Torque

For other uses, see Torque (disambiguation).
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 the terminology below) is the tendency of a force to rotate an object around an axis, [1] fulcrum, or pivot. Just as a 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.

Loosely speaking, torque is a measure of the turning force on an object such as a bolt or a flywheel. For example, pushing or pulling the handle of a wrench connected to a nut or bolt produces a torque (turning force) that loosens or tightens the nut or bolt.

The symbol for torque is typically , 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:

where

is the torque vector and 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.

Terminology

This article follows US physics terminology in its use of the word torque. [3] In the UK and in US mechanical engineering, this is called 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.