# Torque

Relationship between force F, torque τ, linear momentum p, and angular momentum L in a system which has rotation constrained in one plane only (forces and moments due to gravity and friction not considered).

Torque, moment, or moment of force (see "Defining terminology" below) is rotational force. [1] Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object. Mathematically, torque is defined as the cross product of the vector by which the force's application point is offset relative to the fixed suspension point ( distance vector) and the force vector, which tends to produce rotational motion.

The symbol for torque is typically ${\displaystyle \tau }$, the lowercase Greek letter tau. When it is called moment of force, it is commonly denoted by M.

The magnitude of torque depends on three quantities: the force applied, the length of the lever arm [2] connecting the axis to the point of force application, and the angle between the force vector and the lever arm. In symbols:

${\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \,\!}$
${\displaystyle \tau =\|\mathbf {r} \|\,\|\mathbf {F} \|\sin \theta \,\!}$

where

${\displaystyle {\boldsymbol {\tau }}}$ is the torque vector and ${\displaystyle \tau }$ is the magnitude of the torque,
r is the position vector (a vector from the origin of the coordinate system defined to the point where the force is applied)
F is the force vector,
× denotes the cross product,
θ 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.

## Defining terminology

Torque is referred to using different vocabulary depending on geographical location and field of study. This article refers to the definition used in US physics in its usage of the word torque. [3] In the UK and in US mechanical engineering, torque is referred to as moment of force, usually shortened to moment. [4] In US physics [3] and UK physics terminology these terms are interchangeable, unlike in US mechanical engineering, where the term torque is used for the closely related "resultant moment of a couple". [4]

Torque is defined mathematically as the rate of change of angular momentum of an object. The definition of torque states that one or both of the angular velocity or the moment of inertia of an object are changing. Moment is the general term used for the tendency of one or more applied forces to rotate an object about an axis, but not necessarily to change the angular momentum of the object (the concept which is called torque in physics). [4] For example, a rotational force applied to a shaft causing acceleration, such as a drill bit accelerating from rest, results in a moment called a torque. By contrast, a lateral force on a beam produces a moment (called a bending moment), but since the angular momentum of the beam is not changing, this bending moment is not called a torque. Similarly with any force couple on an object that has no change to its angular momentum, such moment is also not called a torque.

This article follows the US physics terminology by calling all moments by the term torque, whether or not they cause the angular momentum of an object to change.

Other Languages
Afrikaans: Wringkrag
العربية: عزم الدوران
অসমীয়া: ভ্ৰামক
azərbaycanca: Moment
বাংলা: টর্ক
беларуская: Момант сілы
беларуская (тарашкевіца)‎: Момант сілы
български: Момент на сила
Boarisch: Drehmaument
bosanski: Moment sile
čeština: Točivý moment
Cymraeg: Moment
Deutsch: Drehmoment
eesti: Jõumoment
Ελληνικά: Ροπή
español: Par motor
Esperanto: Torda momanto
euskara: Indar momentu
Gaeilge: Casmhóimint
한국어: 돌림힘
Հայերեն: Ուժի մոմենտ
हिन्दी: बलाघूर्ण
hrvatski: Moment sile
Ido: Momento
Bahasa Indonesia: Torsi
íslenska: Snúningsvægi
עברית: מומנט כוח
қазақша: Күш моменті
Kreyòl ayisyen: Moman tòsyon
Kurdî: Torq
latviešu: Spēka moments
lietuvių: Jėgos momentas
македонски: Момент на сила
മലയാളം: ചുഴറ്റുബലം
मराठी: आघूर्ण
Bahasa Melayu: Tork

norsk nynorsk: Dreiemoment
پنجابی: ٹارک
polski: Moment siły
português: Torque
русский: Момент силы
Scots: Torque
shqip: Momenti
Simple English: Torque
slovenčina: Krútiaci moment
slovenščina: Navor
کوردی: زەبر
српски / srpski: Момент силе
srpskohrvatski / српскохрватски: Moment sile
svenska: Vridmoment
తెలుగు: టార్క్
Türkçe: Tork
українська: Момент сили
اردو: تدویر
Tiếng Việt: Mô men lực
ייִדיש: טוירק