933:
2170:
1765:
1186:
5185:
2165:{\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 }})}
4940:
5018:
946:
5381:
5661:
4795:
5252:
2513:
5180:{\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}}}
3820:
6212:, 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."
3651:
5376:
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
5012:
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
4147:
3241:
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
2802:
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
2798:
4952:
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
4022:
4935:{\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}}}
2398:
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3723:
3574:
1397:
1057:. 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
5716:
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
4427:
5455:
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
5319:
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
4031:
2703:
3494:
3908:
5008:
3584:
2885:
1660:
5419:, 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:
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3009:
3886:
4436:
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4603:
2333:
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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.
5568:
4800:
219:
4231:(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).
2296:
5237:
3118:
2508:{\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} .}
5307:
2379:
5023:
1140:", 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.
2181:
2265:
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
287:
3658:
2911:
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.
311:
3501:
1708:
1322:
3815:{\displaystyle {\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}=\left|{\boldsymbol {\tau }}\right|\left|\mathrm {d} {\boldsymbol {\theta }}\right|\cos 0=\tau \,\mathrm {d} \theta }
3422:
5324:, 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:
1144:
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
4313:
4304:
1293:: 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
5810:
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
5505:
1309:
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
3395:
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3451:
1424:
1038:
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5534:
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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
1614:
5476:
3444:
2686:
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1500:
1468:
7009:
2563:
2541:
3301:
4212:. 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
3653:, 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
1579:
1533:
4759:
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.
3232:
2945:
1746:
1444:
1317:
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:
112:
3827:
3646:{\displaystyle \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} =\mathbf {r} \times \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}}
3242:(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).
3268:
977:
2836:
4142:{\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} .}
566:
3155:
5329:
2793:{\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} _{\mathrm {net} }={\boldsymbol {\tau }}_{\mathrm {net} }.}
6394:
2931:. Similarly, if torque is allowed to act through an angular displacement, it is doing work. Mathematically, for rotation about a fixed axis through the
685:
5013:
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:
4017:{\displaystyle \tau =\mathbf {r} _{1}\times \mathbf {F} _{1}+\mathbf {r} _{2}\times \mathbf {F} _{2}+\ldots +\mathbf {r} _{N}\times \mathbf {F} _{N}.}
7099:
6369:
6229:
3903:
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:
2268:
658:
3063:
5264:
2346:
1269:) 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
6288:
932:
6387:
6312:
5760:). 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
2301:
1677:
5990:
47:
3727:
If the torque and the angular displacement are in the same direction, then the scalar product reduces to a product of magnitudes; i.e.,
640:
169:
6186:
6136:
6103:
5913:
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5192:
4582:{\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}}}}
3896:
6058:
4268:
7135:
7110:
7071:
6013:
2635:{\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} +\mathbf {v} \times \mathbf {p} }
4750:{\displaystyle P_{\rm {hp}}={\frac {\tau _{\rm {lbf{\cdot }ft}}\cdot 2\pi _{\rm {rad/rev}}\cdot \nu _{\rm {rev/min}}}{33,000}}.}
4598:(mechanical) for power, foot-pounds (lbf⋅ft) for torque and rpm for rotational speed. This results in the formula changing to:
306:
243:
6205:
7406:
6334:
4026:
From this it follows that the torques resulting from N number of forces acting around a pivot on an object are balanced when
301:
561:
6413:
5646:{\displaystyle {\boldsymbol {\tau }}_{2}={\boldsymbol {\tau }}_{1}+(\mathbf {r} _{2}-\mathbf {r} _{1})\times \mathbf {F} }
4243:(unit: revolution per minute or second) is used in place of angular speed (unit: radian per second), we must multiply by 2
1132:(around an axis). It is better to use a term which treats this action as a single definite entity than to use terms like "
3400:
556:
963:
950:
711:
634:
399:
4200:, which is the unit of energy, the latter can never used for torque. In the case of torque, the unit is assigned to a
630:
431:
2688:
is zero because velocity and momentum are parallel, so the second term vanishes. Therefore, torque on a particle is
1069:
from the fulcrum, for example, exerts the same torque as a force of one newton applied six metres from the fulcrum.
5773:
2254:{\displaystyle {d{\boldsymbol {\hat {e_{i}}}} \over dt}={\boldsymbol {\omega }}\times {\boldsymbol {\hat {e_{i}}}}}
850:
739:
665:
525:
458:
3040:
7421:
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6847:
6701:
5259:
A very useful special case, often given as the definition of torque in fields other than physics, is as follows:
3718:{\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}{\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}}
604:
1474:(a vector from the point about which the torque is being measured to the point where the force is applied), and
6814:
6361:
6293:
Demonstration that, as in most US industrial settings, the torque ranges are given in ft-lb rather than lbf-ft.
5481:
4223:(lbf-ft), or, for small values, the pound inch (lbf-in). In the US, torque is most commonly referred to as the
3569:{\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} }
1097:
880:
724:
5796:
of the road wheels is decreased while the torque is increased, product of which (i.e. power) does not change.
3373:
3273:
1392:{\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \implies \tau =rF_{\perp }=rF\sin \theta }
6825:
6030:
5780:, which in turn conveys the received power to the road as the output power of the bicycle. Depending on the
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594:
31:
1407:
1021:
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875:
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6366:
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546:
364:
4422:{\displaystyle P_{\rm {W}}=\tau _{\rm {N{\cdot }m}}\cdot 2\pi _{\rm {rad/rev}}\cdot \nu _{\rm {rev/s}}}
3900:
5539:
5510:
7282:
7207:
6835:
6607:
6262:
6153:"Survey of Human–Robot Collaboration in Industrial Settings: Awareness, Intelligence, and Compliance"
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162:
4239:
A conversion factor may be necessary when using different units of power or torque. For example, if
1273:
of a force from the point around which it is being determined. In three dimensions, the torque is a
7013:
6742:
6690:
6410:
5884:
5849:
5834:
5693:
5692:
output of an engine is expressed as its torque multiplied by the angular speed of the drive shaft.
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The construction of the "moment arm" is shown in the figure to the right, along with the vectors
4201:
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394:
354:
6985:
3489:{\displaystyle \mathrm {d} \mathbf {s} =\mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} }
7411:
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820:
777:
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729:
670:
446:
436:
329:
6253:
Page, Chester H. (1979). "Rebuttal to de Boer's 'Group properties of quantities and units'".
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pair. By using a larger rear gear, or by switching to a lower gear in multi-speed bicycles,
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5728:: Bicycles are typically composed of two road wheels, front and rear gears (referred to as
5003:{\displaystyle {\text{power}}={\text{torque}}\cdot 2\pi \cdot {\text{rotational speed}}.\,}
2517:
This result can easily be proven by splitting the vectors into components and applying the
1429:
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in a system which has rotation constrained to only one plane (forces and moments due to
6266:
5752:, the person who rides the bicycle, provides the input power by turning pedals, thereby
2880:{\displaystyle \mathbf {P} ={\frac {\mathrm {d} {\boldsymbol {\tau }}}{\mathrm {d} t}},}
2696:
of its angular momentum with respect to time. If multiple forces are applied, according
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6129:
Physics for
Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics
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3235:
2932:
1655:{\displaystyle {\boldsymbol {\tau }}={\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}}
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for a small car). One can measure the varying torque output over that range with a
5677:
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is given by integrating the force with respect to an elemental linear displacement
2518:
1590:
1274:
890:
815:
504:
384:
150:
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5740:
if the bicycle's transmission system allows multiple gear ratios to be used (i.e.
5664:
Torque curve of a motorcycle ("BMW K 1200 R 2005"). The horizontal axis shows the
1092:
6341:
An article showing how power, torque, and gearing affect a vehicle's performance.
3361:{\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} \mathbf {s} }
1289:
and the force vector. The direction of the torque can be determined by using the
6625:
5705:
4260:
2175:
1513:
is the amount of force directed perpendicularly to the position of the particle,
6379:
5380:
1261:
A force applied perpendicularly to a lever multiplied by its distance from the
46:
5781:
5673:
4595:
4216:, which treats the radian as a base unit rather than as a dimensionless unit.
3004:{\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \ \mathrm {d} \theta ,}
2693:
1310:
1003:
675:
349:
6113:
3881:{\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \,\mathrm {d} \theta }
6718:
6645:
6633:
5729:
1266:
995:
697:
3250:
The work done by a variable force acting over a finite linear displacement
6356:
5724:
In practice, the relationship between power and torque can be observed in
5660:
1305:
vectors and defines the plane in which the two vectors lie. The resulting
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and appeared in print in April, 1884. Usage is attested the same year by
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474:
81:
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per hour for power) would require a different custom conversion factor.
2393:
is the position vector from the origin. The time-derivative of this is:
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5854:
5749:
5725:
5403:
5251:
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991:
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77:
17:
2328:{\displaystyle {\boldsymbol {\alpha }}={\dot {\boldsymbol {\omega }}}}
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6619:
6518:
6483:
5718:
5685:
4205:
4175:
3184:{\displaystyle P={\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }},}
1605:
The net torque on a body determines the rate of change of the body's
1119:
648:
404:
6274:
5814:. Such a mechanism multiplies torque, as rotation rate is reduced.
5367:{\displaystyle \tau =({\text{distance to centre}})({\text{force}}).}
4591:
where rotational speed is in revolutions per minute (rpm, rev/min).
4192:, is properly denoted N⋅m, as the unit for torque; although this is
5949:
Dynamo-electric machinery: A Manual For
Students Of Electrotechnics
2343:
The definition of angular momentum for a single point particle is:
7296:
7221:
7155:
6759:
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5447:
equilibrium problems in two-dimensions, three equations are used.
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6098:(3rd technology update ed.). Boston: Pearson. p. 199.
5765:
3146:
2828:
489:
452:
214:{\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-2}}
6383:
1581:
is the angle between the force vector and the lever arm vector.
5701:
4763:
2291:{\displaystyle {\boldsymbol {\tau }}=I{\boldsymbol {\alpha }}}
1045:
5952:(4th ed.). New York, Harvard publishing co. p. 108.
5232:{\displaystyle 5252.113122\approx {\frac {33,000}{2\pi }}.\,}
3113:{\displaystyle E_{\mathrm {r} }={\tfrac {1}{2}}I\omega ^{2},}
2521:. But because the rate of change of linear momentum is force
1197:
is applied to the particle, only the perpendicular component
5302:{\displaystyle \tau =({\text{moment arm}})({\text{force}}).}
2374:{\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} }
5986:
by
Hendricks, Subramony, and Van Blerk, Chinappi page 148,
5696:
engines produce useful torque only over a limited range of
4183:
6350:
4431:
Dividing by 60 seconds per minute gives us the following.
4174:
and those fundamental dimensions are the same as that for
1163:. This terminology can be traced back to at least 1811 in
1126:
may be defined as that which produces or tends to produce
282:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
5680:) that the engine is capable of providing at that speed.
5402:
in the direction of that torque. This causes the top to
6305:
5377:
the plane of movement and perpendicular to the wrench.
3498:
Substitution in the above expression for work, , gives
3153:
3061:
2943:
4594:
Some people (e.g., American automotive engineers) use
3083:
2549:
2527:
1718:
1703:{\displaystyle \mathbf {L} =I{\boldsymbol {\omega }},}
6988:
6094:
Knight, Randall; Jones, Brian; Field, Stuart (2016).
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is turning, and the vertical axis is the torque (in
1313:
depends on three quantities: the force applied, the
1181:
Definition and relation to other physical quantities
6228:. Bureau International des Poids et Mesures. 2019.
5684:Torque forms part of the basic specification of an
4247:radians per revolution. In the following formulas,
3417:{\displaystyle \mathrm {d} {\boldsymbol {\theta }}}
3397:is related to a corresponding angular displacement
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39:
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4219:The traditional imperial units for torque are the
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2927:is allowed to act through a distance, it is doing
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2245:
2204:
1096:, 'to twist') is said to have been suggested by
6346:Torque and Angular Momentum in Circular Motion
3370:However, the infinitesimal linear displacement
3032:represent (respectively) the initial and final
2543:and the rate of change of position is velocity
1193:relative to its axis of rotation. When a force
1110:
5788:pair is converted to a (torque, angular speed)
6395:
5384:The torque caused by the two opposing forces
1672:is time. For the motion of a point particle,
971:
8:
5904:Serway, R. A. and Jewett, J. W. Jr. (2003).
5756:the front sprocket (commonly referred to as
4299:{\displaystyle P=\tau \cdot 2\pi \cdot \nu }
2923:can also be used to understand torque. If a
2261:This equation is the rotational analogue of
1593:(N⋅m). For more on the units of torque, see
1168:
6169:Kleppner, Daniel; Kolenkow, Robert (1973).
5941:
5939:
5929:Collected Papers in Physics and Engineering
4953:distance are increased proportionately by 2
4227:(denoted as either lb-ft or ft-lb) and the
2902:
1118:is that which produces or tends to produce
6402:
6388:
6380:
6005:Kane, T.R. Kane and D.A. Levinson (1985).
1351:
1347:
1108:. Thompson motivates the term as follows:
978:
964:
225:
45:
6990:
6989:
6987:
6083:. John Wiley & Sons. pp. 184–85.
6079:Halliday, David; Resnick, Robert (1970).
5961:
5959:
5784:of the bicycle, a (torque, angular speed)
5638:
5626:
5621:
5611:
5606:
5593:
5588:
5578:
5573:
5570:
5549:
5544:
5541:
5520:
5515:
5512:
5500:{\displaystyle {\boldsymbol {\tau }}_{1}}
5491:
5486:
5483:
5463:
5461:
5353:
5342:
5331:
5288:
5277:
5266:
5228:
5202:
5194:
5154:
5146:
5143:
5119:
5111:
5108:
5090:
5076:
5071:
5066:
5063:
5055:
5038:
5026:
5022:
5020:
4999:
4991:
4974:
4966:
4964:
4920:
4912:
4882:
4854:
4847:
4826:
4818:
4815:
4803:
4799:
4797:
4713:
4703:
4702:
4678:
4668:
4667:
4643:
4633:
4632:
4625:
4612:
4611:
4605:
4562:
4552:
4534:
4524:
4523:
4499:
4489:
4488:
4467:
4463:
4462:
4455:
4445:
4444:
4438:
4408:
4398:
4397:
4373:
4363:
4362:
4341:
4337:
4336:
4322:
4321:
4315:
4270:
4131:
4122:
4117:
4107:
4102:
4086:
4081:
4071:
4066:
4056:
4051:
4041:
4036:
4033:
4005:
4000:
3990:
3985:
3969:
3964:
3954:
3949:
3939:
3934:
3924:
3919:
3910:
3870:
3869:
3858:
3853:
3846:
3841:
3829:
3804:
3803:
3778:
3773:
3759:
3747:
3742:
3734:
3732:
3710:
3705:
3697:
3689:
3684:
3677:
3672:
3660:
3638:
3633:
3625:
3617:
3609:
3601:
3596:
3588:
3586:
3561:
3553:
3548:
3540:
3532:
3527:
3520:
3515:
3503:
3481:
3473:
3468:
3460:
3455:
3453:
3431:
3429:
3409:
3404:
3402:
3382:
3377:
3375:
3353:
3348:
3340:
3332:
3327:
3320:
3315:
3303:
3282:
3277:
3275:
3255:
3219:
3173:
3165:
3157:
3101:
3082:
3072:
3071:
3065:
2990:
2976:
2971:
2964:
2959:
2947:
2863:
2856:
2851:
2848:
2840:
2838:
2774:
2773:
2768:
2751:
2750:
2745:
2736:
2722:
2715:
2710:
2707:
2705:
2673:
2671:
2651:
2649:
2627:
2619:
2611:
2603:
2589:
2582:
2577:
2574:
2572:
2550:
2548:
2528:
2526:
2497:
2483:
2476:
2471:
2468:
2454:
2447:
2442:
2439:
2431:
2417:
2410:
2405:
2402:
2400:
2366:
2358:
2350:
2348:
2314:
2313:
2305:
2303:
2283:
2272:
2270:
2239:
2233:
2232:
2224:
2198:
2192:
2191:
2185:
2183:
2154:
2140:
2126:
2125:
2096:
2090:
2089:
2083:
2077:
2067:
2037:
2031:
2030:
2024:
2018:
2008:
1978:
1972:
1971:
1965:
1959:
1949:
1930:
1924:
1923:
1911:
1905:
1904:
1898:
1879:
1873:
1872:
1860:
1854:
1853:
1847:
1828:
1822:
1821:
1809:
1803:
1802:
1796:
1776:
1775:
1770:
1767:
1732:
1717:
1692:
1681:
1679:
1641:
1634:
1629:
1626:
1618:
1616:
1566:
1520:
1506:is the magnitude of the force vector and
1487:
1485:
1455:
1453:
1431:
1411:
1409:
1365:
1342:
1334:
1326:
1324:
1025:
1023:
263:
257:
248:
247:
245:
202:
196:
195:
188:
182:
181:
174:
173:
171:
99:
6422:
5700:(typically from around 1,000–6,000
5398:causes a change in the angular momentum
3895:The principle of moments, also known as
3578:The expression inside the integral is a
3390:{\displaystyle \mathrm {d} \mathbf {s} }
3290:{\displaystyle \mathrm {d} \mathbf {s} }
1478:is the magnitude of the position vector,
5926:Thomson, James; Larmor, Joseph (1912).
5897:
5589:
5574:
5487:
3779:
3760:
3748:
3735:
3711:
3698:
3639:
3602:
3554:
3474:
3410:
3174:
3166:
2857:
2769:
2339:Proof of the equivalence of definitions
2316:
2306:
2284:
2273:
2240:
2236:
2225:
2199:
2195:
2155:
2141:
2128:
2093:
2034:
1975:
1927:
1876:
1825:
1771:
1693:
1619:
1412:
1327:
1026:
297:
233:
5776:transmits the input power to the road
1601:Relationship with the angular momentum
1257:and is directed outward from the page.
1018:). The symbol for torque is typically
197:
183:
175:
36:
6096:College Physics: A Strategic Approach
2803:each point within the mass, and then
1419:{\displaystyle {\boldsymbol {\tau }}}
1033:{\displaystyle {\boldsymbol {\tau }}}
660:Newton's law of universal gravitation
7:
6289:"Dial Torque Wrenches from Grainger"
5946:Thompson, Silvanus Phillips (1893).
5906:Physics for Scientists and Engineers
1112:Just as the Newtonian definition of
1053:of force, it is commonly denoted by
6357:An interactive simulation of torque
5435:, and the torque a third equation:
1668:is the angular momentum vector and
1177:of Poisson's work appears in 1842.
641:Mechanics of planar particle motion
249:
6376:An order-of-magnitude interactive.
6223:"SI brochure Ed. 9, Section 2.3.4"
4724:
4721:
4718:
4710:
4707:
4704:
4689:
4686:
4683:
4675:
4672:
4669:
4651:
4648:
4640:
4637:
4634:
4616:
4613:
4573:
4570:
4567:
4559:
4545:
4542:
4539:
4531:
4528:
4525:
4510:
4507:
4504:
4496:
4493:
4490:
4472:
4464:
4446:
4413:
4405:
4402:
4399:
4384:
4381:
4378:
4370:
4367:
4364:
4346:
4338:
4323:
3871:
3805:
3774:
3743:
3706:
3634:
3597:
3549:
3469:
3456:
3405:
3378:
3349:
3278:
3073:
3047:also represents the change in the
2991:
2915:Relationship with power and energy
2907:meaning 'to rotate', but the term
2864:
2852:
2781:
2778:
2775:
2758:
2755:
2752:
2723:
2711:
2590:
2578:
2484:
2472:
2455:
2443:
2418:
2406:
1783:
1780:
1777:
1642:
1630:
1539:, which produces a vector that is
1189:A particle is located at position
25:
6303:Erjavec, Jack (22 January 2010).
6036:Traité de mécanique, tome premier
6007:Dynamics, Theory and Applications
5708:, and show it as a torque curve.
4957:in the above derivation to give:
7243:
6307:. Cengage Learning. p. 38.
5932:. University Press. p. civ.
5744:), all of which attached to the
5639:
5622:
5607:
5558:{\displaystyle \mathbf {r} _{2}}
5545:
5536:, then the torque measured from
5529:{\displaystyle \mathbf {r} _{1}}
5516:
5464:
4132:
4118:
4103:
4082:
4067:
4052:
4037:
4001:
3986:
3965:
3950:
3935:
3920:
3626:
3618:
3610:
3589:
3562:
3541:
3482:
3461:
3432:
3383:
3354:
3341:
3283:
2841:
2746:
2737:
2716:
2674:
2652:
2628:
2620:
2612:
2604:
2583:
2551:
2529:
2498:
2477:
2448:
2432:
2411:
2367:
2359:
2351:
2131:
2097:
2038:
1979:
1931:
1880:
1829:
1682:
1635:
1488:
1456:
1343:
1335:
1010:. It is also referred to as the
945:
944:
931:
264:
6426:Linear/translational quantities
6235:from the original on 2020-07-26
6131:(5th ed.). W. H. Freeman.
6061:from the original on 2007-08-19
1446:is the magnitude of the torque,
1204:produces a torque. This torque
5632:
5602:
5358:
5350:
5347:
5339:
5293:
5285:
5282:
5274:
4893:
4873:
4762:The use of other units (e.g.,
2897:This word is derived from the
2644:The cross product of momentum
2159:
2148:
2102:
2043:
1984:
1936:
1885:
1834:
1760:pseudovector. It follows that
1348:
1:
6431:Angular/rotational quantities
5242:Special cases and other facts
3899:(not to be confused with the
2666:with its associated velocity
1297:is perpendicular to both the
567:Koopman–von Neumann mechanics
6173:An Introduction to Mechanics
6055:"Right Hand Rule for Torque"
5507:is the torque measured from
5471:{\displaystyle \mathbf {F} }
3439:{\displaystyle \mathbf {r} }
2681:{\displaystyle \mathbf {v} }
2659:{\displaystyle \mathbf {p} }
1495:{\displaystyle \mathbf {F} }
1463:{\displaystyle \mathbf {r} }
1049:. When being referred to as
635:Non-inertial reference frame
27:Turning force around an axis
6255:American Journal of Physics
4774:For a rotating object, the
1155:, torque is referred to as
562:Appell's equation of motion
432:Inertial frame of reference
7438:
7004:{\displaystyle {\dot {m}}}
6428:
5803:
2174:using the derivative of a
1594:
1076:
29:
6702:specific angular momentum
6430:
6425:
6420:
5971:Oxford English Dictionary
4235:Conversion to other units
3049:rotational kinetic energy
2558:{\textstyle \mathbf {v} }
2536:{\textstyle \mathbf {F} }
1426:is the torque vector and
1106:Dynamo-Electric Machinery
44:
6177:. McGraw-Hill. pp.
5764:) and the torque at the
4194:dimensionally equivalent
1104:in the first edition of
725:Rotating reference frame
557:Hamilton–Jacobi equation
6826:rotational acceleration
6332:"Horsepower and Torque"
6081:Fundamentals of Physics
5984:Physics for Engineering
5908:. 6th ed. Brooks Cole.
5451:Net force versus torque
5415:For an object to be in
4263:) is rotational speed.
1574:{\displaystyle \theta }
1528:{\displaystyle \times }
1159:, usually shortened to
666:Newton's laws of motion
526:Newton's laws of motion
32:Torque (disambiguation)
7005:
5845:Mechanical equilibrium
5681:
5647:
5559:
5530:
5501:
5472:
5445:statically determinate
5407:
5368:
5303:
5256:
5233:
5181:
5004:
4936:
4751:
4583:
4423:
4300:
4214:orientational analysis
4208:, it is assigned to a
4143:
4018:
3882:
3816:
3719:
3647:
3570:
3490:
3440:
3424:and the radius vector
3418:
3391:
3362:
3291:
3264:
3228:
3227:{\displaystyle \cdot }
3185:
3114:
3057:of the body, given by
3005:
2921:conservation of energy
2903:
2888:
2881:
2807:over the entire mass.
2794:
2682:
2660:
2636:
2559:
2537:
2509:
2375:
2329:
2292:
2255:
2166:
1742:
1704:
1656:
1575:
1529:
1496:
1464:
1440:
1420:
1393:
1258:
1175:An English translation
1169:
1153:mechanical engineering
1142:
1091:
1034:
693:Simple harmonic motion
606:Euler's laws of motion
400:D'Alembert's principle
283:
215:
108:
7407:Mechanical quantities
7006:
6362:Torque Unit Converter
6127:Tipler, Paul (2004).
6031:Poisson, Siméon-Denis
5663:
5648:
5560:
5531:
5502:
5473:
5383:
5369:
5304:
5254:
5234:
5182:
5005:
4937:
4752:
4584:
4424:
4301:
4186:literature indicates
4144:
4019:
3883:
3817:
3720:
3648:
3580:scalar triple product
3571:
3491:
3441:
3419:
3392:
3363:
3292:
3265:
3229:
3186:
3145:is the work per unit
3115:
3041:work–energy principle
3006:
2882:
2832:
2823:is the derivative of
2811:Derivatives of torque
2795:
2683:
2661:
2637:
2560:
2538:
2510:
2376:
2330:
2293:
2256:
2167:
1743:
1741:{\textstyle I=mr^{2}}
1705:
1657:
1576:
1530:
1502:is the force vector,
1497:
1465:
1441:
1439:{\displaystyle \tau }
1421:
1394:
1281:, it is given by the
1188:
1035:
1014:(also abbreviated to
547:Hamiltonian mechanics
365:Statistical mechanics
284:
216:
109:
107:{\displaystyle \tau }
51:Relationship between
6986:
6836:angular acceleration
6608:angular displacement
5738:derailleur mechanism
5569:
5540:
5511:
5482:
5460:
5443:. That is, to solve
5330:
5265:
5193:
5019:
4963:
4796:
4604:
4437:
4314:
4269:
4032:
3909:
3891:Principle of moments
3828:
3731:
3659:
3585:
3502:
3452:
3428:
3401:
3374:
3302:
3274:
3254:
3218:
3156:
3064:
3039:It follows from the
2946:
2939:can be expressed as
2837:
2704:
2670:
2648:
2571:
2547:
2525:
2399:
2347:
2302:
2269:
2182:
1766:
1716:
1678:
1615:
1565:
1519:
1484:
1452:
1430:
1408:
1323:
1291:right hand grip rule
1165:Siméon Denis Poisson
1151:In the UK and in US
1102:Silvanus P. Thompson
1022:
770:Angular acceleration
762:Rotational frequency
542:Lagrangian mechanics
535:Analytical mechanics
291:Second law of motion
244:
170:
98:
30:For other uses, see
6926:weighted position:
6743:rotational velocity
6691:kinematic viscosity
6411:Classical mechanics
6267:1979AmJPh..47..820P
6203:official SI website
5885:Torsion (mechanics)
5850:Rigid body dynamics
5835:Conversion of units
5742:multi-speed bicycle
5694:Internal-combustion
3901:geometrical theorem
3865:
3696:
3539:
3339:
2983:
2698:Newton's second law
2263:Newton's second law
1287:displacement vector
1265:(the length of the
1170:Traité de mécanique
1122:(along a line), so
1061:. A force of three
1006:analogue of linear
622:Harmonic oscillator
600:Equations of motion
235:Classical mechanics
229:Part of a series on
7001:
6372:2021-05-08 at the
6337:2007-03-28 at the
6208:2021-04-19 at the
6016:2015-06-19 at the
5993:2017-07-11 at the
5870:Torque screwdriver
5682:
5643:
5555:
5526:
5497:
5468:
5417:static equilibrium
5411:Static equilibrium
5408:
5364:
5344:distance to centre
5299:
5257:
5255:Moment arm diagram
5247:Moment arm formula
5229:
5177:
5175:
5000:
4932:
4930:
4864:
4747:
4579:
4419:
4296:
4139:
4014:
3897:Varignon's theorem
3878:
3837:
3812:
3715:
3668:
3643:
3566:
3511:
3486:
3436:
3414:
3387:
3358:
3311:
3287:
3260:
3224:
3181:
3110:
3092:
3001:
2955:
2877:
2790:
2678:
2656:
2632:
2555:
2533:
2505:
2385:is the particle's
2371:
2325:
2288:
2251:
2162:
1738:
1700:
1652:
1589:for torque is the
1571:
1525:
1492:
1460:
1436:
1416:
1389:
1259:
1079:Couple (mechanics)
1030:
938:Physics portal
552:Routhian mechanics
427:Frame of reference
279:
211:
152:SI base units
104:
7389:
7388:
7384:
7383:
6998:
6951:moment of inertia
6367:A feel for torque
6314:978-1-4354-3933-7
6291:. Grainger. 2020.
5806:Torque multiplier
5800:Torque multiplier
5768:of the bicycle's
5732:) meshing with a
5698:rotational speeds
5478:is not zero, and
5356:
5345:
5291:
5280:
5223:
5171:
5157:
5149:
5131:
5128:
5127:
5122:
5114:
5094:
5085:
5084:
5079:
5069:
5058:
5041:
5029:
4994:
4977:
4969:
4923:
4915:
4900:
4885:
4863:
4859:
4835:
4834:
4829:
4821:
4806:
4742:
4577:
4558:
3263:{\displaystyle s}
3129:moment of inertia
3091:
3034:angular positions
2989:
2872:
2731:
2598:
2492:
2463:
2426:
2322:
2248:
2219:
2207:
2134:
2117:
2105:
2058:
2046:
1999:
1987:
1939:
1920:
1888:
1869:
1837:
1818:
1750:moment of inertia
1650:
988:
987:
735:Centrifugal force
730:Centripetal force
686:Euler's equations
671:Relative velocity
447:Moment of inertia
277:
251:
224:
223:
16:(Redirected from
7429:
7422:Moment (physics)
7376:
7372:
7360:
7356:
7336:
7332:
7320:
7316:
7294:
7290:
7280:
7270:
7255:
7251:
7241:
7219:
7215:
7205:
7195:
7180:
7176:
7163:
7139:
7133:
7125:
7114:
7108:
7097:
7090:angular momentum
7075:
7069:
7061:
7046:
7040:
7030:
7017:
7011:
7010:
7008:
7007:
7002:
7000:
6999:
6991:
6964:
6958:
6942:
6919:
6900:
6895:
6873:
6851:
6845:
6828:
6812:
6790:
6784:
6775:angular velocity
6772:
6753:
6752:
6739:
6738:
6731:rotational speed
6727:
6726:
6709:
6698:
6683:
6673:
6654:
6653:
6636:
6631:
6617:
6605:
6585:
6566:
6565:
6559:
6553:
6542:
6516:
6496:
6481:
6465:
6458:
6423:
6404:
6397:
6390:
6381:
6319:
6318:
6300:
6294:
6292:
6285:
6279:
6278:
6250:
6244:
6243:
6241:
6240:
6234:
6227:
6219:
6213:
6199:
6193:
6192:
6176:
6166:
6157:
6156:
6149:
6143:
6142:
6124:
6118:
6117:
6091:
6085:
6084:
6076:
6070:
6069:
6067:
6066:
6051:
6045:
6044:
6027:
6021:
6003:
5997:
5981:
5975:
5974:
5963:
5954:
5953:
5943:
5934:
5933:
5923:
5917:
5902:
5860:Torque converter
5772:. The bicycle's
5666:rotational speed
5652:
5650:
5649:
5644:
5642:
5631:
5630:
5625:
5616:
5615:
5610:
5598:
5597:
5592:
5583:
5582:
5577:
5564:
5562:
5561:
5556:
5554:
5553:
5548:
5535:
5533:
5532:
5527:
5525:
5524:
5519:
5506:
5504:
5503:
5498:
5496:
5495:
5490:
5477:
5475:
5474:
5469:
5467:
5442:
5434:
5426:
5373:
5371:
5370:
5365:
5357:
5354:
5346:
5343:
5308:
5306:
5305:
5300:
5292:
5289:
5281:
5278:
5238:
5236:
5235:
5230:
5224:
5222:
5214:
5203:
5186:
5184:
5183:
5178:
5176:
5172:
5170:
5159:
5158:
5155:
5150:
5147:
5144:
5136:
5132:
5130:
5129:
5125:
5124:
5123:
5120:
5115:
5112:
5109:
5092:
5091:
5086:
5082:
5081:
5080:
5077:
5075:
5070:
5067:
5064:
5059:
5057:rotational speed
5056:
5042:
5039:
5030:
5027:
5009:
5007:
5006:
5001:
4995:
4993:rotational speed
4992:
4978:
4975:
4970:
4967:
4956:
4941:
4939:
4938:
4933:
4931:
4924:
4921:
4916:
4913:
4905:
4901:
4896:
4886:
4883:
4869:
4865:
4857:
4856:
4848:
4840:
4836:
4832:
4831:
4830:
4827:
4822:
4819:
4816:
4807:
4804:
4756:
4754:
4753:
4748:
4743:
4741:
4730:
4729:
4728:
4727:
4717:
4694:
4693:
4692:
4682:
4656:
4655:
4654:
4647:
4626:
4621:
4620:
4619:
4588:
4586:
4585:
4580:
4578:
4576:
4566:
4556:
4551:
4550:
4549:
4548:
4538:
4515:
4514:
4513:
4503:
4477:
4476:
4475:
4471:
4456:
4451:
4450:
4449:
4428:
4426:
4425:
4420:
4418:
4417:
4416:
4412:
4389:
4388:
4387:
4377:
4351:
4350:
4349:
4345:
4328:
4327:
4326:
4305:
4303:
4302:
4297:
4246:
4241:rotational speed
4173:
4170:
4167:
4148:
4146:
4145:
4140:
4135:
4127:
4126:
4121:
4112:
4111:
4106:
4091:
4090:
4085:
4076:
4075:
4070:
4061:
4060:
4055:
4046:
4045:
4040:
4023:
4021:
4020:
4015:
4010:
4009:
4004:
3995:
3994:
3989:
3974:
3973:
3968:
3959:
3958:
3953:
3944:
3943:
3938:
3929:
3928:
3923:
3887:
3885:
3884:
3879:
3874:
3864:
3863:
3862:
3852:
3851:
3850:
3821:
3819:
3818:
3813:
3808:
3787:
3783:
3782:
3777:
3767:
3763:
3751:
3746:
3738:
3724:
3722:
3721:
3716:
3714:
3709:
3701:
3695:
3694:
3693:
3683:
3682:
3681:
3652:
3650:
3649:
3644:
3642:
3637:
3629:
3621:
3613:
3605:
3600:
3592:
3575:
3573:
3572:
3567:
3565:
3557:
3552:
3544:
3538:
3537:
3536:
3526:
3525:
3524:
3495:
3493:
3492:
3487:
3485:
3477:
3472:
3464:
3459:
3445:
3443:
3442:
3437:
3435:
3423:
3421:
3420:
3415:
3413:
3408:
3396:
3394:
3393:
3388:
3386:
3381:
3367:
3365:
3364:
3359:
3357:
3352:
3344:
3338:
3337:
3336:
3326:
3325:
3324:
3296:
3294:
3293:
3288:
3286:
3281:
3269:
3267:
3266:
3261:
3233:
3231:
3230:
3225:
3212:angular velocity
3191:
3188:
3187:
3182:
3177:
3169:
3131:of the body and
3120:
3117:
3116:
3111:
3106:
3105:
3093:
3084:
3078:
3077:
3076:
3011:
3008:
3007:
3002:
2994:
2987:
2982:
2981:
2980:
2970:
2969:
2968:
2906:
2886:
2884:
2883:
2878:
2873:
2871:
2867:
2861:
2860:
2855:
2849:
2844:
2827:with respect to
2799:
2797:
2796:
2791:
2786:
2785:
2784:
2772:
2763:
2762:
2761:
2749:
2740:
2732:
2730:
2726:
2720:
2719:
2714:
2708:
2694:first derivative
2687:
2685:
2684:
2679:
2677:
2665:
2663:
2662:
2657:
2655:
2641:
2639:
2638:
2633:
2631:
2623:
2615:
2607:
2599:
2597:
2593:
2587:
2586:
2581:
2575:
2564:
2562:
2561:
2556:
2554:
2542:
2540:
2539:
2534:
2532:
2514:
2512:
2511:
2506:
2501:
2493:
2491:
2487:
2481:
2480:
2475:
2469:
2464:
2462:
2458:
2452:
2451:
2446:
2440:
2435:
2427:
2425:
2421:
2415:
2414:
2409:
2403:
2380:
2378:
2377:
2372:
2370:
2362:
2354:
2334:
2332:
2331:
2326:
2324:
2323:
2315:
2309:
2297:
2295:
2294:
2289:
2287:
2276:
2260:
2258:
2257:
2252:
2250:
2249:
2244:
2243:
2234:
2228:
2220:
2218:
2210:
2209:
2208:
2203:
2202:
2193:
2186:
2171:
2169:
2168:
2163:
2158:
2144:
2136:
2135:
2127:
2118:
2116:
2108:
2107:
2106:
2101:
2100:
2091:
2084:
2082:
2081:
2072:
2071:
2059:
2057:
2049:
2048:
2047:
2042:
2041:
2032:
2025:
2023:
2022:
2013:
2012:
2000:
1998:
1990:
1989:
1988:
1983:
1982:
1973:
1966:
1964:
1963:
1954:
1953:
1941:
1940:
1935:
1934:
1925:
1922:
1921:
1916:
1915:
1906:
1903:
1902:
1890:
1889:
1884:
1883:
1874:
1871:
1870:
1865:
1864:
1855:
1852:
1851:
1839:
1838:
1833:
1832:
1823:
1820:
1819:
1814:
1813:
1804:
1801:
1800:
1788:
1787:
1786:
1774:
1758:angular velocity
1747:
1745:
1744:
1739:
1737:
1736:
1709:
1707:
1706:
1701:
1696:
1685:
1661:
1659:
1658:
1653:
1651:
1649:
1645:
1639:
1638:
1633:
1627:
1622:
1607:angular momentum
1580:
1578:
1577:
1572:
1554:
1548:
1534:
1532:
1531:
1526:
1501:
1499:
1498:
1493:
1491:
1469:
1467:
1466:
1461:
1459:
1445:
1443:
1442:
1437:
1425:
1423:
1422:
1417:
1415:
1398:
1396:
1395:
1390:
1370:
1369:
1346:
1338:
1330:
1315:lever arm vector
1256:
1251:
1245:
1239:
1230:
1219:
1172:
1056:
1040:, the lowercase
1039:
1037:
1036:
1031:
1029:
980:
973:
966:
953:
948:
947:
940:
936:
935:
841:Johann Bernoulli
836:Daniel Bernoulli
757:Tangential speed
661:
637:
612:Fictitious force
607:
459:Mechanical power
449:
390:Angular momentum
288:
286:
285:
280:
278:
276:
268:
267:
258:
253:
252:
226:
220:
218:
217:
212:
210:
209:
201:
200:
193:
192:
187:
186:
179:
178:
153:
138:pound-force-feet
113:
111:
110:
105:
84:not considered).
71:angular momentum
49:
37:
21:
7437:
7436:
7432:
7431:
7430:
7428:
7427:
7426:
7392:
7391:
7390:
7385:
7374:
7373:
7368:
7358:
7357:
7352:
7334:
7333:
7328:
7318:
7317:
7312:
7292:
7291:
7286:
7276:
7266:
7253:
7252:
7247:
7235:
7217:
7216:
7211:
7201:
7191:
7178:
7177:
7175:
7169:
7159:
7137:
7134:
7131:
7123:
7112:
7109:
7103:
7100:angular impulse
7093:
7073:
7070:
7067:
7059:
7044:
7041:
7036:
7026:
7015:
7012:
6984:
6983:
6982:
6962:
6959:
6954:
6927:
6920:
6915:
6898:
6896:
6889:
6874:
6869:
6849:
6846:
6839:
6829:
6824:
6813:
6808:
6788:
6785:
6778:
6768:
6754:
6746:
6741:
6734:
6729:
6722:
6717:
6710:
6705:
6700:
6694:
6684:
6679:
6669:
6655:
6649:
6644:
6632:
6629:
6624:
6618:
6611:
6601:
6586:
6581:
6571:
6561:
6555:
6549:
6544:
6538:
6517:
6512:
6497:
6492:
6482:
6477:
6461:
6454:
6416:
6408:
6374:Wayback Machine
6351:Project PHYSNET
6339:Wayback Machine
6328:
6323:
6322:
6315:
6302:
6301:
6297:
6287:
6286:
6282:
6275:10.1119/1.11704
6252:
6251:
6247:
6238:
6236:
6232:
6225:
6221:
6220:
6216:
6210:Wayback Machine
6200:
6196:
6189:
6168:
6167:
6160:
6151:
6150:
6146:
6139:
6126:
6125:
6121:
6106:
6093:
6092:
6088:
6078:
6077:
6073:
6064:
6062:
6053:
6052:
6048:
6029:
6028:
6024:
6018:Wayback Machine
6004:
6000:
5995:Wayback Machine
5982:
5978:
5965:
5964:
5957:
5945:
5944:
5937:
5925:
5924:
5920:
5903:
5899:
5894:
5889:
5840:Friction torque
5820:
5808:
5802:
5791:
5787:
5714:electric motors
5658:
5620:
5605:
5587:
5572:
5567:
5566:
5543:
5538:
5537:
5514:
5509:
5508:
5485:
5480:
5479:
5458:
5457:
5453:
5436:
5428:
5420:
5413:
5397:
5390:
5328:
5327:
5263:
5262:
5249:
5244:
5215:
5204:
5191:
5190:
5174:
5173:
5160:
5145:
5134:
5133:
5110:
5095:
5065:
5031:
5017:
5016:
4961:
4960:
4954:
4929:
4928:
4903:
4902:
4850:
4849:
4838:
4837:
4828:linear distance
4817:
4808:
4794:
4793:
4778:covered at the
4776:linear distance
4772:
4731:
4698:
4663:
4628:
4627:
4607:
4602:
4601:
4519:
4484:
4458:
4457:
4440:
4435:
4434:
4393:
4358:
4332:
4317:
4312:
4311:
4308:Showing units:
4267:
4266:
4261:Greek letter nu
4255:is torque, and
4244:
4237:
4171:
4168:
4165:
4164:, symbolically
4160:of force times
4156:Torque has the
4154:
4116:
4101:
4080:
4065:
4050:
4035:
4030:
4029:
3999:
3984:
3963:
3948:
3933:
3918:
3907:
3906:
3893:
3854:
3842:
3826:
3825:
3772:
3768:
3755:
3729:
3728:
3685:
3673:
3657:
3656:
3583:
3582:
3528:
3516:
3500:
3499:
3450:
3449:
3426:
3425:
3399:
3398:
3372:
3371:
3328:
3316:
3300:
3299:
3272:
3271:
3252:
3251:
3248:
3234:represents the
3216:
3215:
3154:
3152:
3097:
3067:
3062:
3060:
3056:
3031:
3024:
3018:is torque, and
2972:
2960:
2944:
2942:
2929:mechanical work
2917:
2862:
2850:
2835:
2834:
2813:
2767:
2744:
2721:
2709:
2702:
2701:
2700:it follows that
2668:
2667:
2646:
2645:
2588:
2576:
2569:
2568:
2545:
2544:
2523:
2522:
2482:
2470:
2453:
2441:
2416:
2404:
2397:
2396:
2387:linear momentum
2345:
2344:
2341:
2300:
2299:
2267:
2266:
2235:
2211:
2194:
2187:
2180:
2179:
2109:
2092:
2085:
2073:
2063:
2050:
2033:
2026:
2014:
2004:
1991:
1974:
1967:
1955:
1945:
1926:
1907:
1894:
1875:
1856:
1843:
1824:
1805:
1792:
1769:
1764:
1763:
1756:is the orbital
1728:
1714:
1713:
1676:
1675:
1640:
1628:
1613:
1612:
1603:
1563:
1562:
1557:right-hand rule
1550:
1544:
1517:
1516:
1512:
1482:
1481:
1472:position vector
1450:
1449:
1428:
1427:
1406:
1405:
1361:
1321:
1320:
1279:point particles
1263:lever's fulcrum
1247:
1241:
1240:| = |
1238:
1232:
1226:
1221:
1205:
1203:
1183:
1157:moment of force
1081:
1075:
1054:
1020:
1019:
1012:moment of force
984:
943:
930:
929:
922:
921:
920:
795:
787:
786:
766:
720:Circular motion
714:
704:
703:
702:
659:
629:
626:
605:
584:
576:
575:
572:
571:
529:
519:
511:
510:
509:
468:
464:Mechanical work
457:
441:
379:
371:
370:
369:
324:
316:
293:
269:
259:
242:
241:
194:
180:
168:
167:
151:
134:
96:
95:
92:
85:
64:linear momentum
35:
28:
23:
22:
15:
12:
11:
5:
7435:
7433:
7425:
7424:
7419:
7414:
7409:
7404:
7394:
7393:
7387:
7386:
7382:
7381:
7362:
7346:
7344:
7341:
7322:
7306:
7304:
7300:
7299:
7260:
7229:
7227:
7224:
7185:
7173:
7153:
7151:
7147:
7146:
7117:
7087:
7085:
7082:
7053:
7020:
6997:
6994:
6979:Mass flow rate
6976:
6972:
6971:
6969:
6967:
6948:
6945:
6943:
6924:
6909:
6905:
6904:
6902:
6883:
6881:
6878:
6876:
6863:
6861:
6857:
6856:
6854:
6833:
6822:
6819:
6817:
6802:
6800:
6796:
6795:
6793:
6762:
6715:
6712:
6688:
6663:
6642:
6638:
6637:
6622:
6595:
6593:
6590:
6575:
6532:
6530:
6526:
6525:
6523:
6521:
6506:
6503:
6501:
6486:
6471:
6467:
6466:
6459:
6452:
6449:
6446:
6443:
6440:
6437:
6433:
6432:
6429:
6427:
6421:
6418:
6417:
6409:
6407:
6406:
6399:
6392:
6384:
6378:
6377:
6364:
6359:
6354:
6342:
6327:
6326:External links
6324:
6321:
6320:
6313:
6295:
6280:
6245:
6214:
6194:
6187:
6158:
6144:
6137:
6119:
6104:
6086:
6071:
6046:
6022:
5998:
5976:
5955:
5935:
5918:
5896:
5895:
5893:
5890:
5888:
5887:
5882:
5877:
5872:
5867:
5865:Torque limiter
5862:
5857:
5852:
5847:
5842:
5837:
5832:
5830:Bending moment
5827:
5821:
5819:
5816:
5804:Main article:
5801:
5798:
5789:
5785:
5657:
5656:Machine torque
5654:
5641:
5637:
5634:
5629:
5624:
5619:
5614:
5609:
5604:
5601:
5596:
5591:
5586:
5581:
5576:
5552:
5547:
5523:
5518:
5494:
5489:
5466:
5452:
5449:
5412:
5409:
5395:
5388:
5363:
5360:
5352:
5349:
5341:
5338:
5335:
5298:
5295:
5287:
5284:
5276:
5273:
5270:
5248:
5245:
5243:
5240:
5227:
5221:
5218:
5213:
5210:
5207:
5201:
5198:
5169:
5166:
5163:
5153:
5142:
5139:
5137:
5135:
5118:
5107:
5104:
5101:
5098:
5089:
5074:
5062:
5054:
5051:
5048:
5045:
5037:
5034:
5032:
5025:
5024:
4998:
4990:
4987:
4984:
4981:
4973:
4927:
4919:
4911:
4908:
4906:
4904:
4899:
4895:
4892:
4889:
4881:
4878:
4875:
4872:
4868:
4862:
4853:
4846:
4843:
4841:
4839:
4825:
4814:
4811:
4809:
4802:
4801:
4771:
4768:
4746:
4740:
4737:
4734:
4726:
4723:
4720:
4716:
4712:
4709:
4706:
4701:
4697:
4691:
4688:
4685:
4681:
4677:
4674:
4671:
4666:
4662:
4659:
4653:
4650:
4646:
4642:
4639:
4636:
4631:
4624:
4618:
4615:
4610:
4575:
4572:
4569:
4565:
4561:
4555:
4547:
4544:
4541:
4537:
4533:
4530:
4527:
4522:
4518:
4512:
4509:
4506:
4502:
4498:
4495:
4492:
4487:
4483:
4480:
4474:
4470:
4466:
4461:
4454:
4448:
4443:
4415:
4411:
4407:
4404:
4401:
4396:
4392:
4386:
4383:
4380:
4376:
4372:
4369:
4366:
4361:
4357:
4354:
4348:
4344:
4340:
4335:
4331:
4325:
4320:
4295:
4292:
4289:
4286:
4283:
4280:
4277:
4274:
4236:
4233:
4204:, whereas for
4153:
4150:
4138:
4134:
4130:
4125:
4120:
4115:
4110:
4105:
4100:
4097:
4094:
4089:
4084:
4079:
4074:
4069:
4064:
4059:
4054:
4049:
4044:
4039:
4013:
4008:
4003:
3998:
3993:
3988:
3983:
3980:
3977:
3972:
3967:
3962:
3957:
3952:
3947:
3942:
3937:
3932:
3927:
3922:
3917:
3914:
3892:
3889:
3877:
3873:
3868:
3861:
3857:
3849:
3845:
3840:
3836:
3833:
3811:
3807:
3802:
3799:
3796:
3793:
3790:
3786:
3781:
3776:
3771:
3766:
3762:
3758:
3754:
3750:
3745:
3741:
3737:
3713:
3708:
3704:
3700:
3692:
3688:
3680:
3676:
3671:
3667:
3664:
3641:
3636:
3632:
3628:
3624:
3620:
3616:
3612:
3608:
3604:
3599:
3595:
3591:
3564:
3560:
3556:
3551:
3547:
3543:
3535:
3531:
3523:
3519:
3514:
3510:
3507:
3484:
3480:
3476:
3471:
3467:
3463:
3458:
3434:
3412:
3407:
3385:
3380:
3356:
3351:
3347:
3343:
3335:
3331:
3323:
3319:
3314:
3310:
3307:
3285:
3280:
3259:
3247:
3244:
3236:scalar product
3223:
3180:
3176:
3172:
3168:
3164:
3161:
3109:
3104:
3100:
3096:
3090:
3087:
3081:
3075:
3070:
3054:
3029:
3022:
3000:
2997:
2993:
2986:
2979:
2975:
2967:
2963:
2958:
2954:
2951:
2933:center of mass
2916:
2913:
2876:
2870:
2866:
2859:
2854:
2847:
2843:
2812:
2809:
2789:
2783:
2780:
2777:
2771:
2766:
2760:
2757:
2754:
2748:
2743:
2739:
2735:
2729:
2725:
2718:
2713:
2676:
2654:
2630:
2626:
2622:
2618:
2614:
2610:
2606:
2602:
2596:
2592:
2585:
2580:
2553:
2531:
2504:
2500:
2496:
2490:
2486:
2479:
2474:
2467:
2461:
2457:
2450:
2445:
2438:
2434:
2430:
2424:
2420:
2413:
2408:
2369:
2365:
2361:
2357:
2353:
2340:
2337:
2321:
2318:
2312:
2308:
2286:
2282:
2279:
2275:
2247:
2242:
2238:
2231:
2227:
2223:
2217:
2214:
2206:
2201:
2197:
2190:
2161:
2157:
2153:
2150:
2147:
2143:
2139:
2133:
2130:
2124:
2121:
2115:
2112:
2104:
2099:
2095:
2088:
2080:
2076:
2070:
2066:
2062:
2056:
2053:
2045:
2040:
2036:
2029:
2021:
2017:
2011:
2007:
2003:
1997:
1994:
1986:
1981:
1977:
1970:
1962:
1958:
1952:
1948:
1944:
1938:
1933:
1929:
1919:
1914:
1910:
1901:
1897:
1893:
1887:
1882:
1878:
1868:
1863:
1859:
1850:
1846:
1842:
1836:
1831:
1827:
1817:
1812:
1808:
1799:
1795:
1791:
1785:
1782:
1779:
1773:
1735:
1731:
1727:
1724:
1721:
1699:
1695:
1691:
1688:
1684:
1648:
1644:
1637:
1632:
1625:
1621:
1602:
1599:
1583:
1582:
1570:
1560:
1555:following the
1524:
1514:
1510:
1490:
1479:
1458:
1447:
1435:
1414:
1388:
1385:
1382:
1379:
1376:
1373:
1368:
1364:
1360:
1357:
1354:
1350:
1345:
1341:
1337:
1333:
1329:
1271:line of action
1236:
1220:has magnitude
1201:
1182:
1179:
1074:
1071:
1028:
986:
985:
983:
982:
975:
968:
960:
957:
956:
955:
954:
941:
924:
923:
919:
918:
913:
908:
903:
898:
893:
888:
883:
878:
873:
868:
863:
858:
853:
848:
843:
838:
833:
828:
823:
818:
813:
808:
803:
797:
796:
793:
792:
789:
788:
785:
784:
765:
764:
759:
754:
749:
747:Coriolis force
744:
743:
742:
732:
727:
722:
716:
715:
710:
709:
706:
705:
701:
700:
695:
690:
689:
688:
683:
673:
668:
663:
656:
645:
644:
643:
638:
625:
624:
619:
614:
609:
602:
597:
592:
586:
585:
582:
581:
578:
577:
574:
573:
570:
569:
564:
559:
554:
549:
544:
538:
532:
530:
523:
520:
517:
516:
513:
512:
508:
507:
502:
497:
492:
487:
482:
477:
472:
466:
461:
455:
450:
439:
434:
429:
424:
419:
418:
417:
412:
402:
397:
392:
387:
381:
380:
377:
376:
373:
372:
368:
367:
362:
357:
352:
347:
342:
337:
332:
326:
325:
322:
321:
318:
317:
315:
314:
309:
304:
298:
295:
294:
289:
275:
272:
266:
262:
256:
238:
237:
231:
230:
222:
221:
208:
205:
199:
191:
185:
177:
165:
159:
158:
155:
146:
145:
135:
132:
129:
128:
125:
119:
118:
103:
93:
91:Common symbols
90:
87:
86:
50:
42:
41:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
7434:
7423:
7420:
7418:
7415:
7413:
7410:
7408:
7405:
7403:
7400:
7399:
7397:
7380:
7371:
7366:
7363:
7355:
7350:
7347:
7345:
7342:
7340:
7331:
7326:
7323:
7315:
7310:
7307:
7305:
7302:
7301:
7298:
7289:
7284:
7279:
7274:
7269:
7264:
7261:
7259:
7250:
7245:
7240:
7239:
7233:
7230:
7228:
7225:
7223:
7214:
7209:
7204:
7199:
7194:
7189:
7186:
7184:
7172:
7167:
7162:
7157:
7154:
7152:
7149:
7148:
7145:
7141:
7129:
7121:
7118:
7116:
7107:
7101:
7096:
7091:
7088:
7086:
7083:
7081:
7077:
7065:
7057:
7054:
7052:
7048:
7039:
7034:
7029:
7024:
7021:
7019:
6995:
6992:
6980:
6977:
6974:
6973:
6970:
6968:
6966:
6957:
6952:
6949:
6946:
6944:
6941:
6938:
6934:
6930:
6925:
6923:
6918:
6913:
6910:
6907:
6906:
6903:
6894:
6893:
6887:
6884:
6882:
6879:
6877:
6872:
6867:
6864:
6862:
6859:
6858:
6855:
6853:
6844:
6843:
6837:
6834:
6832:
6827:
6823:
6820:
6818:
6816:
6811:
6806:
6803:
6801:
6798:
6797:
6794:
6792:
6783:
6782:
6776:
6771:
6766:
6765:angular speed
6763:
6761:
6757:
6751:
6750:
6744:
6737:
6732:
6725:
6720:
6716:
6713:
6708:
6703:
6697:
6692:
6689:
6687:
6682:
6677:
6672:
6667:
6664:
6662:
6658:
6652:
6647:
6643:
6640:
6639:
6635:
6627:
6623:
6621:
6616:
6615:
6609:
6604:
6599:
6596:
6594:
6591:
6589:
6584:
6579:
6576:
6574:
6570:
6564:
6558:
6552:
6547:
6541:
6536:
6533:
6531:
6528:
6527:
6524:
6522:
6520:
6515:
6510:
6507:
6504:
6502:
6500:
6495:
6490:
6487:
6485:
6480:
6475:
6472:
6469:
6468:
6464:
6460:
6457:
6453:
6450:
6447:
6444:
6441:
6438:
6435:
6434:
6424:
6419:
6415:
6412:
6405:
6400:
6398:
6393:
6391:
6386:
6385:
6382:
6375:
6371:
6368:
6365:
6363:
6360:
6358:
6355:
6352:
6348:
6347:
6343:
6340:
6336:
6333:
6330:
6329:
6325:
6316:
6310:
6306:
6299:
6296:
6290:
6284:
6281:
6276:
6272:
6268:
6264:
6260:
6256:
6249:
6246:
6231:
6224:
6218:
6215:
6211:
6207:
6204:
6198:
6195:
6190:
6188:9780070350489
6184:
6180:
6175:
6174:
6165:
6163:
6159:
6154:
6148:
6145:
6140:
6138:0-7167-0809-4
6134:
6130:
6123:
6120:
6115:
6111:
6107:
6105:9780134143323
6101:
6097:
6090:
6087:
6082:
6075:
6072:
6060:
6056:
6050:
6047:
6042:
6038:
6037:
6032:
6026:
6023:
6019:
6015:
6012:
6011:Free download
6008:
6002:
5999:
5996:
5992:
5989:
5985:
5980:
5977:
5972:
5968:
5962:
5960:
5956:
5951:
5950:
5942:
5940:
5936:
5931:
5930:
5922:
5919:
5915:
5914:0-534-40842-7
5911:
5907:
5901:
5898:
5891:
5886:
5883:
5881:
5880:Torque wrench
5878:
5876:
5875:Torque tester
5873:
5871:
5868:
5866:
5863:
5861:
5858:
5856:
5853:
5851:
5848:
5846:
5843:
5841:
5838:
5836:
5833:
5831:
5828:
5826:
5823:
5822:
5817:
5815:
5813:
5807:
5799:
5797:
5795:
5794:angular speed
5783:
5779:
5775:
5771:
5767:
5763:
5759:
5755:
5751:
5747:
5743:
5739:
5735:
5731:
5727:
5722:
5720:
5715:
5711:
5710:Steam engines
5707:
5703:
5699:
5695:
5691:
5687:
5679:
5678:newton-metres
5675:
5671:
5667:
5662:
5655:
5653:
5635:
5627:
5617:
5612:
5599:
5594:
5584:
5579:
5550:
5521:
5492:
5450:
5448:
5446:
5440:
5432:
5424:
5418:
5410:
5405:
5401:
5394:
5387:
5382:
5378:
5374:
5361:
5336:
5333:
5325:
5323:
5318:
5314:
5309:
5296:
5271:
5268:
5260:
5253:
5246:
5241:
5239:
5225:
5219:
5216:
5211:
5208:
5205:
5199:
5196:
5187:
5167:
5164:
5161:
5151:
5140:
5138:
5116:
5105:
5102:
5099:
5096:
5087:
5072:
5060:
5052:
5049:
5046:
5043:
5035:
5033:
5014:
5010:
4996:
4988:
4985:
4982:
4979:
4971:
4958:
4951:
4947:
4942:
4925:
4922:angular speed
4917:
4909:
4907:
4897:
4890:
4887:
4884:angular speed
4879:
4876:
4870:
4866:
4860:
4851:
4844:
4842:
4823:
4812:
4810:
4791:
4789:
4784:
4781:
4780:circumference
4777:
4769:
4767:
4765:
4760:
4757:
4744:
4738:
4735:
4732:
4714:
4699:
4695:
4679:
4664:
4660:
4657:
4644:
4629:
4622:
4608:
4599:
4597:
4592:
4589:
4563:
4553:
4535:
4520:
4516:
4500:
4485:
4481:
4478:
4468:
4459:
4452:
4441:
4432:
4429:
4409:
4394:
4390:
4374:
4359:
4355:
4352:
4342:
4333:
4329:
4318:
4309:
4306:
4293:
4290:
4287:
4284:
4281:
4278:
4275:
4272:
4264:
4262:
4258:
4254:
4250:
4242:
4234:
4232:
4230:
4226:
4222:
4217:
4215:
4211:
4207:
4203:
4199:
4195:
4191:
4190:
4185:
4181:
4177:
4163:
4159:
4151:
4149:
4136:
4128:
4123:
4113:
4108:
4098:
4095:
4092:
4087:
4077:
4072:
4062:
4057:
4047:
4042:
4027:
4024:
4011:
4006:
3996:
3991:
3981:
3978:
3975:
3970:
3960:
3955:
3945:
3940:
3930:
3925:
3915:
3912:
3904:
3902:
3898:
3890:
3888:
3875:
3866:
3859:
3855:
3847:
3843:
3838:
3834:
3831:
3823:
3809:
3800:
3797:
3794:
3791:
3788:
3784:
3769:
3764:
3756:
3752:
3739:
3725:
3702:
3690:
3686:
3678:
3674:
3669:
3665:
3662:
3654:
3630:
3622:
3614:
3606:
3593:
3581:
3576:
3558:
3545:
3533:
3529:
3521:
3517:
3512:
3508:
3505:
3496:
3478:
3465:
3447:
3368:
3345:
3333:
3329:
3321:
3317:
3312:
3308:
3305:
3297:
3257:
3245:
3243:
3239:
3237:
3221:
3213:
3209:
3208:
3203:
3202:
3197:
3192:
3190:
3178:
3170:
3162:
3159:
3150:
3148:
3144:
3140:
3138:
3137:angular speed
3134:
3130:
3126:
3121:
3119:
3107:
3102:
3098:
3094:
3088:
3085:
3079:
3068:
3058:
3053:
3050:
3046:
3042:
3037:
3036:of the body.
3035:
3028:
3021:
3017:
3012:
3010:
2998:
2995:
2984:
2977:
2973:
2965:
2961:
2956:
2952:
2949:
2940:
2938:
2934:
2930:
2926:
2922:
2914:
2912:
2910:
2905:
2900:
2895:
2893:
2887:
2874:
2868:
2845:
2831:
2830:
2826:
2822:
2818:
2810:
2808:
2806:
2800:
2787:
2764:
2741:
2733:
2727:
2699:
2695:
2691:
2642:
2624:
2616:
2608:
2600:
2594:
2566:
2520:
2515:
2502:
2494:
2488:
2465:
2459:
2436:
2428:
2422:
2394:
2392:
2388:
2384:
2363:
2355:
2338:
2336:
2319:
2310:
2280:
2277:
2264:
2229:
2221:
2215:
2212:
2188:
2177:
2172:
2151:
2145:
2137:
2122:
2119:
2113:
2110:
2086:
2078:
2074:
2068:
2064:
2060:
2054:
2051:
2027:
2019:
2015:
2009:
2005:
2001:
1995:
1992:
1968:
1960:
1956:
1950:
1946:
1942:
1917:
1912:
1908:
1899:
1895:
1891:
1866:
1861:
1857:
1848:
1844:
1840:
1815:
1810:
1806:
1797:
1793:
1789:
1761:
1759:
1755:
1751:
1733:
1729:
1725:
1722:
1719:
1710:
1697:
1689:
1686:
1673:
1671:
1667:
1662:
1646:
1623:
1610:
1608:
1600:
1598:
1596:
1592:
1588:
1568:
1561:
1558:
1553:
1547:
1542:
1541:perpendicular
1538:
1537:cross product
1522:
1515:
1509:
1505:
1480:
1477:
1473:
1448:
1433:
1404:
1403:
1402:
1399:
1386:
1383:
1380:
1377:
1374:
1371:
1366:
1362:
1358:
1355:
1352:
1339:
1331:
1318:
1316:
1312:
1308:
1307:torque vector
1304:
1300:
1296:
1295:torque vector
1292:
1288:
1284:
1283:cross product
1280:
1276:
1272:
1268:
1264:
1255:
1250:
1246:| |
1244:
1235:
1231:| |
1229:
1224:
1218:
1214:
1210:
1209:
1200:
1196:
1192:
1187:
1180:
1178:
1176:
1171:
1166:
1162:
1158:
1154:
1149:
1147:
1141:
1139:
1135:
1131:
1130:
1125:
1121:
1117:
1116:
1109:
1107:
1103:
1099:
1098:James Thomson
1095:
1094:
1090:
1086:
1080:
1072:
1070:
1068:
1064:
1060:
1052:
1048:
1047:
1043:
1017:
1013:
1009:
1005:
1001:
997:
993:
981:
976:
974:
969:
967:
962:
961:
959:
958:
952:
942:
939:
934:
928:
927:
926:
925:
917:
914:
912:
909:
907:
904:
902:
899:
897:
894:
892:
889:
887:
884:
882:
879:
877:
874:
872:
869:
867:
864:
862:
859:
857:
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852:
849:
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844:
842:
839:
837:
834:
832:
829:
827:
824:
822:
819:
817:
814:
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809:
807:
804:
802:
799:
798:
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790:
783:
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767:
763:
760:
758:
755:
753:
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748:
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738:
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736:
733:
731:
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723:
721:
718:
717:
713:
708:
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687:
684:
682:
679:
678:
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669:
667:
664:
662:
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654:
650:
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642:
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632:
628:
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623:
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579:
568:
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539:
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531:
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430:
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423:
420:
416:
413:
411:
408:
407:
406:
403:
401:
398:
396:
393:
391:
388:
386:
383:
382:
375:
374:
366:
363:
361:
358:
356:
353:
351:
348:
346:
343:
341:
338:
336:
333:
331:
328:
327:
320:
319:
313:
310:
308:
305:
303:
300:
299:
296:
292:
273:
270:
260:
254:
240:
239:
236:
232:
228:
227:
206:
203:
189:
166:
164:
160:
156:
154:
147:
144:⋅inch, ozf⋅in
143:
139:
136:
130:
126:
124:
120:
117:
101:
94:
88:
83:
79:
75:
72:
68:
65:
61:
57:
54:
48:
43:
38:
33:
19:
7369:
7353:
7329:
7313:
7287:
7277:
7267:
7248:
7237:
7236:
7231:
7212:
7202:
7192:
7170:
7160:
7105:
7094:
7037:
7027:
6955:
6939:
6936:
6932:
6928:
6916:
6891:
6890:
6886:angular jerk
6870:
6841:
6840:
6809:
6805:acceleration
6780:
6779:
6769:
6748:
6747:
6735:
6723:
6706:
6695:
6680:
6670:
6650:
6613:
6612:
6602:
6582:
6569:displacement
6562:
6556:
6550:
6539:
6513:
6493:
6478:
6462:
6455:
6345:
6304:
6298:
6283:
6258:
6254:
6248:
6237:. Retrieved
6217:
6197:
6172:
6147:
6128:
6122:
6095:
6089:
6080:
6074:
6063:. Retrieved
6049:
6035:
6025:
6006:
6001:
5983:
5979:
5970:
5948:
5928:
5921:
5905:
5900:
5809:
5761:
5723:
5683:
5454:
5438:
5430:
5422:
5414:
5399:
5392:
5385:
5375:
5326:
5321:
5316:
5312:
5310:
5261:
5258:
5188:
5015:
5011:
4959:
4949:
4945:
4943:
4792:
4785:
4775:
4773:
4761:
4758:
4600:
4593:
4590:
4433:
4430:
4310:
4307:
4265:
4256:
4252:
4248:
4238:
4228:
4224:
4218:
4189:newton-metre
4187:
4155:
4028:
4025:
3905:
3894:
3824:
3726:
3655:
3577:
3497:
3448:
3369:
3298:
3249:
3240:
3206:
3205:
3200:
3199:
3195:
3193:
3151:
3141:
3132:
3124:
3122:
3059:
3051:
3044:
3038:
3026:
3019:
3015:
3013:
2941:
2936:
2918:
2908:
2896:
2891:
2889:
2833:
2824:
2820:
2814:
2801:
2689:
2643:
2567:
2519:product rule
2516:
2395:
2390:
2382:
2342:
2173:
1762:
1753:
1711:
1674:
1669:
1665:
1663:
1611:
1604:
1595:§ Units
1591:newton-metre
1584:
1551:
1545:
1535:denotes the
1507:
1503:
1475:
1400:
1319:
1314:
1306:
1302:
1298:
1294:
1275:pseudovector
1260:
1253:
1248:
1242:
1233:
1227:
1222:
1216:
1212:
1207:
1206:
1198:
1194:
1190:
1160:
1156:
1150:
1145:
1143:
1127:
1123:
1113:
1111:
1105:
1084:
1082:
1065:applied two
1044:
1042:Greek letter
1015:
1011:
999:
989:
780: /
776: /
774:displacement
772: /
633: /
595:Displacement
533:
524:
518:Formulations
505:Virtual work
494:
445: /
385:Acceleration
378:Fundamentals
123:SI unit
115:
73:
66:
59:
55:
6626:solid angle
6009:pp. 90–99:
5706:dynamometer
5672:) that the
5197:5252.113122
4944:The radius
4182:. Official
3204:is torque,
3149:, given by
2935:, the work
2919:The law of
2894:is torque.
2805:integrating
1252:| sin
916:von Neumann
583:Core topics
133:Other units
7396:Categories
7361:m s, N m s
7337:m s,
7283:Lagrangian
7208:Lagrangian
6448:Dimensions
6436:Dimensions
6261:(9): 820.
6239:2020-05-29
6065:2007-09-08
6039:. p.
5892:References
5782:gear ratio
5774:drivetrain
5674:crankshaft
5279:moment arm
5093:horsepower
4770:Derivation
4596:horsepower
4251:is power,
4229:inch-pound
4225:foot-pound
4221:pound foot
3198:is power,
1311:rigid body
1077:See also:
1004:rotational
851:d'Alembert
831:Maupertuis
794:Scientists
676:Rigid body
350:Kinematics
7377:ms,
6996:˙
6719:frequency
6646:frequency
6201:From the
6114:922464227
5758:chainring
5730:sprockets
5636:×
5618:−
5590:τ
5575:τ
5488:τ
5334:τ
5269:τ
5220:π
5200:≈
5152:⋅
5141:≈
5117:⋅
5106:⋅
5088:⋅
5073:⋅
5061:⋅
5053:⋅
5050:π
5044:⋅
4989:⋅
4986:π
4980:⋅
4948:and time
4918:⋅
4888:⋅
4880:⋅
4871:⋅
4824:⋅
4700:ν
4696:⋅
4665:π
4658:⋅
4645:⋅
4630:τ
4521:ν
4517:⋅
4486:π
4479:⋅
4469:⋅
4460:τ
4395:ν
4391:⋅
4360:π
4353:⋅
4343:⋅
4334:τ
4294:ν
4291:⋅
4288:π
4282:⋅
4279:τ
4158:dimension
4114:×
4096:…
4078:×
4048:×
3997:×
3979:…
3961:×
3931:×
3913:τ
3876:θ
3867:τ
3856:θ
3844:θ
3839:∫
3810:θ
3801:τ
3792:
3780:θ
3761:τ
3749:θ
3740:⋅
3736:τ
3712:θ
3703:⋅
3699:τ
3687:θ
3675:θ
3670:∫
3640:θ
3631:⋅
3623:×
3607:×
3603:θ
3594:⋅
3559:×
3555:θ
3546:⋅
3513:∫
3479:×
3475:θ
3411:θ
3346:⋅
3313:∫
3222:⋅
3175:ω
3171:⋅
3167:τ
3099:ω
2996:θ
2985:τ
2974:θ
2962:θ
2957:∫
2858:τ
2770:τ
2742:×
2625:×
2609:×
2495:×
2437:×
2364:×
2320:˙
2317:ω
2307:α
2285:α
2274:τ
2246:^
2230:×
2226:ω
2205:^
2156:ω
2146:×
2142:ω
2132:˙
2129:ω
2103:^
2075:ω
2044:^
2016:ω
1985:^
1957:ω
1937:^
1918:˙
1909:ω
1886:^
1867:˙
1858:ω
1835:^
1816:˙
1807:ω
1772:τ
1694:ω
1620:τ
1569:θ
1523:×
1434:τ
1413:τ
1387:θ
1384:
1367:⊥
1353:τ
1349:⟹
1340:×
1328:τ
1267:lever arm
1083:The term
1027:τ
996:mechanics
896:Liouville
778:frequency
698:Vibration
415:potential
340:Continuum
335:Celestial
312:Textbooks
204:−
163:Dimension
102:τ
58:, torque
7412:Rotation
7321:m s, N s
7144:J s
7140:m s
7115:m s
7076:m s
7047:m s
7023:momentum
6676:velocity
6546:position
6535:distance
6489:absement
6414:SI units
6370:Archived
6335:Archived
6230:Archived
6206:Archived
6059:Archived
6033:(1811).
6014:Archived
5991:Archived
5988:Web link
5967:"torque"
5818:See also
5812:gear box
5770:crankset
5754:cranking
5736:, and a
5726:bicycles
5189:because
4162:distance
1543:both to
1299:position
1225:= |
1093:torquēre
951:Category
876:Hamilton
861:Lagrange
856:Clairaut
821:Horrocks
782:velocity
752:Pendulum
740:reactive
712:Rotation
681:dynamics
631:Inertial
617:Friction
500:Velocity
475:Momentum
355:Kinetics
345:Dynamics
323:Branches
307:Timeline
82:friction
7349:rotatum
7128:actergy
7064:actergy
7033:impulse
6953::
6704::
6634:rad, sr
6263:Bibcode
6179:267–268
5973:. 1933.
5855:Statics
5766:spindle
5750:cyclist
5404:precess
4196:to the
3822:giving
3210:is the
3135:is its
3127:is the
2909:rotatum
2904:rotātus
2821:rotatum
2817:physics
2692:to the
1748:is the
1587:SI unit
1549:and to
1470:is the
1285:of the
1136:" and "
1129:torsion
1073:History
1063:newtons
1002:is the
992:physics
911:Koopman
871:Poisson
866:Laplace
811:Huygens
806:Galileo
651: (
590:Damping
443:Inertia
437:Impulse
410:kinetic
360:Statics
330:Applied
302:History
78:gravity
18:Torques
7402:Torque
7263:energy
7244:moment
7232:torque
7188:energy
7166:weight
7138:
7120:action
7113:
7074:
7056:action
7045:
7016:
6963:
6935:⟩ = ∑
6899:
6850:
6789:
6311:
6185:
6135:
6112:
6102:
5912:
5825:Moment
5790:output
5719:clutch
5688:: the
5686:engine
5148:torque
5040:torque
4976:torque
4914:torque
4858:torque
4557:
4210:scalar
4206:energy
4202:vector
4176:energy
3214:, and
3194:where
3123:where
3014:where
2988:
2890:where
2825:torque
2381:where
2298:where
2176:vector
1712:where
1664:where
1401:where
1277:; for
1161:moment
1146:torque
1138:moment
1134:couple
1124:torque
1120:motion
1087:(from
1085:torque
1067:metres
1051:moment
1016:moment
1000:torque
949:
901:Appell
886:Cauchy
881:Jacobi
826:Halley
816:Newton
801:Kepler
653:linear
649:Motion
495:Torque
470:Moment
405:Energy
395:Couple
157:kg⋅m⋅s
69:, and
40:Torque
7417:Force
7365:power
7325:power
7295:m s,
7256:m s,
7220:m s,
7181:m s,
7156:force
6666:speed
6598:angle
6233:(PDF)
6226:(PDF)
5786:input
5778:wheel
5746:frame
5734:chain
5690:power
5391:and −
5355:force
5290:force
5028:power
4968:power
4820:force
4805:power
4788:power
4198:joule
4152:Units
3246:Proof
3143:Power
3043:that
2925:force
2901:word
2899:Latin
2690:equal
1303:force
1115:force
1089:Latin
1008:force
906:Gibbs
891:Routh
846:Euler
485:Speed
480:Space
422:Force
53:force
7309:yank
7273:work
7198:work
6912:mass
6866:jerk
6578:area
6509:time
6474:time
6309:ISBN
6183:ISBN
6133:ISBN
6110:OCLC
6100:ISBN
5910:ISBN
5748:. A
5712:and
5668:(in
5427:and
5315:and
4833:time
4180:work
3446:as
3147:time
3025:and
2829:time
2389:and
1752:and
1585:The
1301:and
1059:axis
994:and
490:Time
453:Mass
80:and
7343:MLT
7258:N m
7226:MLT
7179:kg
7084:MLT
7080:J s
7051:N s
6897:rad
6875:m s
6848:rad
6815:m s
6787:rad
6711:m s
6686:m s
6620:rad
6499:m s
6349:on
6271:doi
5702:rpm
5670:rpm
5565:is
5441:= 0
5433:= 0
5425:= 0
5212:000
5168:252
5156:RPM
5126:min
5121:lbf
5103:000
5083:min
5078:lbf
4764:BTU
4739:000
4178:or
3789:cos
2815:In
2335:.
1381:sin
1167:'s
1046:tau
990:In
149:In
142:lbf
127:N⋅m
7398::
7375:kg
7367::
7359:kg
7351::
7335:kg
7327::
7319:kg
7311::
7303:MT
7293:kg
7285::
7281:,
7275::
7271:,
7265::
7254:kg
7246::
7242:,
7234::
7218:kg
7210::
7206:,
7200::
7196:,
7190::
7168::
7164:,
7158::
7150:MT
7142:,
7136:kg
7130::
7126:,
7124:𝒮
7122::
7111:kg
7102::
7098:,
7092::
7078:,
7072:kg
7066::
7062:,
7060:𝒮
7058::
7049:,
7043:kg
7035::
7031:,
7025::
7014:kg
6981::
6975:MT
6961:kg
6947:ML
6922:kg
6914::
6888::
6868::
6838::
6807::
6777::
6773:,
6767::
6760:Hz
6758:,
6745::
6740:,
6733::
6728:,
6721::
6693::
6678::
6674:,
6668::
6661:Hz
6659:,
6648::
6628::
6610::
6606:,
6600::
6580::
6567:,
6560:,
6554:,
6548::
6543:,
6537::
6511::
6491::
6476::
6269:.
6259:47
6257:.
6181:.
6161:^
6108:.
6057:.
6041:67
5969:.
5958:^
5938:^
5721:.
5206:33
5113:ft
5097:33
5068:ft
4790::
4733:33
4554:60
4184:SI
3238:.
3139:.
2819:,
2565:,
2178:is
1609:,
1597:.
1215:×
1211:=
1173:.
1148:.
998:,
140:,
114:,
62:,
7379:W
7370:P
7354:P
7339:W
7330:P
7314:Y
7297:J
7288:L
7278:W
7268:E
7249:M
7238:τ
7222:J
7213:L
7203:W
7193:E
7183:N
7174:g
7171:F
7161:F
7132:ℵ
7106:L
7104:Δ
7095:L
7068:ℵ
7038:J
7028:p
7018:s
6993:m
6965:m
6956:I
6940:x
6937:m
6933:x
6931:⟨
6929:M
6917:m
6908:M
6901:s
6892:ζ
6880:T
6871:j
6860:T
6852:s
6842:α
6831:s
6821:T
6810:a
6799:T
6791:s
6781:ω
6770:ω
6756:s
6749:n
6736:n
6724:f
6714:T
6707:h
6699:,
6696:ν
6681:v
6671:v
6657:s
6651:f
6641:T
6630:Ω
6614:θ
6603:θ
6592:1
6588:m
6583:A
6573:m
6563:x
6557:s
6551:r
6540:d
6529:1
6519:s
6514:t
6505:T
6494:A
6484:s
6479:t
6470:T
6463:θ
6456:θ
6451:1
6445:L
6442:L
6439:1
6403:e
6396:t
6389:v
6353:.
6317:.
6277:.
6273::
6265::
6242:.
6191:.
6155:.
6141:.
6116:.
6068:.
6043:.
6020:.
5916:.
5762:π
5640:F
5633:)
5628:1
5623:r
5613:2
5608:r
5603:(
5600:+
5595:1
5585:=
5580:2
5551:2
5546:r
5522:1
5517:r
5493:1
5465:F
5439:τ
5437:Σ
5431:V
5429:Σ
5423:H
5421:Σ
5406:.
5400:L
5396:g
5393:F
5389:g
5386:F
5362:.
5359:)
5351:(
5348:)
5340:(
5337:=
5322:r
5317:F
5313:r
5297:.
5294:)
5286:(
5283:)
5275:(
5272:=
5226:.
5217:2
5209:,
5165:,
5162:5
5100:,
5047:2
5036:=
4997:.
4983:2
4972:=
4955:π
4950:t
4946:r
4926:.
4910:=
4898:t
4894:)
4891:t
4877:r
4874:(
4867:)
4861:r
4852:(
4845:=
4813:=
4745:.
4736:,
4725:n
4722:i
4719:m
4715:/
4711:v
4708:e
4705:r
4690:v
4687:e
4684:r
4680:/
4676:d
4673:a
4670:r
4661:2
4652:t
4649:f
4641:f
4638:b
4635:l
4623:=
4617:p
4614:h
4609:P
4574:n
4571:i
4568:m
4564:/
4560:s
4546:n
4543:i
4540:m
4536:/
4532:v
4529:e
4526:r
4511:v
4508:e
4505:r
4501:/
4497:d
4494:a
4491:r
4482:2
4473:m
4465:N
4453:=
4447:W
4442:P
4414:s
4410:/
4406:v
4403:e
4400:r
4385:v
4382:e
4379:r
4375:/
4371:d
4368:a
4365:r
4356:2
4347:m
4339:N
4330:=
4324:W
4319:P
4285:2
4276:=
4273:P
4259:(
4257:ν
4253:τ
4249:P
4245:π
4172:M
4169:L
4166:T
4137:.
4133:0
4129:=
4124:N
4119:F
4109:N
4104:r
4099:+
4093:+
4088:2
4083:F
4073:2
4068:r
4063:+
4058:1
4053:F
4043:1
4038:r
4012:.
4007:N
4002:F
3992:N
3987:r
3982:+
3976:+
3971:2
3966:F
3956:2
3951:r
3946:+
3941:1
3936:F
3926:1
3921:r
3916:=
3872:d
3860:2
3848:1
3835:=
3832:W
3806:d
3798:=
3795:0
3785:|
3775:d
3770:|
3765:|
3757:|
3753:=
3744:d
3707:d
3691:2
3679:1
3666:=
3663:W
3635:d
3627:F
3619:r
3615:=
3611:r
3598:d
3590:F
3563:r
3550:d
3542:F
3534:2
3530:s
3522:1
3518:s
3509:=
3506:W
3483:r
3470:d
3466:=
3462:s
3457:d
3433:r
3406:d
3384:s
3379:d
3355:s
3350:d
3342:F
3334:2
3330:s
3322:1
3318:s
3309:=
3306:W
3284:s
3279:d
3258:s
3207:ω
3201:τ
3196:P
3179:,
3163:=
3160:P
3133:ω
3125:I
3108:,
3103:2
3095:I
3089:2
3086:1
3080:=
3074:r
3069:E
3055:r
3052:E
3045:W
3030:2
3027:θ
3023:1
3020:θ
3016:τ
2999:,
2992:d
2978:2
2966:1
2953:=
2950:W
2937:W
2892:τ
2875:,
2869:t
2865:d
2853:d
2846:=
2842:P
2788:.
2782:t
2779:e
2776:n
2765:=
2759:t
2756:e
2753:n
2747:F
2738:r
2734:=
2728:t
2724:d
2717:L
2712:d
2675:v
2653:p
2629:p
2621:v
2617:+
2613:F
2605:r
2601:=
2595:t
2591:d
2584:L
2579:d
2552:v
2530:F
2503:.
2499:p
2489:t
2485:d
2478:r
2473:d
2466:+
2460:t
2456:d
2449:p
2444:d
2433:r
2429:=
2423:t
2419:d
2412:L
2407:d
2391:r
2383:p
2368:p
2360:r
2356:=
2352:L
2311:=
2281:I
2278:=
2241:i
2237:e
2222:=
2216:t
2213:d
2200:i
2196:e
2189:d
2160:)
2152:I
2149:(
2138:+
2123:I
2120:=
2114:t
2111:d
2098:3
2094:e
2087:d
2079:3
2069:3
2065:I
2061:+
2055:t
2052:d
2039:2
2035:e
2028:d
2020:2
2010:2
2006:I
2002:+
1996:t
1993:d
1980:1
1976:e
1969:d
1961:1
1951:1
1947:I
1943:+
1932:3
1928:e
1913:3
1900:3
1896:I
1892:+
1881:2
1877:e
1862:2
1849:2
1845:I
1841:+
1830:1
1826:e
1811:1
1798:1
1794:I
1790:=
1784:t
1781:e
1778:n
1754:ω
1734:2
1730:r
1726:m
1723:=
1720:I
1698:,
1690:I
1687:=
1683:L
1670:t
1666:L
1647:t
1643:d
1636:L
1631:d
1624:=
1559:,
1552:F
1546:r
1511:⊥
1508:F
1504:F
1489:F
1476:r
1457:r
1378:F
1375:r
1372:=
1363:F
1359:r
1356:=
1344:F
1336:r
1332:=
1254:θ
1249:F
1243:r
1237:⊥
1234:F
1228:r
1223:τ
1217:F
1213:r
1208:τ
1202:⊥
1199:F
1195:F
1191:r
1055:M
979:e
972:t
965:v
655:)
274:t
271:d
265:p
261:d
255:=
250:F
207:2
198:T
190:2
184:L
176:M
116:M
74:L
67:p
60:τ
56:F
34:.
20:)
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