# Torque

## Turning force around an axis / From Wikipedia, the free encyclopedia

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In physics and mechanics, **torque** is the rotational analogue of linear force.[1] It is also referred to as the **moment of force** (also abbreviated to **moment**). It describes the rate of change of angular momentum that would be imparted to an isolated body.

**Quick facts: Torque, Common symbols, SI unit, Other u...**▼

Torque | |
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Common symbols | $\tau$, M |

SI unit | N⋅m |

Other units | pound-force-feet, lbf⋅inch, ozf⋅in |

In SI base units | kg⋅m^{2}⋅s^{−2} |

Dimension | ${\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-2}$ |

Part of a series on |

Classical mechanics |
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${\textbf {F}}={\frac {d}{dt}}(m{\textbf {v}})$ |

Core topics |

The concept originated with the studies by Archimedes of the usage of levers, which is reflected in his famous quote: "Give me a lever and a place to stand and I will move the Earth". 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. Torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined. The law of conservation of energy can also be used to understand torque. The symbol for torque is typically ${\boldsymbol {\tau }}$, the lowercase Greek letter *tau*. When being referred to as moment of force, it is commonly denoted by M.

In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the displacement vector and the force vector. The magnitude of torque applied to a rigid body depends on three quantities: the force applied, the *lever arm vector*[2] 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:

where

- ${\boldsymbol {\tau }}$ is the torque vector and $\tau$ is the magnitude of the torque,
- $\mathbf {r}$ is the position vector (a vector from the point about which the torque is being measured to the point where the force is applied), and
*r*is the magnitude of the position vector, - $\mathbf {F}$ is the force vector, and
*F*is the magnitude of the force vector, - $\times$ denotes the cross product, which produces a vector that is perpendicular both to
**r**and to**F**following the right-hand rule, - $\theta$ is the angle between the force vector and the lever arm vector.

The SI unit for torque is the newton-metre (N⋅m). For more on the units of torque, see § Units.

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