _{2}{\frac {d{\hat {\boldsymbol {e_{2}}}}}{dt}}+I_{3}\omega _{3}{\frac {d{\hat {\boldsymbol {e_{3}}}}}{dt}}=I{\boldsymbol {\dot {\omega }}}+{\boldsymbol {\omega }}\times (I{\boldsymbol {\omega }})}
935:
5370:
4929:
5007:
5650:
5241:
4784:
2502:
5169:{\displaystyle {\begin{aligned}{\text{power}}&={\text{torque}}\cdot 2\pi \cdot {\text{rotational speed}}\cdot {\frac {{\text{ft}}{\cdot }{\text{lbf}}}{\text{min}}}\cdot {\frac {\text{horsepower}}{33,000\cdot {\frac {{\text{ft}}\cdot {\text{lbf}}}{\text{min}}}}}\\&\approx {\frac {{\text{torque}}\cdot {\text{RPM}}}{5,252}}\end{aligned}}}
3809:
6201:, The International System of Units – 9th edition – Text in English Section 2.3.4: "For example, the quantity torque is the cross product of a position vector and a force vector. The SI unit is newton-metre. Even though torque has the same dimension as energy (SI unit joule), the joule is never used for expressing torque."
3640:
5365:
For example, if a person places a force of 10 N at the terminal end of a wrench that is 0.5 m long (or a force of 10 N acting 0.5 m from the twist point of a wrench of any length), the torque will be 5 N⋅m – assuming that the person moves the wrench by applying force in
5001:
If torque is in newton-metres and rotational speed in revolutions per second, the above equation gives power in newton-metres per second or watts. If
Imperial units are used, and if torque is in pounds-force feet and rotational speed in revolutions per minute, the above equation gives power in foot
4136:
3230:
Algebraically, the equation may be rearranged to compute torque for a given angular speed and power output. The power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied
2791:
This is a general proof for point particles, but it can be generalized to a system of point particles by applying the above proof to each of the point particles and then summing over all the point particles. Similarly, the proof can be generalized to a continuous mass by applying the above proof to
2787:
4941:
have dropped out of the equation. However, angular speed must be in radians per unit of time, by the assumed direct relationship between linear speed and angular speed at the beginning of the derivation. If the rotational speed is measured in revolutions per unit of time, the linear speed and
4011:
4924:{\displaystyle {\begin{aligned}{\text{power}}&={\frac {{\text{force}}\cdot {\text{linear distance}}}{\text{time}}}\\&={\frac {\left({\dfrac {\text{torque}}{r}}\right)\cdot (r\cdot {\text{angular speed}}\cdot t)}{t}}\\&={\text{torque}}\cdot {\text{angular speed}}.\end{aligned}}}
2387:
4576:
2629:
4744:
5640:
3719:
2248:
3712:
3563:
1386:
1046:. Just as a linear force is a push or a pull applied to a body, a torque can be thought of as a twist applied to an object with respect to a chosen point; for example, driving a screw uses torque, which is applied by the screwdriver rotating around its
5705:
tend to produce maximum torque close to zero rpm, with the torque diminishing as rotational speed rises (due to increasing friction and other constraints). Reciprocating steam-engines and electric motors can start heavy loads from zero rpm without a
4416:
5444:
When the net force on the system is zero, the torque measured from any point in space is the same. For example, the torque on a current-carrying loop in a uniform magnetic field is the same regardless of the point of reference. If the net force
5308:
mentioned above. The problem with this definition is that it does not give the direction of the torque but only the magnitude, and hence it is difficult to use in three-dimensional cases. If the force is perpendicular to the displacement vector
4020:
2692:
3483:
3897:
4997:
3573:
2874:
1649:
5408:, not only must the sum of the forces be zero, but also the sum of the torques (moments) about any point. For a two-dimensional situation with horizontal and vertical forces, the sum of the forces requirement is two equations:
3355:
2998:
3875:
4425:
2559:
4592:
2322:
3178:
5361:
4771:
of rotation is the product of the radius with the angle covered. That is: linear distance = radius × angular distance. And by definition, linear distance = linear speed × time = radius × angular speed × time.
5557:
4789:
208:
4220:(denoted as in-lb). Practitioners depend on context and the hyphen in the abbreviation to know that these refer to torque and not to energy or moment of mass (as the symbolism ft-lb would properly imply).
2285:
5226:
3107:
2497:{\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times {\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {r} }{\mathrm {d} t}}\times \mathbf {p} .}
5296:
2368:
5012:
1129:", which suggest more complex ideas. The single notion of a twist applied to turn a shaft is better than the more complex notion of applying a linear force (or a pair of forces) with a certain leverage.
2170:
2254:
for point particles, and is valid for any type of trajectory. In some simple cases like a rotating disc, where only the moment of inertia on rotating axis is, the rotational Newton's second law can be
276:
3647:
2900:
is not universally recognized but is commonly used. There is not a universally accepted lexicon to indicate the successive derivatives of rotatum, even if sometimes various proposals have been made.
3490:
1697:
1311:
3804:{\displaystyle {\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}=\left|{\boldsymbol {\tau }}\right|\left|\mathrm {d} {\boldsymbol {\theta }}\right|\cos 0=\tau \,\mathrm {d} \theta }
3411:
5313:, the moment arm will be equal to the distance to the centre, and torque will be a maximum for the given force. The equation for the magnitude of a torque, arising from a perpendicular force:
1133:
Today, torque is referred to using different vocabulary depending on geographical location and field of study. This article follows the definition used in US physics in its usage of the word
4302:
4293:
1282:: if the fingers of the right hand are curled from the direction of the lever arm to the direction of the force, then the thumb points in the direction of the torque. It follows that the
5799:
Torque can be multiplied via three methods: by locating the fulcrum such that the length of a lever is increased; by using a longer lever; or by the use of a speed-reducing gearset or
5494:
1298:
direction is determined by the right-hand rule. Therefore any force directed parallel to the particle's position vector does not produce a torque. The magnitude of torque applied to a
3384:
3284:
36:
3440:
1413:
1027:
4951:
5552:
5523:
300:
4775:
By the definition of torque: torque = radius × force. We can rearrange this to determine force = torque ÷ radius. These two values can be substituted into the definition of
1603:
5465:
3433:
2675:
2653:
1489:
1457:
6998:
2552:
2530:
3290:
4201:. This means that the dimensional equivalence of the newton-metre and the joule may be applied in the former but not in the latter case. This problem is addressed in
3642:, but as per the definition of torque, and since the parameter of integration has been changed from linear displacement to angular displacement, the equation becomes
1568:
1522:
4748:
The constant below (in foot-pounds per minute) changes with the definition of the horsepower; for example, using metric horsepower, it becomes approximately 32,550.
3221:
2934:
1735:
1433:
1306:
connecting the point about which the torque is being measured to the point of force application, and the angle between the force and lever arm vectors. In symbols:
101:
3816:
3635:{\displaystyle \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} =\mathbf {r} \times \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}}
3231:(this is equivalent to the linear case where the power injected by a force depends only on the instantaneous speed – not on the resulting acceleration, if any).
3257:
6390:
7088:
2825:
4131:{\displaystyle \mathbf {r} _{1}\times \mathbf {F} _{1}+\mathbf {r} _{2}\times \mathbf {F} _{2}+\ldots +\mathbf {r} _{N}\times \mathbf {F} _{N}=\mathbf {0} .}
3144:
5318:
2782:{\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} _{\mathrm {net} }={\boldsymbol {\tau }}_{\mathrm {net} }.}
2920:. Similarly, if torque is allowed to act through an angular displacement, it is doing work. Mathematically, for rotation about a fixed axis through the
5002:
pounds-force per minute. The horsepower form of the equation is then derived by applying the conversion factor 33,000 ft⋅lbf/min per horsepower:
4006:{\displaystyle \tau =\mathbf {r} _{1}\times \mathbf {F} _{1}+\mathbf {r} _{2}\times \mathbf {F} _{2}+\ldots +\mathbf {r} _{N}\times \mathbf {F} _{N}.}
6358:
6218:
5730:
3892:
of the same name) states that the resultant torques due to several forces applied to about a point is equal to the sum of the contributing torques:
2257:
3052:
5253:
2335:
1258:) is its torque. Therefore, torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the
6277:
966:
5749:). The input power provided by the cyclist is equal to the product of angular speed (i.e. the number of pedal revolutions per minute times 2
2290:
1666:
5979:
4202:
555:
3716:
If the torque and the angular displacement are in the same direction, then the scalar product reduces to a product of magnitudes; i.e.,
6383:
674:
158:
5181:
4571:{\displaystyle P_{\rm {W}}={\frac {\tau _{\rm {N{\cdot }m}}\cdot 2\pi _{\rm {rad/rev}}\cdot \nu _{\rm {rev/min}}}{\rm {60~s/min}}}}
647:
6047:
4257:
6002:
2624:{\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} +\mathbf {v} \times \mathbf {p} }
4739:{\displaystyle P_{\rm {hp}}={\frac {\tau _{\rm {lbf{\cdot }ft}}\cdot 2\pi _{\rm {rad/rev}}\cdot \nu _{\rm {rev/min}}}{33,000}}.}
4587:(mechanical) for power, foot-pounds (lbf⋅ft) for torque and rpm for rotational speed. This results in the formula changing to:
232:
6194:
6376:
6323:
6301:
4015:
From this it follows that the torques resulting from N number of forces acting around a pivot on an object are balanced when
5635:{\displaystyle {\boldsymbol {\tau }}_{2}={\boldsymbol {\tau }}_{1}+(\mathbf {r} _{2}-\mathbf {r} _{1})\times \mathbf {F} }
4232:(unit: revolution per minute or second) is used in place of angular speed (unit: radian per second), we must multiply by 2
1121:(around an axis). It is better to use a term which treats this action as a single definite entity than to use terms like "
3389:
629:
4189:, which is the unit of energy, the latter can never used for torque. In the case of torque, the unit is assigned to a
6175:
6125:
6092:
5902:
3885:
959:
2677:
is zero because velocity and momentum are parallel, so the second term vanishes. Therefore, torque on a particle is
1058:
from the fulcrum, for example, exerts the same torque as a force of one newton applied six metres from the fulcrum.
7124:
7099:
7060:
5823:
2243:{\displaystyle {d{\boldsymbol {\hat {e_{i}}}} \over dt}={\boldsymbol {\omega }}\times {\boldsymbol {\hat {e_{i}}}}}
921:
5248:
A very useful special case, often given as the definition of torque in fields other than physics, is as follows:
3707:{\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}{\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}}
295:
1463:(a vector from the point about which the torque is being measured to the point where the force is applied), and
7395:
6350:
6282:
Demonstration that, as in most US industrial settings, the torque ranges are given in ft-lb rather than lbf-ft.
5470:
4212:(lbf-ft), or, for small values, the pound inch (lbf-in). In the US, torque is most commonly referred to as the
3558:{\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} }
550:
290:
5785:
of the road wheels is decreased while the torque is increased, product of which (i.e. power) does not change.
3362:
3262:
1381:{\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \implies \tau =rF_{\perp }=rF\sin \theta }
6402:
5769:, which in turn conveys the received power to the road as the output power of the bicycle. Depending on the
1396:
1010:
952:
939:
700:
623:
545:
388:
6141:
6355:
6211:
619:
420:
398:
5762:
4411:{\displaystyle P_{\rm {W}}=\tau _{\rm {N{\cdot }m}}\cdot 2\pi _{\rm {rad/rev}}\cdot \nu _{\rm {rev/s}}}
839:
728:
654:
514:
447:
151:
5528:
5499:
7410:
7031:
6836:
6690:
6142:"Survey of Human–Robot Collaboration in Industrial Settings: Awareness, Intelligence, and Compliance"
3029:
593:
4228:
A conversion factor may be necessary when using different units of power or torque. For example, if
2682:
1262:
of a force from the point around which it is being determined. In three dimensions, the torque is a
6803:
5681:
output of an engine is expressed as its torque multiplied by the angular speed of the drive shaft.
1086:
869:
713:
5936:
5916:
5448:
3416:
2658:
2636:
1472:
1440:
6814:
5955:
5300:
The construction of the "moment arm" is shown in the figure to the right, along with the vectors
3142:
3050:
2932:
819:
583:
20:
6974:
6874:
6019:
1153:
859:
5833:
5658:
5433:
3478:{\displaystyle \mathrm {d} \mathbf {s} =\mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} }
2909:
2686:
2251:
1141:
864:
681:
6167:
5976:
2535:
2513:
6949:
6819:
6557:
6242:
Page, Chester H. (1979). "Rebuttal to de Boer's 'Group properties of quantities and units'".
3889:
3568:
1553:
1507:
874:
849:
535:
353:
5781:
pair. By using a larger rear gear, or by switching to a lower gear in multi-speed bicycles,
3206:
1163:
7271:
7196:
6824:
6596:
6251:
5717:: Bicycles are typically composed of two road wheels, front and rear gears (referred to as
4992:{\displaystyle {\text{power}}={\text{torque}}\cdot 2\pi \cdot {\text{rotational speed}}.\,}
4182:
2506:
This result can easily be proven by splitting the vectors into components and applying the
1418:
1279:
1090:
894:
854:
762:
758:
750:
740:
530:
523:
279:
86:
1704:
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8:
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4146:
1117:
669:
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588:
333:
328:
323:
223:
126:
65:
in a system which has rotation constrained to only one plane (forces and moments due to
6255:
5741:, the person who rides the bicycle, provides the input power by turning pedals, thereby
2869:{\displaystyle \mathbf {P} ={\frac {\mathrm {d} {\boldsymbol {\tau }}}{\mathrm {d} t}},}
2685:
of its angular momentum with respect to time. If multiple forces are applied, according
6118:
Physics for
Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics
6043:
5858:
5405:
4190:
3242:
1644:{\displaystyle {\boldsymbol {\tau }}={\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}}
1122:
1067:
799:
540:
415:
383:
343:
5999:
7400:
7021:
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6333:
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318:
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7078:
7044:
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6719:
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6259:
5848:
5813:
5726:
5693:
for a small car). One can measure the varying torque output over that range with a
5686:
5654:
4229:
4198:
3259:
is given by integrating the force with respect to an elemental linear displacement
3200:
3022:
1746:
1595:
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1039:
904:
884:
829:
824:
770:
745:
600:
458:
403:
378:
59:
6320:
5729:
if the bicycle's transmission system allows multiple gear ratios to be used (i.e.
5653:
Torque curve of a motorcycle ("BMW K 1200 R 2005"). The horizontal axis shows the
1081:
7390:
7353:
7313:
6362:
6330:
An article showing how power, torque, and gearing affect a vehicle's performance.
6327:
6198:
6006:
5983:
5828:
5678:
4776:
4168:
3350:{\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} \mathbf {s} }
3131:
2917:
2375:
1545:
1460:
1278:
and the force vector. The direction of the torque can be determined by using the
1267:
899:
844:
794:
789:
708:
52:
7116:
7052:
1502:
is the amount of force directed perpendicularly to the position of the particle,
7405:
7297:
7261:
7186:
6967:
6854:
6744:
6645:
6368:
5853:
5818:
5702:
3224:
2921:
1259:
1250:
A force applied perpendicularly to a lever multiplied by its distance from the
1030:
926:
834:
735:
452:
4205:, which treats the radian as a base unit rather than as a dimensionless unit.
2993:{\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \ \mathrm {d} \theta ,}
1174:
7384:
7171:
7039:
6753:
6102:
5868:
5863:
5746:
5734:
5722:
4768:
3870:{\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \,\mathrm {d} \theta }
3125:
1529:
1525:
1271:
1051:
814:
641:
130:
7246:
7132:
7068:
6793:
6576:
6487:
5698:
5666:
4177:
3239:
The work done by a variable force acting over a finite linear displacement
2507:
1579:
1263:
879:
804:
493:
373:
139:
6345:
5713:
In practice, the relationship between power and torque can be observed in
1294:
vectors and defines the plane in which the two vectors lie. The resulting
6614:
5694:
4249:
2164:
1089:
and appeared in print in April, 1884. Usage is attested the same year by
4755:
per hour for power) would require a different custom conversion factor.
2382:
is the position vector from the origin. The time-derivative of this is:
5770:
5662:
4584:
1299:
1169:
992:
664:
338:
2317:{\displaystyle {\boldsymbol {\alpha }}={\dot {\boldsymbol {\omega }}}}
6707:
6634:
6622:
5718:
3173:{\displaystyle P={\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }},}
1594:
The net torque on a body determines the rate of change of the body's
1255:
984:
686:
6263:
5803:. Such a mechanism multiplies torque, as rotation rate is reduced.
5356:{\displaystyle \tau =({\text{distance to centre}})({\text{force}}).}
4580:
where rotational speed is in revolutions per minute (rpm, rev/min).
4181:, is properly denoted N⋅m, as the unit for torque; although this is
7011:
6910:
6664:
6523:
6477:
5938:
Dynamo-electric machinery: A Manual For
Students Of Electrotechnics
5800:
5758:
5369:
4150:
2332:
The definition of angular momentum for a single point particle is:
1575:
605:
488:
463:
70:
35:
5436:
equilibrium problems in two-dimensions, three equations are used.
7337:
5843:
5738:
5714:
5392:
2805:
980:
578:
431:
348:
111:
66:
6087:(3rd technology update ed.). Boston: Pearson. p. 199.
203:{\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-2}}
7251:
7176:
7154:
6608:
6507:
6472:
5707:
5674:
5649:
4194:
4164:
1570:
is the angle between the force vector and the lever arm vector.
1108:
637:
393:
2280:{\displaystyle {\boldsymbol {\tau }}=I{\boldsymbol {\alpha }}}
7285:
7210:
7144:
6748:
6654:
6649:
6586:
6561:
5941:(4th ed.). New York, Harvard publishing co. p. 108.
5766:
5240:
5221:{\displaystyle 5252.113122\approx {\frac {33,000}{2\pi }}.\,}
4186:
3102:{\displaystyle E_{\mathrm {r} }={\tfrac {1}{2}}I\omega ^{2},}
2913:
2887:
2510:. But because the rate of change of linear momentum is force
1251:
1186:
is applied to the particle, only the perpendicular component
1103:
1077:
1055:
996:
473:
468:
410:
41:
5291:{\displaystyle \tau =({\text{moment arm}})({\text{force}}).}
2363:{\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} }
7367:
7327:
6900:
6566:
6497:
6462:
5975:
by
Hendricks, Subramony, and Van Blerk, Chinappi page 148,
5754:
5685:
engines produce useful torque only over a limited range of
3135:
2817:
478:
441:
6339:
4420:
Dividing by 60 seconds per minute gives us the following.
4163:
and those fundamental dimensions are the same as that for
2327:
1152:. This terminology can be traced back to at least 1811 in
1115:
may be defined as that which produces or tends to produce
5690:
4752:
1589:
1034:
271:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
5669:) that the engine is capable of providing at that speed.
5391:
in the direction of that torque. This causes the top to
6294:
5366:
the plane of movement and perpendicular to the wrench.
4172:
3487:
Substitution in the above expression for work, , gives
4583:
Some people (e.g., American automotive engineers) use
3072:
2538:
2516:
1707:
1692:{\displaystyle \mathbf {L} =I{\boldsymbol {\omega }},}
6977:
6083:
Knight, Randall; Jones, Brian; Field, Stuart (2016).
5560:
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235:
161:
89:
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is turning, and the vertical axis is the torque (in
1302:
depends on three quantities: the force applied, the
1170:
Definition and relation to other physical quantities
6217:. Bureau International des Poids et Mesures. 2019.
5673:Torque forms part of the basic specification of an
4236:radians per revolution. In the following formulas,
3406:{\displaystyle \mathrm {d} {\boldsymbol {\theta }}}
3386:is related to a corresponding angular displacement
6992:
6159:
6153:
6151:
5634:
5546:
5517:
5488:
5459:
5355:
5290:
5220:
5168:
4991:
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4410:
4287:
4208:The traditional imperial units for torque are the
4130:
4005:
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3477:
3427:
3405:
3378:
3349:
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2916:is allowed to act through a distance, it is doing
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1427:
1407:
1380:
1021:
270:
202:
95:
2234:
2193:
7382:
6398:
6157:
6082:
5230:
1085:, 'to twist') is said to have been suggested by
6335:Torque and Angular Momentum in Circular Motion
6148:
6067:
3359:However, the infinitesimal linear displacement
3021:represent (respectively) the initial and final
2532:and the rate of change of position is velocity
1182:relative to its axis of rotation. When a force
6061:
5777:pair is converted to a (torque, angular speed)
6384:
5914:
5373:The torque caused by the two opposing forces
1661:is time. For the motion of a point particle,
960:
5893:Serway, R. A. and Jewett, J. W. Jr. (2003).
5745:the front sprocket (commonly referred to as
4288:{\displaystyle P=\tau \cdot 2\pi \cdot \nu }
4223:
2912:can also be used to understand torque. If a
2250:This equation is the rotational analogue of
1582:(N⋅m). For more on the units of torque, see
1157:
6158:Kleppner, Daniel; Kolenkow, Robert (1973).
5930:
5928:
5918:Collected Papers in Physics and Engineering
4942:distance are increased proportionately by 2
4216:(denoted as either lb-ft or ft-lb) and the
2891:
1107:is that which produces or tends to produce
6391:
6377:
5994:Kane, T.R. Kane and D.A. Levinson (1985).
5439:
1340:
1336:
1097:. Thompson motivates the term as follows:
967:
953:
34:
6072:. John Wiley & Sons. pp. 184–85.
6068:Halliday, David; Resnick, Robert (1970).
5950:
5948:
5773:of the bicycle, a (torque, angular speed)
5489:{\displaystyle {\boldsymbol {\tau }}_{1}}
5217:
4988:
3858:
3792:
1495:is the magnitude of the force vector and
6270:
6204:
5966:
5934:
5925:
5689:(typically from around 1,000–6,000
5648:
5387:causes a change in the angular momentum
5368:
5239:
3884:The principle of moments, also known as
3567:The expression inside the integral is a
3379:{\displaystyle \mathrm {d} \mathbf {s} }
3279:{\displaystyle \mathrm {d} \mathbf {s} }
2799:
1467:is the magnitude of the position vector,
1173:
6291:
6184:
6018:
5915:Thomson, James; Larmor, Joseph (1912).
5578:
5563:
5476:
3879:
3768:
3749:
3737:
3724:
3700:
3687:
3628:
3591:
3543:
3463:
3399:
3163:
3155:
2846:
2758:
2328:Proof of the equivalence of definitions
2305:
2295:
2273:
2262:
2229:
2225:
2214:
2188:
2184:
2144:
2130:
2117:
2082:
2023:
1964:
1916:
1865:
1814:
1760:
1682:
1608:
1401:
1316:
1015:
7383:
6115:
5945:
5765:transmits the input power to the road
1590:Relationship with the angular momentum
1246:and is directed outward from the page.
1007:). The symbol for torque is typically
186:
172:
164:
6372:
6085:College Physics: A Strategic Approach
5399:
5235:
3141:
3049:
2931:
2792:each point within the mass, and then
1408:{\displaystyle {\boldsymbol {\tau }}}
1022:{\displaystyle {\boldsymbol {\tau }}}
649:Newton's law of universal gravitation
6278:"Dial Torque Wrenches from Grainger"
6241:
5935:Thompson, Silvanus Phillips (1893).
5895:Physics for Scientists and Engineers
5788:
1101:Just as the Newtonian definition of
1042:of force, it is commonly denoted by
6346:An interactive simulation of torque
5988:
5424:, and the torque a third equation:
1657:is the angular momentum vector and
1166:of Poisson's work appears in 1842.
630:Mechanics of planar particle motion
238:
13:
6365:An order-of-magnitude interactive.
6212:"SI brochure Ed. 9, Section 2.3.4"
4713:
4710:
4707:
4699:
4696:
4693:
4678:
4675:
4672:
4664:
4661:
4658:
4640:
4637:
4629:
4626:
4623:
4605:
4602:
4562:
4559:
4556:
4548:
4534:
4531:
4528:
4520:
4517:
4514:
4499:
4496:
4493:
4485:
4482:
4479:
4461:
4453:
4435:
4402:
4394:
4391:
4388:
4373:
4370:
4367:
4359:
4356:
4353:
4335:
4327:
4312:
3860:
3794:
3763:
3732:
3695:
3623:
3586:
3538:
3458:
3445:
3394:
3367:
3338:
3267:
3062:
3036:also represents the change in the
2980:
2904:Relationship with power and energy
2896:meaning 'to rotate', but the term
2853:
2841:
2770:
2767:
2764:
2747:
2744:
2741:
2712:
2700:
2579:
2567:
2473:
2461:
2444:
2432:
2407:
2395:
1772:
1769:
1766:
1631:
1619:
1528:, which produces a vector that is
1178:A particle is located at position
14:
7422:
6314:
6292:Erjavec, Jack (22 January 2010).
6025:Traité de mécanique, tome premier
5996:Dynamics, Theory and Applications
5697:, and show it as a torque curve.
5644:
4946:in the above derivation to give:
7232:
6296:. Cengage Learning. p. 38.
5921:. University Press. p. civ.
5733:), all of which attached to the
5628:
5611:
5596:
5547:{\displaystyle \mathbf {r} _{2}}
5534:
5525:, then the torque measured from
5518:{\displaystyle \mathbf {r} _{1}}
5505:
5453:
4121:
4107:
4092:
4071:
4056:
4041:
4026:
3990:
3975:
3954:
3939:
3924:
3909:
3615:
3607:
3599:
3578:
3551:
3530:
3471:
3450:
3421:
3372:
3343:
3330:
3272:
2830:
2735:
2726:
2705:
2663:
2641:
2617:
2609:
2601:
2593:
2572:
2540:
2518:
2487:
2466:
2437:
2421:
2400:
2356:
2348:
2340:
2120:
2086:
2027:
1968:
1920:
1869:
1818:
1671:
1624:
1477:
1445:
1332:
1324:
999:. It is also referred to as the
934:
933:
920:
253:
6415:Linear/translational quantities
6285:
6235:
6224:from the original on 2020-07-26
6134:
6120:(5th ed.). W. H. Freeman.
6109:
6076:
6050:from the original on 2007-08-19
1435:is the magnitude of the torque,
1193:produces a torque. This torque
6036:
6012:
5908:
5887:
5621:
5591:
5347:
5339:
5336:
5328:
5282:
5274:
5271:
5263:
4882:
4862:
4751:The use of other units (e.g.,
2886:This word is derived from the
2633:The cross product of momentum
2148:
2137:
2091:
2032:
1973:
1925:
1874:
1823:
1749:pseudovector. It follows that
1337:
1:
6420:Angular/rotational quantities
5880:
5231:Special cases and other facts
4758:
3888:(not to be confused with the
2655:with its associated velocity
1286:is perpendicular to both the
556:Koopman–von Neumann mechanics
6162:An Introduction to Mechanics
6044:"Right Hand Rule for Torque"
5496:is the torque measured from
5460:{\displaystyle \mathbf {F} }
3428:{\displaystyle \mathbf {r} }
2670:{\displaystyle \mathbf {v} }
2648:{\displaystyle \mathbf {p} }
1484:{\displaystyle \mathbf {F} }
1452:{\displaystyle \mathbf {r} }
1038:. When being referred to as
624:Non-inertial reference frame
16:Turning force around an axis
7:
6244:American Journal of Physics
5806:
4763:For a rotating object, the
1144:, torque is referred to as
551:Appell's equation of motion
421:Inertial frame of reference
10:
7427:
6993:{\displaystyle {\dot {m}}}
6417:
5792:
2163:using the derivative of a
1583:
1065:
1061:
18:
6691:specific angular momentum
6419:
6414:
6409:
5960:Oxford English Dictionary
4224:Conversion to other units
3038:rotational kinetic energy
2547:{\textstyle \mathbf {v} }
2525:{\textstyle \mathbf {F} }
1415:is the torque vector and
1095:Dynamo-Electric Machinery
150:
137:
120:
110:
78:
33:
28:
6166:. McGraw-Hill. pp.
5753:) and the torque at the
4183:dimensionally equivalent
4140:
3234:
1093:in the first edition of
714:Rotating reference frame
546:Hamilton–Jacobi equation
6815:rotational acceleration
6321:"Horsepower and Torque"
6070:Fundamentals of Physics
5973:Physics for Engineering
5897:. 6th ed. Brooks Cole.
5440:Net force versus torque
5404:For an object to be in
4252:) is rotational speed.
1563:{\displaystyle \theta }
1517:{\displaystyle \times }
1148:, usually shortened to
655:Newton's laws of motion
515:Newton's laws of motion
21:Torque (disambiguation)
6994:
5834:Mechanical equilibrium
5670:
5636:
5548:
5519:
5490:
5461:
5434:statically determinate
5396:
5357:
5292:
5245:
5222:
5170:
4993:
4925:
4740:
4572:
4412:
4289:
4203:orientational analysis
4197:, it is assigned to a
4132:
4007:
3871:
3805:
3708:
3636:
3559:
3479:
3429:
3413:and the radius vector
3407:
3380:
3351:
3280:
3253:
3217:
3216:{\displaystyle \cdot }
3174:
3103:
3046:of the body, given by
2994:
2910:conservation of energy
2892:
2877:
2870:
2796:over the entire mass.
2783:
2671:
2649:
2625:
2548:
2526:
2498:
2364:
2318:
2281:
2244:
2155:
1731:
1693:
1645:
1564:
1518:
1485:
1453:
1429:
1409:
1382:
1247:
1164:An English translation
1158:
1142:mechanical engineering
1131:
1080:
1023:
682:Simple harmonic motion
595:Euler's laws of motion
389:D'Alembert's principle
272:
204:
97:
7396:Mechanical quantities
6995:
6351:Torque Unit Converter
6116:Tipler, Paul (2004).
6020:Poisson, Siméon-Denis
5652:
5637:
5549:
5520:
5491:
5462:
5372:
5358:
5293:
5243:
5223:
5171:
4994:
4926:
4741:
4573:
4413:
4290:
4175:literature indicates
4133:
4008:
3872:
3806:
3709:
3637:
3569:scalar triple product
3560:
3480:
3430:
3408:
3381:
3352:
3281:
3254:
3218:
3175:
3134:is the work per unit
3104:
3030:work–energy principle
2995:
2871:
2821:
2812:is the derivative of
2800:Derivatives of torque
2784:
2672:
2650:
2626:
2549:
2527:
2499:
2365:
2319:
2282:
2245:
2156:
1732:
1730:{\textstyle I=mr^{2}}
1694:
1646:
1565:
1519:
1491:is the force vector,
1486:
1454:
1430:
1428:{\displaystyle \tau }
1410:
1383:
1270:, it is given by the
1177:
1099:
1024:
1003:(also abbreviated to
536:Hamiltonian mechanics
354:Statistical mechanics
273:
205:
98:
96:{\displaystyle \tau }
40:Relationship between
6975:
6825:angular acceleration
6597:angular displacement
5727:derailleur mechanism
5558:
5529:
5500:
5471:
5449:
5432:. That is, to solve
5319:
5254:
5182:
5008:
4952:
4785:
4593:
4426:
4303:
4258:
4021:
3898:
3880:Principle of moments
3817:
3720:
3648:
3574:
3491:
3441:
3417:
3390:
3363:
3291:
3263:
3243:
3207:
3145:
3053:
3028:It follows from the
2935:
2928:can be expressed as
2826:
2693:
2659:
2637:
2560:
2536:
2514:
2388:
2336:
2291:
2258:
2171:
1755:
1705:
1667:
1604:
1554:
1508:
1473:
1441:
1419:
1397:
1312:
1280:right hand grip rule
1154:Siméon Denis Poisson
1140:In the UK and in US
1091:Silvanus P. Thompson
1011:
759:Angular acceleration
751:Rotational frequency
531:Lagrangian mechanics
524:Analytical mechanics
280:Second law of motion
233:
159:
87:
19:For other uses, see
6915:weighted position:
6732:rotational velocity
6680:kinematic viscosity
6400:Classical mechanics
6256:1979AmJPh..47..820P
6192:official SI website
5874:Torsion (mechanics)
5839:Rigid body dynamics
5824:Conversion of units
5731:multi-speed bicycle
5683:Internal-combustion
3890:geometrical theorem
3854:
3685:
3528:
3328:
2972:
2687:Newton's second law
2252:Newton's second law
1276:displacement vector
1254:(the length of the
1159:Traité de mécanique
1111:(along a line), so
1050:. A force of three
995:analogue of linear
611:Harmonic oscillator
589:Equations of motion
224:Classical mechanics
218:Part of a series on
6990:
6361:2021-05-08 at the
6326:2007-03-28 at the
6197:2021-04-19 at the
6005:2015-06-19 at the
5982:2017-07-11 at the
5859:Torque screwdriver
5671:
5632:
5544:
5515:
5486:
5457:
5406:static equilibrium
5400:Static equilibrium
5397:
5353:
5333:distance to centre
5288:
5246:
5244:Moment arm diagram
5236:Moment arm formula
5218:
5166:
5164:
4989:
4921:
4919:
4853:
4736:
4568:
4408:
4285:
4128:
4003:
3886:Varignon's theorem
3867:
3826:
3801:
3704:
3657:
3632:
3555:
3500:
3475:
3425:
3403:
3376:
3347:
3300:
3276:
3249:
3213:
3170:
3099:
3081:
2990:
2944:
2866:
2779:
2667:
2645:
2621:
2544:
2522:
2494:
2374:is the particle's
2360:
2314:
2277:
2240:
2151:
1727:
1689:
1641:
1578:for torque is the
1560:
1514:
1481:
1449:
1425:
1405:
1378:
1248:
1068:Couple (mechanics)
1019:
927:Physics portal
541:Routhian mechanics
416:Frame of reference
268:
200:
141:SI base units
93:
7378:
7377:
7373:
7372:
6987:
6940:moment of inertia
6356:A feel for torque
6303:978-1-4354-3933-7
6280:. Grainger. 2020.
5795:Torque multiplier
5789:Torque multiplier
5757:of the bicycle's
5721:) meshing with a
5687:rotational speeds
5467:is not zero, and
5345:
5334:
5280:
5269:
5212:
5160:
5146:
5138:
5120:
5117:
5116:
5111:
5103:
5083:
5074:
5073:
5068:
5058:
5047:
5030:
5018:
4983:
4966:
4958:
4912:
4904:
4889:
4874:
4852:
4848:
4824:
4823:
4818:
4810:
4795:
4731:
4566:
4547:
3252:{\displaystyle s}
3118:moment of inertia
3080:
3023:angular positions
2978:
2861:
2720:
2587:
2481:
2452:
2415:
2311:
2237:
2208:
2196:
2123:
2106:
2094:
2047:
2035:
1988:
1976:
1928:
1909:
1877:
1858:
1826:
1807:
1739:moment of inertia
1639:
977:
976:
724:Centrifugal force
719:Centripetal force
675:Euler's equations
660:Relative velocity
436:Moment of inertia
266:
240:
213:
212:
7418:
7411:Moment (physics)
7365:
7361:
7349:
7345:
7325:
7321:
7309:
7305:
7283:
7279:
7269:
7259:
7244:
7240:
7230:
7208:
7204:
7194:
7184:
7169:
7165:
7152:
7128:
7122:
7114:
7103:
7097:
7086:
7079:angular momentum
7064:
7058:
7050:
7035:
7029:
7019:
7006:
7000:
6999:
6997:
6996:
6991:
6989:
6988:
6980:
6953:
6947:
6931:
6908:
6889:
6884:
6862:
6840:
6834:
6817:
6801:
6779:
6773:
6764:angular velocity
6761:
6742:
6741:
6728:
6727:
6720:rotational speed
6716:
6715:
6698:
6687:
6672:
6662:
6643:
6642:
6625:
6620:
6606:
6594:
6574:
6555:
6554:
6548:
6542:
6531:
6505:
6485:
6470:
6454:
6447:
6412:
6411:
6393:
6386:
6379:
6370:
6369:
6308:
6307:
6289:
6283:
6281:
6274:
6268:
6267:
6239:
6233:
6232:
6230:
6229:
6223:
6216:
6208:
6202:
6188:
6182:
6181:
6165:
6155:
6146:
6145:
6138:
6132:
6131:
6113:
6107:
6106:
6080:
6074:
6073:
6065:
6059:
6058:
6056:
6055:
6040:
6034:
6033:
6016:
6010:
5992:
5986:
5970:
5964:
5963:
5952:
5943:
5942:
5932:
5923:
5922:
5912:
5906:
5891:
5849:Torque converter
5761:. The bicycle's
5655:rotational speed
5641:
5639:
5638:
5633:
5631:
5620:
5619:
5614:
5605:
5604:
5599:
5587:
5586:
5581:
5572:
5571:
5566:
5553:
5551:
5550:
5545:
5543:
5542:
5537:
5524:
5522:
5521:
5516:
5514:
5513:
5508:
5495:
5493:
5492:
5487:
5485:
5484:
5479:
5466:
5464:
5463:
5458:
5456:
5431:
5423:
5415:
5362:
5360:
5359:
5354:
5346:
5343:
5335:
5332:
5297:
5295:
5294:
5289:
5281:
5278:
5270:
5267:
5227:
5225:
5224:
5219:
5213:
5211:
5203:
5192:
5175:
5173:
5172:
5167:
5165:
5161:
5159:
5148:
5147:
5144:
5139:
5136:
5133:
5125:
5121:
5119:
5118:
5114:
5113:
5112:
5109:
5104:
5101:
5098:
5081:
5080:
5075:
5071:
5070:
5069:
5066:
5064:
5059:
5056:
5053:
5048:
5046:rotational speed
5045:
5031:
5028:
5019:
5016:
4998:
4996:
4995:
4990:
4984:
4982:rotational speed
4981:
4967:
4964:
4959:
4956:
4945:
4930:
4928:
4927:
4922:
4920:
4913:
4910:
4905:
4902:
4894:
4890:
4885:
4875:
4872:
4858:
4854:
4846:
4845:
4837:
4829:
4825:
4821:
4820:
4819:
4816:
4811:
4808:
4805:
4796:
4793:
4745:
4743:
4742:
4737:
4732:
4730:
4719:
4718:
4717:
4716:
4706:
4683:
4682:
4681:
4671:
4645:
4644:
4643:
4636:
4615:
4610:
4609:
4608:
4577:
4575:
4574:
4569:
4567:
4565:
4555:
4545:
4540:
4539:
4538:
4537:
4527:
4504:
4503:
4502:
4492:
4466:
4465:
4464:
4460:
4445:
4440:
4439:
4438:
4417:
4415:
4414:
4409:
4407:
4406:
4405:
4401:
4378:
4377:
4376:
4366:
4340:
4339:
4338:
4334:
4317:
4316:
4315:
4294:
4292:
4291:
4286:
4235:
4230:rotational speed
4162:
4159:
4156:
4137:
4135:
4134:
4129:
4124:
4116:
4115:
4110:
4101:
4100:
4095:
4080:
4079:
4074:
4065:
4064:
4059:
4050:
4049:
4044:
4035:
4034:
4029:
4012:
4010:
4009:
4004:
3999:
3998:
3993:
3984:
3983:
3978:
3963:
3962:
3957:
3948:
3947:
3942:
3933:
3932:
3927:
3918:
3917:
3912:
3876:
3874:
3873:
3868:
3863:
3853:
3852:
3851:
3841:
3840:
3839:
3810:
3808:
3807:
3802:
3797:
3776:
3772:
3771:
3766:
3756:
3752:
3740:
3735:
3727:
3713:
3711:
3710:
3705:
3703:
3698:
3690:
3684:
3683:
3682:
3672:
3671:
3670:
3641:
3639:
3638:
3633:
3631:
3626:
3618:
3610:
3602:
3594:
3589:
3581:
3564:
3562:
3561:
3556:
3554:
3546:
3541:
3533:
3527:
3526:
3525:
3515:
3514:
3513:
3484:
3482:
3481:
3476:
3474:
3466:
3461:
3453:
3448:
3434:
3432:
3431:
3426:
3424:
3412:
3410:
3409:
3404:
3402:
3397:
3385:
3383:
3382:
3377:
3375:
3370:
3356:
3354:
3353:
3348:
3346:
3341:
3333:
3327:
3326:
3325:
3315:
3314:
3313:
3285:
3283:
3282:
3277:
3275:
3270:
3258:
3256:
3255:
3250:
3222:
3220:
3219:
3214:
3201:angular velocity
3180:
3177:
3176:
3171:
3166:
3158:
3120:of the body and
3109:
3106:
3105:
3100:
3095:
3094:
3082:
3073:
3067:
3066:
3065:
3000:
2997:
2996:
2991:
2983:
2976:
2971:
2970:
2969:
2959:
2958:
2957:
2895:
2875:
2873:
2872:
2867:
2862:
2860:
2856:
2850:
2849:
2844:
2838:
2833:
2816:with respect to
2788:
2786:
2785:
2780:
2775:
2774:
2773:
2761:
2752:
2751:
2750:
2738:
2729:
2721:
2719:
2715:
2709:
2708:
2703:
2697:
2683:first derivative
2676:
2674:
2673:
2668:
2666:
2654:
2652:
2651:
2646:
2644:
2630:
2628:
2627:
2622:
2620:
2612:
2604:
2596:
2588:
2586:
2582:
2576:
2575:
2570:
2564:
2553:
2551:
2550:
2545:
2543:
2531:
2529:
2528:
2523:
2521:
2503:
2501:
2500:
2495:
2490:
2482:
2480:
2476:
2470:
2469:
2464:
2458:
2453:
2451:
2447:
2441:
2440:
2435:
2429:
2424:
2416:
2414:
2410:
2404:
2403:
2398:
2392:
2369:
2367:
2366:
2361:
2359:
2351:
2343:
2323:
2321:
2320:
2315:
2313:
2312:
2304:
2298:
2286:
2284:
2283:
2278:
2276:
2265:
2249:
2247:
2246:
2241:
2239:
2238:
2233:
2232:
2223:
2217:
2209:
2207:
2199:
2198:
2197:
2192:
2191:
2182:
2175:
2160:
2158:
2157:
2152:
2147:
2133:
2125:
2124:
2116:
2107:
2105:
2097:
2096:
2095:
2090:
2089:
2080:
2073:
2071:
2070:
2061:
2060:
2048:
2046:
2038:
2037:
2036:
2031:
2030:
2021:
2014:
2012:
2011:
2002:
2001:
1989:
1987:
1979:
1978:
1977:
1972:
1971:
1962:
1955:
1953:
1952:
1943:
1942:
1930:
1929:
1924:
1923:
1914:
1911:
1910:
1905:
1904:
1895:
1892:
1891:
1879:
1878:
1873:
1872:
1863:
1860:
1859:
1854:
1853:
1844:
1841:
1840:
1828:
1827:
1822:
1821:
1812:
1809:
1808:
1803:
1802:
1793:
1790:
1789:
1777:
1776:
1775:
1763:
1747:angular velocity
1736:
1734:
1733:
1728:
1726:
1725:
1698:
1696:
1695:
1690:
1685:
1674:
1650:
1648:
1647:
1642:
1640:
1638:
1634:
1628:
1627:
1622:
1616:
1611:
1596:angular momentum
1569:
1567:
1566:
1561:
1543:
1537:
1523:
1521:
1520:
1515:
1490:
1488:
1487:
1482:
1480:
1458:
1456:
1455:
1450:
1448:
1434:
1432:
1431:
1426:
1414:
1412:
1411:
1406:
1404:
1387:
1385:
1384:
1379:
1359:
1358:
1335:
1327:
1319:
1304:lever arm vector
1245:
1240:
1234:
1228:
1219:
1208:
1161:
1045:
1029:, the lowercase
1028:
1026:
1025:
1020:
1018:
969:
962:
955:
942:
937:
936:
929:
925:
924:
830:Johann Bernoulli
825:Daniel Bernoulli
746:Tangential speed
650:
626:
601:Fictitious force
596:
448:Mechanical power
438:
379:Angular momentum
277:
275:
274:
269:
267:
265:
257:
256:
247:
242:
241:
215:
214:
209:
207:
206:
201:
199:
198:
190:
189:
182:
181:
176:
175:
168:
167:
142:
127:pound-force-feet
102:
100:
99:
94:
73:not considered).
60:angular momentum
38:
26:
25:
7426:
7425:
7421:
7420:
7419:
7417:
7416:
7415:
7381:
7380:
7379:
7374:
7363:
7362:
7357:
7347:
7346:
7341:
7323:
7322:
7317:
7307:
7306:
7301:
7281:
7280:
7275:
7265:
7255:
7242:
7241:
7236:
7224:
7206:
7205:
7200:
7190:
7180:
7167:
7166:
7164:
7158:
7148:
7126:
7123:
7120:
7112:
7101:
7098:
7092:
7089:angular impulse
7082:
7062:
7059:
7056:
7048:
7033:
7030:
7025:
7015:
7004:
7001:
6979:
6978:
6976:
6973:
6972:
6971:
6951:
6948:
6943:
6916:
6909:
6904:
6887:
6885:
6878:
6863:
6858:
6838:
6835:
6828:
6818:
6813:
6802:
6797:
6777:
6774:
6767:
6757:
6743:
6735:
6730:
6723:
6718:
6711:
6706:
6699:
6694:
6689:
6683:
6673:
6668:
6658:
6644:
6638:
6633:
6621:
6618:
6613:
6607:
6600:
6590:
6575:
6570:
6560:
6550:
6544:
6538:
6533:
6527:
6506:
6501:
6486:
6481:
6471:
6466:
6450:
6443:
6405:
6397:
6363:Wayback Machine
6340:Project PHYSNET
6328:Wayback Machine
6317:
6312:
6311:
6304:
6290:
6286:
6276:
6275:
6271:
6264:10.1119/1.11704
6240:
6236:
6227:
6225:
6221:
6214:
6210:
6209:
6205:
6199:Wayback Machine
6189:
6185:
6178:
6156:
6149:
6140:
6139:
6135:
6128:
6114:
6110:
6095:
6081:
6077:
6066:
6062:
6053:
6051:
6042:
6041:
6037:
6017:
6013:
6007:Wayback Machine
5993:
5989:
5984:Wayback Machine
5971:
5967:
5954:
5953:
5946:
5933:
5926:
5913:
5909:
5892:
5888:
5883:
5878:
5829:Friction torque
5809:
5797:
5791:
5780:
5776:
5703:electric motors
5647:
5627:
5615:
5610:
5609:
5600:
5595:
5594:
5582:
5577:
5576:
5567:
5562:
5561:
5559:
5556:
5555:
5538:
5533:
5532:
5530:
5527:
5526:
5509:
5504:
5503:
5501:
5498:
5497:
5480:
5475:
5474:
5472:
5469:
5468:
5452:
5450:
5447:
5446:
5442:
5425:
5417:
5409:
5402:
5386:
5379:
5342:
5331:
5320:
5317:
5316:
5277:
5266:
5255:
5252:
5251:
5238:
5233:
5204:
5193:
5191:
5183:
5180:
5179:
5163:
5162:
5149:
5143:
5135:
5134:
5132:
5123:
5122:
5108:
5100:
5099:
5097:
5084:
5079:
5065:
5060:
5055:
5054:
5052:
5044:
5027:
5020:
5015:
5011:
5009:
5006:
5005:
4980:
4963:
4955:
4953:
4950:
4949:
4943:
4918:
4917:
4909:
4901:
4892:
4891:
4871:
4843:
4839:
4838:
4836:
4827:
4826:
4817:linear distance
4815:
4807:
4806:
4804:
4797:
4792:
4788:
4786:
4783:
4782:
4767:covered at the
4765:linear distance
4761:
4720:
4702:
4692:
4691:
4687:
4667:
4657:
4656:
4652:
4632:
4622:
4621:
4617:
4616:
4614:
4601:
4600:
4596:
4594:
4591:
4590:
4551:
4541:
4523:
4513:
4512:
4508:
4488:
4478:
4477:
4473:
4456:
4452:
4451:
4447:
4446:
4444:
4434:
4433:
4429:
4427:
4424:
4423:
4397:
4387:
4386:
4382:
4362:
4352:
4351:
4347:
4330:
4326:
4325:
4321:
4311:
4310:
4306:
4304:
4301:
4300:
4297:Showing units:
4259:
4256:
4255:
4250:Greek letter nu
4244:is torque, and
4233:
4226:
4160:
4157:
4154:
4153:, symbolically
4149:of force times
4145:Torque has the
4143:
4120:
4111:
4106:
4105:
4096:
4091:
4090:
4075:
4070:
4069:
4060:
4055:
4054:
4045:
4040:
4039:
4030:
4025:
4024:
4022:
4019:
4018:
3994:
3989:
3988:
3979:
3974:
3973:
3958:
3953:
3952:
3943:
3938:
3937:
3928:
3923:
3922:
3913:
3908:
3907:
3899:
3896:
3895:
3882:
3859:
3847:
3843:
3842:
3835:
3831:
3830:
3818:
3815:
3814:
3793:
3767:
3762:
3761:
3757:
3748:
3744:
3736:
3731:
3723:
3721:
3718:
3717:
3699:
3694:
3686:
3678:
3674:
3673:
3666:
3662:
3661:
3649:
3646:
3645:
3627:
3622:
3614:
3606:
3598:
3590:
3585:
3577:
3575:
3572:
3571:
3550:
3542:
3537:
3529:
3521:
3517:
3516:
3509:
3505:
3504:
3492:
3489:
3488:
3470:
3462:
3457:
3449:
3444:
3442:
3439:
3438:
3420:
3418:
3415:
3414:
3398:
3393:
3391:
3388:
3387:
3371:
3366:
3364:
3361:
3360:
3342:
3337:
3329:
3321:
3317:
3316:
3309:
3305:
3304:
3292:
3289:
3288:
3271:
3266:
3264:
3261:
3260:
3244:
3241:
3240:
3237:
3223:represents the
3208:
3205:
3204:
3162:
3154:
3146:
3143:
3090:
3086:
3071:
3061:
3060:
3056:
3054:
3051:
3045:
3020:
3013:
3007:is torque, and
2979:
2965:
2961:
2960:
2953:
2949:
2948:
2936:
2933:
2918:mechanical work
2906:
2852:
2851:
2845:
2840:
2839:
2837:
2829:
2827:
2824:
2823:
2802:
2763:
2762:
2757:
2756:
2740:
2739:
2734:
2733:
2725:
2711:
2710:
2704:
2699:
2698:
2696:
2694:
2691:
2690:
2689:it follows that
2662:
2660:
2657:
2656:
2640:
2638:
2635:
2634:
2616:
2608:
2600:
2592:
2578:
2577:
2571:
2566:
2565:
2563:
2561:
2558:
2557:
2539:
2537:
2534:
2533:
2517:
2515:
2512:
2511:
2486:
2472:
2471:
2465:
2460:
2459:
2457:
2443:
2442:
2436:
2431:
2430:
2428:
2420:
2406:
2405:
2399:
2394:
2393:
2391:
2389:
2386:
2385:
2376:linear momentum
2355:
2347:
2339:
2337:
2334:
2333:
2330:
2303:
2302:
2294:
2292:
2289:
2288:
2272:
2261:
2259:
2256:
2255:
2228:
2224:
2222:
2221:
2213:
2200:
2187:
2183:
2181:
2180:
2176:
2174:
2172:
2169:
2168:
2143:
2129:
2115:
2114:
2098:
2085:
2081:
2079:
2078:
2074:
2072:
2066:
2062:
2056:
2052:
2039:
2026:
2022:
2020:
2019:
2015:
2013:
2007:
2003:
1997:
1993:
1980:
1967:
1963:
1961:
1960:
1956:
1954:
1948:
1944:
1938:
1934:
1919:
1915:
1913:
1912:
1900:
1896:
1894:
1893:
1887:
1883:
1868:
1864:
1862:
1861:
1849:
1845:
1843:
1842:
1836:
1832:
1817:
1813:
1811:
1810:
1798:
1794:
1792:
1791:
1785:
1781:
1765:
1764:
1759:
1758:
1756:
1753:
1752:
1745:is the orbital
1721:
1717:
1706:
1703:
1702:
1681:
1670:
1668:
1665:
1664:
1630:
1629:
1623:
1618:
1617:
1615:
1607:
1605:
1602:
1601:
1592:
1555:
1552:
1551:
1546:right-hand rule
1539:
1533:
1509:
1506:
1505:
1501:
1476:
1474:
1471:
1470:
1461:position vector
1444:
1442:
1439:
1438:
1420:
1417:
1416:
1400:
1398:
1395:
1394:
1354:
1350:
1331:
1323:
1315:
1313:
1310:
1309:
1268:point particles
1252:lever's fulcrum
1236:
1230:
1229:| = |
1227:
1221:
1215:
1210:
1194:
1192:
1172:
1146:moment of force
1070:
1064:
1043:
1014:
1012:
1009:
1008:
1001:moment of force
973:
932:
919:
918:
911:
910:
909:
784:
776:
775:
755:
709:Circular motion
703:
693:
692:
691:
648:
618:
615:
594:
573:
565:
564:
561:
560:
518:
508:
500:
499:
498:
457:
453:Mechanical work
446:
430:
368:
360:
359:
358:
313:
305:
282:
258:
252:
248:
246:
237:
236:
234:
231:
230:
191:
185:
184:
183:
177:
171:
170:
169:
163:
162:
160:
157:
156:
140:
123:
88:
85:
84:
81:
74:
53:linear momentum
24:
17:
12:
11:
5:
7424:
7414:
7413:
7408:
7403:
7398:
7393:
7376:
7375:
7371:
7370:
7351:
7335:
7333:
7330:
7311:
7295:
7293:
7289:
7288:
7249:
7218:
7216:
7213:
7174:
7162:
7142:
7140:
7136:
7135:
7106:
7076:
7074:
7071:
7042:
7009:
6986:
6983:
6968:Mass flow rate
6965:
6961:
6960:
6958:
6956:
6937:
6934:
6932:
6913:
6898:
6894:
6893:
6891:
6872:
6870:
6867:
6865:
6852:
6850:
6846:
6845:
6843:
6822:
6811:
6808:
6806:
6791:
6789:
6785:
6784:
6782:
6751:
6704:
6701:
6677:
6652:
6631:
6627:
6626:
6611:
6584:
6582:
6579:
6564:
6521:
6519:
6515:
6514:
6512:
6510:
6495:
6492:
6490:
6475:
6460:
6456:
6455:
6448:
6441:
6438:
6435:
6432:
6429:
6426:
6422:
6421:
6418:
6416:
6410:
6407:
6406:
6396:
6395:
6388:
6381:
6373:
6367:
6366:
6353:
6348:
6343:
6331:
6316:
6315:External links
6313:
6310:
6309:
6302:
6284:
6269:
6234:
6203:
6183:
6176:
6147:
6133:
6126:
6108:
6093:
6075:
6060:
6035:
6011:
5987:
5965:
5944:
5924:
5907:
5885:
5884:
5882:
5879:
5877:
5876:
5871:
5866:
5861:
5856:
5854:Torque limiter
5851:
5846:
5841:
5836:
5831:
5826:
5821:
5819:Bending moment
5816:
5810:
5808:
5805:
5793:Main article:
5790:
5787:
5778:
5774:
5646:
5645:Machine torque
5643:
5630:
5626:
5623:
5618:
5613:
5608:
5603:
5598:
5593:
5590:
5585:
5580:
5575:
5570:
5565:
5541:
5536:
5512:
5507:
5483:
5478:
5455:
5441:
5438:
5401:
5398:
5384:
5377:
5352:
5349:
5341:
5338:
5330:
5327:
5324:
5287:
5284:
5276:
5273:
5265:
5262:
5259:
5237:
5234:
5232:
5229:
5216:
5210:
5207:
5202:
5199:
5196:
5190:
5187:
5158:
5155:
5152:
5142:
5131:
5128:
5126:
5124:
5107:
5096:
5093:
5090:
5087:
5078:
5063:
5051:
5043:
5040:
5037:
5034:
5026:
5023:
5021:
5014:
5013:
4987:
4979:
4976:
4973:
4970:
4962:
4916:
4908:
4900:
4897:
4895:
4893:
4888:
4884:
4881:
4878:
4870:
4867:
4864:
4861:
4857:
4851:
4842:
4835:
4832:
4830:
4828:
4814:
4803:
4800:
4798:
4791:
4790:
4760:
4757:
4735:
4729:
4726:
4723:
4715:
4712:
4709:
4705:
4701:
4698:
4695:
4690:
4686:
4680:
4677:
4674:
4670:
4666:
4663:
4660:
4655:
4651:
4648:
4642:
4639:
4635:
4631:
4628:
4625:
4620:
4613:
4607:
4604:
4599:
4564:
4561:
4558:
4554:
4550:
4544:
4536:
4533:
4530:
4526:
4522:
4519:
4516:
4511:
4507:
4501:
4498:
4495:
4491:
4487:
4484:
4481:
4476:
4472:
4469:
4463:
4459:
4455:
4450:
4443:
4437:
4432:
4404:
4400:
4396:
4393:
4390:
4385:
4381:
4375:
4372:
4369:
4365:
4361:
4358:
4355:
4350:
4346:
4343:
4337:
4333:
4329:
4324:
4320:
4314:
4309:
4284:
4281:
4278:
4275:
4272:
4269:
4266:
4263:
4225:
4222:
4193:, whereas for
4142:
4139:
4127:
4123:
4119:
4114:
4109:
4104:
4099:
4094:
4089:
4086:
4083:
4078:
4073:
4068:
4063:
4058:
4053:
4048:
4043:
4038:
4033:
4028:
4002:
3997:
3992:
3987:
3982:
3977:
3972:
3969:
3966:
3961:
3956:
3951:
3946:
3941:
3936:
3931:
3926:
3921:
3916:
3911:
3906:
3903:
3881:
3878:
3866:
3862:
3857:
3850:
3846:
3838:
3834:
3829:
3825:
3822:
3800:
3796:
3791:
3788:
3785:
3782:
3779:
3775:
3770:
3765:
3760:
3755:
3751:
3747:
3743:
3739:
3734:
3730:
3726:
3702:
3697:
3693:
3689:
3681:
3677:
3669:
3665:
3660:
3656:
3653:
3630:
3625:
3621:
3617:
3613:
3609:
3605:
3601:
3597:
3593:
3588:
3584:
3580:
3553:
3549:
3545:
3540:
3536:
3532:
3524:
3520:
3512:
3508:
3503:
3499:
3496:
3473:
3469:
3465:
3460:
3456:
3452:
3447:
3423:
3401:
3396:
3374:
3369:
3345:
3340:
3336:
3332:
3324:
3320:
3312:
3308:
3303:
3299:
3296:
3274:
3269:
3248:
3236:
3233:
3225:scalar product
3212:
3169:
3165:
3161:
3157:
3153:
3150:
3098:
3093:
3089:
3085:
3079:
3076:
3070:
3064:
3059:
3043:
3018:
3011:
2989:
2986:
2982:
2975:
2968:
2964:
2956:
2952:
2947:
2943:
2940:
2922:center of mass
2905:
2902:
2865:
2859:
2855:
2848:
2843:
2836:
2832:
2801:
2798:
2778:
2772:
2769:
2766:
2760:
2755:
2749:
2746:
2743:
2737:
2732:
2728:
2724:
2718:
2714:
2707:
2702:
2665:
2643:
2619:
2615:
2611:
2607:
2603:
2599:
2595:
2591:
2585:
2581:
2574:
2569:
2542:
2520:
2493:
2489:
2485:
2479:
2475:
2468:
2463:
2456:
2450:
2446:
2439:
2434:
2427:
2423:
2419:
2413:
2409:
2402:
2397:
2358:
2354:
2350:
2346:
2342:
2329:
2326:
2310:
2307:
2301:
2297:
2275:
2271:
2268:
2264:
2236:
2231:
2227:
2220:
2216:
2212:
2206:
2203:
2195:
2190:
2186:
2179:
2150:
2146:
2142:
2139:
2136:
2132:
2128:
2122:
2119:
2113:
2110:
2104:
2101:
2093:
2088:
2084:
2077:
2069:
2065:
2059:
2055:
2051:
2045:
2042:
2034:
2029:
2025:
2018:
2010:
2006:
2000:
1996:
1992:
1986:
1983:
1975:
1970:
1966:
1959:
1951:
1947:
1941:
1937:
1933:
1927:
1922:
1918:
1908:
1903:
1899:
1890:
1886:
1882:
1876:
1871:
1867:
1857:
1852:
1848:
1839:
1835:
1831:
1825:
1820:
1816:
1806:
1801:
1797:
1788:
1784:
1780:
1774:
1771:
1768:
1762:
1724:
1720:
1716:
1713:
1710:
1688:
1684:
1680:
1677:
1673:
1637:
1633:
1626:
1621:
1614:
1610:
1591:
1588:
1572:
1571:
1559:
1549:
1544:following the
1513:
1503:
1499:
1479:
1468:
1447:
1436:
1424:
1403:
1377:
1374:
1371:
1368:
1365:
1362:
1357:
1353:
1349:
1346:
1343:
1339:
1334:
1330:
1326:
1322:
1318:
1260:line of action
1225:
1209:has magnitude
1190:
1171:
1168:
1063:
1060:
1017:
975:
974:
972:
971:
964:
957:
949:
946:
945:
944:
943:
930:
913:
912:
908:
907:
902:
897:
892:
887:
882:
877:
872:
867:
862:
857:
852:
847:
842:
837:
832:
827:
822:
817:
812:
807:
802:
797:
792:
786:
785:
782:
781:
778:
777:
774:
773:
754:
753:
748:
743:
738:
736:Coriolis force
733:
732:
731:
721:
716:
711:
705:
704:
699:
698:
695:
694:
690:
689:
684:
679:
678:
677:
672:
662:
657:
652:
645:
634:
633:
632:
627:
614:
613:
608:
603:
598:
591:
586:
581:
575:
574:
571:
570:
567:
566:
563:
562:
559:
558:
553:
548:
543:
538:
533:
527:
521:
519:
512:
509:
506:
505:
502:
501:
497:
496:
491:
486:
481:
476:
471:
466:
461:
455:
450:
444:
439:
428:
423:
418:
413:
408:
407:
406:
401:
391:
386:
381:
376:
370:
369:
366:
365:
362:
361:
357:
356:
351:
346:
341:
336:
331:
326:
321:
315:
314:
311:
310:
307:
306:
304:
303:
298:
293:
287:
284:
283:
278:
264:
261:
255:
251:
245:
227:
226:
220:
219:
211:
210:
197:
194:
188:
180:
174:
166:
154:
148:
147:
144:
135:
134:
124:
121:
118:
117:
114:
108:
107:
92:
82:
80:Common symbols
79:
76:
75:
39:
31:
30:
15:
9:
6:
4:
3:
2:
7423:
7412:
7409:
7407:
7404:
7402:
7399:
7397:
7394:
7392:
7389:
7388:
7386:
7369:
7360:
7355:
7352:
7344:
7339:
7336:
7334:
7331:
7329:
7320:
7315:
7312:
7304:
7299:
7296:
7294:
7291:
7290:
7287:
7278:
7273:
7268:
7263:
7258:
7253:
7250:
7248:
7239:
7234:
7229:
7228:
7222:
7219:
7217:
7214:
7212:
7203:
7198:
7193:
7188:
7183:
7178:
7175:
7173:
7161:
7156:
7151:
7146:
7143:
7141:
7138:
7137:
7134:
7130:
7118:
7110:
7107:
7105:
7096:
7090:
7085:
7080:
7077:
7075:
7072:
7070:
7066:
7054:
7046:
7043:
7041:
7037:
7028:
7023:
7018:
7013:
7010:
7008:
6984:
6981:
6969:
6966:
6963:
6962:
6959:
6957:
6955:
6946:
6941:
6938:
6935:
6933:
6930:
6927:
6923:
6919:
6914:
6912:
6907:
6902:
6899:
6896:
6895:
6892:
6883:
6882:
6876:
6873:
6871:
6868:
6866:
6861:
6856:
6853:
6851:
6848:
6847:
6844:
6842:
6833:
6832:
6826:
6823:
6821:
6816:
6812:
6809:
6807:
6805:
6800:
6795:
6792:
6790:
6787:
6786:
6783:
6781:
6772:
6771:
6765:
6760:
6755:
6754:angular speed
6752:
6750:
6746:
6740:
6739:
6733:
6726:
6721:
6714:
6709:
6705:
6702:
6697:
6692:
6686:
6681:
6678:
6676:
6671:
6666:
6661:
6656:
6653:
6651:
6647:
6641:
6636:
6632:
6629:
6628:
6624:
6616:
6612:
6610:
6605:
6604:
6598:
6593:
6588:
6585:
6583:
6580:
6578:
6573:
6568:
6565:
6563:
6559:
6553:
6547:
6541:
6536:
6530:
6525:
6522:
6520:
6517:
6516:
6513:
6511:
6509:
6504:
6499:
6496:
6493:
6491:
6489:
6484:
6479:
6476:
6474:
6469:
6464:
6461:
6458:
6457:
6453:
6449:
6446:
6442:
6439:
6436:
6433:
6430:
6427:
6424:
6423:
6413:
6408:
6404:
6401:
6394:
6389:
6387:
6382:
6380:
6375:
6374:
6371:
6364:
6360:
6357:
6354:
6352:
6349:
6347:
6344:
6341:
6337:
6336:
6332:
6329:
6325:
6322:
6319:
6318:
6305:
6299:
6295:
6288:
6279:
6273:
6265:
6261:
6257:
6253:
6249:
6245:
6238:
6220:
6213:
6207:
6200:
6196:
6193:
6187:
6179:
6177:9780070350489
6173:
6169:
6164:
6163:
6154:
6152:
6143:
6137:
6129:
6127:0-7167-0809-4
6123:
6119:
6112:
6104:
6100:
6096:
6094:9780134143323
6090:
6086:
6079:
6071:
6064:
6049:
6045:
6039:
6031:
6027:
6026:
6021:
6015:
6008:
6004:
6001:
6000:Free download
5997:
5991:
5985:
5981:
5978:
5974:
5969:
5961:
5957:
5951:
5949:
5940:
5939:
5931:
5929:
5920:
5919:
5911:
5904:
5903:0-534-40842-7
5900:
5896:
5890:
5886:
5875:
5872:
5870:
5869:Torque wrench
5867:
5865:
5864:Torque tester
5862:
5860:
5857:
5855:
5852:
5850:
5847:
5845:
5842:
5840:
5837:
5835:
5832:
5830:
5827:
5825:
5822:
5820:
5817:
5815:
5812:
5811:
5804:
5802:
5796:
5786:
5784:
5783:angular speed
5772:
5768:
5764:
5760:
5756:
5752:
5748:
5744:
5740:
5736:
5732:
5728:
5724:
5720:
5716:
5711:
5709:
5704:
5700:
5699:Steam engines
5696:
5692:
5688:
5684:
5680:
5676:
5668:
5667:newton-metres
5664:
5660:
5656:
5651:
5642:
5624:
5616:
5606:
5601:
5588:
5583:
5573:
5568:
5539:
5510:
5481:
5437:
5435:
5429:
5421:
5413:
5407:
5394:
5390:
5383:
5376:
5371:
5367:
5363:
5350:
5325:
5322:
5314:
5312:
5307:
5303:
5298:
5285:
5260:
5257:
5249:
5242:
5228:
5214:
5208:
5205:
5200:
5197:
5194:
5188:
5185:
5176:
5156:
5153:
5150:
5140:
5129:
5127:
5105:
5094:
5091:
5088:
5085:
5076:
5061:
5049:
5041:
5038:
5035:
5032:
5024:
5022:
5003:
4999:
4985:
4977:
4974:
4971:
4968:
4960:
4947:
4940:
4936:
4931:
4914:
4911:angular speed
4906:
4898:
4896:
4886:
4879:
4876:
4873:angular speed
4868:
4865:
4859:
4855:
4849:
4840:
4833:
4831:
4812:
4801:
4799:
4780:
4778:
4773:
4770:
4769:circumference
4766:
4756:
4754:
4749:
4746:
4733:
4727:
4724:
4721:
4703:
4688:
4684:
4668:
4653:
4649:
4646:
4633:
4618:
4611:
4597:
4588:
4586:
4581:
4578:
4552:
4542:
4524:
4509:
4505:
4489:
4474:
4470:
4467:
4457:
4448:
4441:
4430:
4421:
4418:
4398:
4383:
4379:
4363:
4348:
4344:
4341:
4331:
4322:
4318:
4307:
4298:
4295:
4282:
4279:
4276:
4273:
4270:
4267:
4264:
4261:
4253:
4251:
4247:
4243:
4239:
4231:
4221:
4219:
4215:
4211:
4206:
4204:
4200:
4196:
4192:
4188:
4184:
4180:
4179:
4174:
4170:
4166:
4152:
4148:
4138:
4125:
4117:
4112:
4102:
4097:
4087:
4084:
4081:
4076:
4066:
4061:
4051:
4046:
4036:
4031:
4016:
4013:
4000:
3995:
3985:
3980:
3970:
3967:
3964:
3959:
3949:
3944:
3934:
3929:
3919:
3914:
3904:
3901:
3893:
3891:
3887:
3877:
3864:
3855:
3848:
3844:
3836:
3832:
3827:
3823:
3820:
3812:
3798:
3789:
3786:
3783:
3780:
3777:
3773:
3758:
3753:
3745:
3741:
3728:
3714:
3691:
3679:
3675:
3667:
3663:
3658:
3654:
3651:
3643:
3619:
3611:
3603:
3595:
3582:
3570:
3565:
3547:
3534:
3522:
3518:
3510:
3506:
3501:
3497:
3494:
3485:
3467:
3454:
3436:
3357:
3334:
3322:
3318:
3310:
3306:
3301:
3297:
3294:
3286:
3246:
3232:
3228:
3226:
3210:
3202:
3198:
3197:
3192:
3191:
3186:
3181:
3179:
3167:
3159:
3151:
3148:
3139:
3137:
3133:
3129:
3127:
3126:angular speed
3123:
3119:
3115:
3110:
3108:
3096:
3091:
3087:
3083:
3077:
3074:
3068:
3057:
3047:
3042:
3039:
3035:
3031:
3026:
3025:of the body.
3024:
3017:
3010:
3006:
3001:
2999:
2987:
2984:
2973:
2966:
2962:
2954:
2950:
2945:
2941:
2938:
2929:
2927:
2923:
2919:
2915:
2911:
2901:
2899:
2894:
2889:
2884:
2882:
2876:
2863:
2857:
2834:
2820:
2819:
2815:
2811:
2807:
2797:
2795:
2789:
2776:
2753:
2730:
2722:
2716:
2688:
2684:
2680:
2631:
2613:
2605:
2597:
2589:
2583:
2555:
2509:
2504:
2491:
2483:
2477:
2454:
2448:
2425:
2417:
2411:
2383:
2381:
2377:
2373:
2352:
2344:
2325:
2308:
2299:
2269:
2266:
2253:
2218:
2210:
2204:
2201:
2177:
2166:
2161:
2140:
2134:
2126:
2111:
2108:
2102:
2099:
2075:
2067:
2063:
2057:
2053:
2049:
2043:
2040:
2016:
2008:
2004:
1998:
1994:
1990:
1984:
1981:
1957:
1949:
1945:
1939:
1935:
1931:
1906:
1901:
1897:
1888:
1884:
1880:
1855:
1850:
1846:
1837:
1833:
1829:
1804:
1799:
1795:
1786:
1782:
1778:
1750:
1748:
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1740:
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1714:
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1708:
1699:
1686:
1678:
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1662:
1660:
1656:
1651:
1635:
1612:
1599:
1597:
1587:
1585:
1581:
1577:
1557:
1550:
1547:
1542:
1536:
1531:
1530:perpendicular
1527:
1526:cross product
1511:
1504:
1498:
1494:
1469:
1466:
1462:
1437:
1422:
1393:
1392:
1391:
1388:
1375:
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1360:
1355:
1351:
1347:
1344:
1341:
1328:
1320:
1307:
1305:
1301:
1297:
1296:torque vector
1293:
1289:
1285:
1284:torque vector
1281:
1277:
1273:
1272:cross product
1269:
1265:
1261:
1257:
1253:
1244:
1239:
1235:| |
1233:
1224:
1220:| |
1218:
1213:
1207:
1203:
1199:
1198:
1189:
1185:
1181:
1176:
1167:
1165:
1160:
1155:
1151:
1147:
1143:
1138:
1136:
1130:
1128:
1124:
1120:
1119:
1114:
1110:
1106:
1105:
1098:
1096:
1092:
1088:
1087:James Thomson
1084:
1083:
1079:
1075:
1069:
1059:
1057:
1053:
1049:
1041:
1037:
1036:
1032:
1006:
1002:
998:
994:
990:
986:
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970:
965:
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950:
948:
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928:
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788:
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739:
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730:
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631:
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621:
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364:
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262:
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225:
222:
221:
217:
216:
195:
192:
178:
155:
153:
149:
145:
143:
136:
133:⋅inch, ozf⋅in
132:
128:
125:
119:
115:
113:
109:
106:
90:
83:
77:
72:
68:
64:
61:
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54:
50:
46:
43:
37:
32:
27:
22:
7358:
7342:
7318:
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7276:
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7237:
7226:
7225:
7220:
7201:
7191:
7181:
7159:
7149:
7094:
7083:
7026:
7016:
6944:
6928:
6925:
6921:
6917:
6905:
6880:
6879:
6875:angular jerk
6859:
6830:
6829:
6798:
6794:acceleration
6769:
6768:
6758:
6737:
6736:
6724:
6712:
6695:
6684:
6669:
6659:
6639:
6602:
6601:
6591:
6571:
6558:displacement
6551:
6545:
6539:
6528:
6502:
6482:
6467:
6451:
6444:
6334:
6293:
6287:
6272:
6247:
6243:
6237:
6226:. Retrieved
6206:
6186:
6161:
6136:
6117:
6111:
6084:
6078:
6069:
6063:
6052:. Retrieved
6038:
6024:
6014:
5995:
5990:
5972:
5968:
5959:
5937:
5917:
5910:
5894:
5889:
5798:
5750:
5712:
5672:
5443:
5427:
5419:
5411:
5403:
5388:
5381:
5374:
5364:
5315:
5310:
5305:
5301:
5299:
5250:
5247:
5177:
5004:
5000:
4948:
4938:
4934:
4932:
4781:
4774:
4764:
4762:
4750:
4747:
4589:
4582:
4579:
4422:
4419:
4299:
4296:
4254:
4245:
4241:
4237:
4227:
4217:
4213:
4207:
4178:newton-metre
4176:
4144:
4017:
4014:
3894:
3883:
3813:
3715:
3644:
3566:
3486:
3437:
3358:
3287:
3238:
3229:
3195:
3194:
3189:
3188:
3184:
3182:
3140:
3130:
3121:
3113:
3111:
3048:
3040:
3033:
3027:
3015:
3008:
3004:
3002:
2930:
2925:
2907:
2897:
2885:
2880:
2878:
2822:
2813:
2809:
2803:
2790:
2678:
2632:
2556:
2508:product rule
2505:
2384:
2379:
2371:
2331:
2162:
1751:
1742:
1700:
1663:
1658:
1654:
1652:
1600:
1593:
1584:§ Units
1580:newton-metre
1573:
1540:
1534:
1524:denotes the
1496:
1492:
1464:
1389:
1308:
1303:
1295:
1291:
1287:
1283:
1264:pseudovector
1249:
1242:
1237:
1231:
1222:
1216:
1211:
1205:
1201:
1196:
1195:
1187:
1183:
1179:
1149:
1145:
1139:
1134:
1132:
1116:
1112:
1102:
1100:
1094:
1073:
1071:
1054:applied two
1033:
1031:Greek letter
1004:
1000:
988:
978:
769: /
765: /
763:displacement
761: /
622: /
584:Displacement
522:
513:
507:Formulations
494:Virtual work
483:
434: /
374:Acceleration
367:Fundamentals
112:SI unit
104:
62:
55:
48:
44:
6615:solid angle
5998:pp. 90–99:
5695:dynamometer
5661:) that the
5186:5252.113122
4933:The radius
4171:. Official
3193:is torque,
3138:, given by
2924:, the work
2908:The law of
2883:is torque.
2794:integrating
1241:| sin
905:von Neumann
572:Core topics
122:Other units
7385:Categories
7350:m s, N m s
7326:m s,
7272:Lagrangian
7197:Lagrangian
6437:Dimensions
6425:Dimensions
6250:(9): 820.
6228:2020-05-29
6054:2007-09-08
6028:. p.
5881:References
5771:gear ratio
5763:drivetrain
5663:crankshaft
5268:moment arm
5082:horsepower
4759:Derivation
4585:horsepower
4240:is power,
4218:inch-pound
4214:foot-pound
4210:pound foot
3187:is power,
1300:rigid body
1066:See also:
993:rotational
840:d'Alembert
820:Maupertuis
783:Scientists
665:Rigid body
339:Kinematics
7366:ms,
6985:˙
6708:frequency
6635:frequency
6190:From the
6103:922464227
5747:chainring
5719:sprockets
5625:×
5607:−
5579:τ
5564:τ
5477:τ
5323:τ
5258:τ
5209:π
5189:≈
5141:⋅
5130:≈
5106:⋅
5095:⋅
5077:⋅
5062:⋅
5050:⋅
5042:⋅
5039:π
5033:⋅
4978:⋅
4975:π
4969:⋅
4937:and time
4907:⋅
4877:⋅
4869:⋅
4860:⋅
4813:⋅
4689:ν
4685:⋅
4654:π
4647:⋅
4634:⋅
4619:τ
4510:ν
4506:⋅
4475:π
4468:⋅
4458:⋅
4449:τ
4384:ν
4380:⋅
4349:π
4342:⋅
4332:⋅
4323:τ
4283:ν
4280:⋅
4277:π
4271:⋅
4268:τ
4147:dimension
4103:×
4085:…
4067:×
4037:×
3986:×
3968:…
3950:×
3920:×
3902:τ
3865:θ
3856:τ
3845:θ
3833:θ
3828:∫
3799:θ
3790:τ
3781:
3769:θ
3750:τ
3738:θ
3729:⋅
3725:τ
3701:θ
3692:⋅
3688:τ
3676:θ
3664:θ
3659:∫
3629:θ
3620:⋅
3612:×
3596:×
3592:θ
3583:⋅
3548:×
3544:θ
3535:⋅
3502:∫
3468:×
3464:θ
3400:θ
3335:⋅
3302:∫
3211:⋅
3164:ω
3160:⋅
3156:τ
3088:ω
2985:θ
2974:τ
2963:θ
2951:θ
2946:∫
2847:τ
2759:τ
2731:×
2614:×
2598:×
2484:×
2426:×
2353:×
2309:˙
2306:ω
2296:α
2274:α
2263:τ
2235:^
2219:×
2215:ω
2194:^
2145:ω
2135:×
2131:ω
2121:˙
2118:ω
2092:^
2064:ω
2033:^
2005:ω
1974:^
1946:ω
1926:^
1907:˙
1898:ω
1875:^
1856:˙
1847:ω
1824:^
1805:˙
1796:ω
1761:τ
1683:ω
1609:τ
1558:θ
1512:×
1423:τ
1402:τ
1376:θ
1373:
1356:⊥
1342:τ
1338:⟹
1329:×
1317:τ
1256:lever arm
1072:The term
1016:τ
985:mechanics
885:Liouville
767:frequency
687:Vibration
404:potential
329:Continuum
324:Celestial
301:Textbooks
193:−
152:Dimension
91:τ
47:, torque
7401:Rotation
7310:m s, N s
7133:J s
7129:m s
7104:m s
7065:m s
7036:m s
7012:momentum
6665:velocity
6535:position
6524:distance
6478:absement
6403:SI units
6359:Archived
6324:Archived
6219:Archived
6195:Archived
6048:Archived
6022:(1811).
6003:Archived
5980:Archived
5977:Web link
5956:"torque"
5807:See also
5801:gear box
5759:crankset
5743:cranking
5725:, and a
5715:bicycles
5178:because
4151:distance
1532:both to
1288:position
1214:= |
1082:torquēre
940:Category
865:Hamilton
850:Lagrange
845:Clairaut
810:Horrocks
771:velocity
741:Pendulum
729:reactive
701:Rotation
670:dynamics
620:Inertial
606:Friction
489:Velocity
464:Momentum
344:Kinetics
334:Dynamics
312:Branches
296:Timeline
71:friction
7338:rotatum
7117:actergy
7053:actergy
7022:impulse
6942::
6693::
6623:rad, sr
6252:Bibcode
6168:267–268
5962:. 1933.
5844:Statics
5755:spindle
5739:cyclist
5393:precess
4185:to the
3811:giving
3199:is the
3124:is its
3116:is the
2898:rotatum
2893:rotātus
2810:rotatum
2806:physics
2681:to the
1737:is the
1576:SI unit
1538:and to
1459:is the
1274:of the
1125:" and "
1118:torsion
1062:History
1052:newtons
991:is the
981:physics
900:Koopman
860:Poisson
855:Laplace
800:Huygens
795:Galileo
640: (
579:Damping
432:Inertia
426:Impulse
399:kinetic
349:Statics
319:Applied
291:History
67:gravity
7391:Torque
7252:energy
7233:moment
7221:torque
7177:energy
7155:weight
7127:
7109:action
7102:
7063:
7045:action
7034:
7005:
6952:
6924:⟩ = ∑
6888:
6839:
6778:
6300:
6174:
6124:
6101:
6091:
5901:
5814:Moment
5779:output
5708:clutch
5677:: the
5675:engine
5137:torque
5029:torque
4965:torque
4903:torque
4847:torque
4546:
4199:scalar
4195:energy
4191:vector
4165:energy
3203:, and
3183:where
3112:where
3003:where
2977:
2879:where
2814:torque
2370:where
2287:where
2165:vector
1701:where
1653:where
1390:where
1266:; for
1150:moment
1135:torque
1127:moment
1123:couple
1113:torque
1109:motion
1076:(from
1074:torque
1056:metres
1040:moment
1005:moment
989:torque
938:
890:Appell
875:Cauchy
870:Jacobi
815:Halley
805:Newton
790:Kepler
642:linear
638:Motion
484:Torque
459:Moment
394:Energy
384:Couple
146:kg⋅m⋅s
58:, and
29:Torque
7406:Force
7354:power
7314:power
7284:m s,
7245:m s,
7209:m s,
7170:m s,
7145:force
6655:speed
6587:angle
6222:(PDF)
6215:(PDF)
5775:input
5767:wheel
5735:frame
5723:chain
5679:power
5380:and −
5344:force
5279:force
5017:power
4957:power
4809:force
4794:power
4777:power
4187:joule
4141:Units
3235:Proof
3132:Power
3032:that
2914:force
2890:word
2888:Latin
2679:equal
1292:force
1104:force
1078:Latin
997:force
895:Gibbs
880:Routh
835:Euler
474:Speed
469:Space
411:Force
42:force
7298:yank
7262:work
7187:work
6901:mass
6855:jerk
6567:area
6498:time
6463:time
6298:ISBN
6172:ISBN
6122:ISBN
6099:OCLC
6089:ISBN
5899:ISBN
5737:. A
5701:and
5657:(in
5416:and
5304:and
4822:time
4169:work
3435:as
3136:time
3014:and
2818:time
2378:and
1741:and
1574:The
1290:and
1048:axis
983:and
479:Time
442:Mass
69:and
7332:MLT
7247:N m
7215:MLT
7168:kg
7073:MLT
7069:J s
7040:N s
6886:rad
6864:m s
6837:rad
6804:m s
6776:rad
6700:m s
6675:m s
6609:rad
6488:m s
6338:on
6260:doi
5691:rpm
5659:rpm
5554:is
5430:= 0
5422:= 0
5414:= 0
5201:000
5157:252
5145:RPM
5115:min
5110:lbf
5092:000
5072:min
5067:lbf
4753:BTU
4728:000
4167:or
3778:cos
2804:In
2324:.
1370:sin
1156:'s
1035:tau
979:In
138:In
131:lbf
116:N⋅m
7387::
7364:kg
7356::
7348:kg
7340::
7324:kg
7316::
7308:kg
7300::
7292:MT
7282:kg
7274::
7270:,
7264::
7260:,
7254::
7243:kg
7235::
7231:,
7223::
7207:kg
7199::
7195:,
7189::
7185:,
7179::
7157::
7153:,
7147::
7139:MT
7131:,
7125:kg
7119::
7115:,
7113:𝒮
7111::
7100:kg
7091::
7087:,
7081::
7067:,
7061:kg
7055::
7051:,
7049:𝒮
7047::
7038:,
7032:kg
7024::
7020:,
7014::
7003:kg
6970::
6964:MT
6950:kg
6936:ML
6911:kg
6903::
6877::
6857::
6827::
6796::
6766::
6762:,
6756::
6749:Hz
6747:,
6734::
6729:,
6722::
6717:,
6710::
6682::
6667::
6663:,
6657::
6650:Hz
6648:,
6637::
6617::
6599::
6595:,
6589::
6569::
6556:,
6549:,
6543:,
6537::
6532:,
6526::
6500::
6480::
6465::
6258:.
6248:47
6246:.
6170:.
6150:^
6097:.
6046:.
6030:67
5958:.
5947:^
5927:^
5710:.
5195:33
5102:ft
5086:33
5057:ft
4779::
4722:33
4543:60
4173:SI
3227:.
3128:.
2808:,
2554:,
2167:is
1598:,
1586:.
1204:×
1200:=
1162:.
1137:.
987:,
129:,
103:,
51:,
7368:W
7359:P
7343:P
7328:W
7319:P
7303:Y
7286:J
7277:L
7267:W
7257:E
7238:M
7227:τ
7211:J
7202:L
7192:W
7182:E
7172:N
7163:g
7160:F
7150:F
7121:ℵ
7095:L
7093:Δ
7084:L
7057:ℵ
7027:J
7017:p
7007:s
6982:m
6954:m
6945:I
6929:x
6926:m
6922:x
6920:⟨
6918:M
6906:m
6897:M
6890:s
6881:ζ
6869:T
6860:j
6849:T
6841:s
6831:α
6820:s
6810:T
6799:a
6788:T
6780:s
6770:ω
6759:ω
6745:s
6738:n
6725:n
6713:f
6703:T
6696:h
6688:,
6685:ν
6670:v
6660:v
6646:s
6640:f
6630:T
6619:Ω
6603:θ
6592:θ
6581:1
6577:m
6572:A
6562:m
6552:x
6546:s
6540:r
6529:d
6518:1
6508:s
6503:t
6494:T
6483:A
6473:s
6468:t
6459:T
6452:θ
6445:θ
6440:1
6434:L
6431:L
6428:1
6392:e
6385:t
6378:v
6342:.
6306:.
6266:.
6262::
6254::
6231:.
6180:.
6144:.
6130:.
6105:.
6057:.
6032:.
6009:.
5905:.
5751:π
5629:F
5622:)
5617:1
5612:r
5602:2
5597:r
5592:(
5589:+
5584:1
5574:=
5569:2
5540:2
5535:r
5511:1
5506:r
5482:1
5454:F
5428:τ
5426:Σ
5420:V
5418:Σ
5412:H
5410:Σ
5395:.
5389:L
5385:g
5382:F
5378:g
5375:F
5351:.
5348:)
5340:(
5337:)
5329:(
5326:=
5311:r
5306:F
5302:r
5286:.
5283:)
5275:(
5272:)
5264:(
5261:=
5215:.
5206:2
5198:,
5154:,
5151:5
5089:,
5036:2
5025:=
4986:.
4972:2
4961:=
4944:π
4939:t
4935:r
4915:.
4899:=
4887:t
4883:)
4880:t
4866:r
4863:(
4856:)
4850:r
4841:(
4834:=
4802:=
4734:.
4725:,
4714:n
4711:i
4708:m
4704:/
4700:v
4697:e
4694:r
4679:v
4676:e
4673:r
4669:/
4665:d
4662:a
4659:r
4650:2
4641:t
4638:f
4630:f
4627:b
4624:l
4612:=
4606:p
4603:h
4598:P
4563:n
4560:i
4557:m
4553:/
4549:s
4535:n
4532:i
4529:m
4525:/
4521:v
4518:e
4515:r
4500:v
4497:e
4494:r
4490:/
4486:d
4483:a
4480:r
4471:2
4462:m
4454:N
4442:=
4436:W
4431:P
4403:s
4399:/
4395:v
4392:e
4389:r
4374:v
4371:e
4368:r
4364:/
4360:d
4357:a
4354:r
4345:2
4336:m
4328:N
4319:=
4313:W
4308:P
4274:2
4265:=
4262:P
4248:(
4246:ν
4242:τ
4238:P
4234:π
4161:M
4158:L
4155:T
4126:.
4122:0
4118:=
4113:N
4108:F
4098:N
4093:r
4088:+
4082:+
4077:2
4072:F
4062:2
4057:r
4052:+
4047:1
4042:F
4032:1
4027:r
4001:.
3996:N
3991:F
3981:N
3976:r
3971:+
3965:+
3960:2
3955:F
3945:2
3940:r
3935:+
3930:1
3925:F
3915:1
3910:r
3905:=
3861:d
3849:2
3837:1
3824:=
3821:W
3795:d
3787:=
3784:0
3774:|
3764:d
3759:|
3754:|
3746:|
3742:=
3733:d
3696:d
3680:2
3668:1
3655:=
3652:W
3624:d
3616:F
3608:r
3604:=
3600:r
3587:d
3579:F
3552:r
3539:d
3531:F
3523:2
3519:s
3511:1
3507:s
3498:=
3495:W
3472:r
3459:d
3455:=
3451:s
3446:d
3422:r
3395:d
3373:s
3368:d
3344:s
3339:d
3331:F
3323:2
3319:s
3311:1
3307:s
3298:=
3295:W
3273:s
3268:d
3247:s
3196:ω
3190:τ
3185:P
3168:,
3152:=
3149:P
3122:ω
3114:I
3097:,
3092:2
3084:I
3078:2
3075:1
3069:=
3063:r
3058:E
3044:r
3041:E
3034:W
3019:2
3016:θ
3012:1
3009:θ
3005:τ
2988:,
2981:d
2967:2
2955:1
2942:=
2939:W
2926:W
2881:τ
2864:,
2858:t
2854:d
2842:d
2835:=
2831:P
2777:.
2771:t
2768:e
2765:n
2754:=
2748:t
2745:e
2742:n
2736:F
2727:r
2723:=
2717:t
2713:d
2706:L
2701:d
2664:v
2642:p
2618:p
2610:v
2606:+
2602:F
2594:r
2590:=
2584:t
2580:d
2573:L
2568:d
2541:v
2519:F
2492:.
2488:p
2478:t
2474:d
2467:r
2462:d
2455:+
2449:t
2445:d
2438:p
2433:d
2422:r
2418:=
2412:t
2408:d
2401:L
2396:d
2380:r
2372:p
2357:p
2349:r
2345:=
2341:L
2300:=
2270:I
2267:=
2230:i
2226:e
2211:=
2205:t
2202:d
2189:i
2185:e
2178:d
2149:)
2141:I
2138:(
2127:+
2112:I
2109:=
2103:t
2100:d
2087:3
2083:e
2076:d
2068:3
2058:3
2054:I
2050:+
2044:t
2041:d
2028:2
2024:e
2017:d
2009:2
1999:2
1995:I
1991:+
1985:t
1982:d
1969:1
1965:e
1958:d
1950:1
1940:1
1936:I
1932:+
1921:3
1917:e
1902:3
1889:3
1885:I
1881:+
1870:2
1866:e
1851:2
1838:2
1834:I
1830:+
1819:1
1815:e
1800:1
1787:1
1783:I
1779:=
1773:t
1770:e
1767:n
1743:ω
1723:2
1719:r
1715:m
1712:=
1709:I
1687:,
1679:I
1676:=
1672:L
1659:t
1655:L
1636:t
1632:d
1625:L
1620:d
1613:=
1548:,
1541:F
1535:r
1500:⊥
1497:F
1493:F
1478:F
1465:r
1446:r
1367:F
1364:r
1361:=
1352:F
1348:r
1345:=
1333:F
1325:r
1321:=
1243:θ
1238:F
1232:r
1226:⊥
1223:F
1217:r
1212:τ
1206:F
1202:r
1197:τ
1191:⊥
1188:F
1184:F
1180:r
1044:M
968:e
961:t
954:v
644:)
263:t
260:d
254:p
250:d
244:=
239:F
196:2
187:T
179:2
173:L
165:M
105:M
63:L
56:p
49:τ
45:F
23:.
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