Back

Torque | |
---|---|

Common symbols | , M |

SI unit | N⋅m |

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

In SI base units | kg⋅m^{2}⋅s^{−2} |

Dimension | M L^{2}T^{−2} |

Part of a series on |

Classical mechanics |
---|

In physics and mechanics, **torque** is the rotational equivalent of linear force.^{[1]} It is also referred to as the **moment**, **moment of force**, **rotational force** or **turning effect**, depending on the field of study. The concept originated with the studies by Archimedes of the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. The symbol for torque is typically , 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 position vector (distance vector) and the force vector. The magnitude of torque of 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

- is the torque vector and is the magnitude of the torque,
- is the position vector (a vector from the point about which the torque is being measured to the point where the force is applied),
- is the force vector,
- denotes the cross product, which produces a vector that is perpendicular to both r and F following the right-hand rule,
- 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.

**^**Serway, R. A. and Jewett, Jr. J.W. (2003).*Physics for Scientists and Engineers*. 6th Ed. Brooks Cole. ISBN 0-534-40842-7.**^**Tipler, Paul (2004).*Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.)*. W. H. Freeman. ISBN 0-7167-0809-4.