**Torque**, **moment** or **moment of force** (see the terminology below), is the tendency of a force to rotate an object about an axis, 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 force and the lever-arm distance, which tends to produce rotation.

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 *τ*, the Greek letter *tau*. When it is called moment, it is commonly denoted *M*.

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

where

**τ**is the torque vector and*τ*is the magnitude of the torque,**r**is the displacement vector (a vector from the point from which torque is measured to the point where force is applied), and*r*is the length (or magnitude) of the lever arm vector,**F**is the force vector, and*F*is the magnitude of the force,- × denotes the cross product,
*θ*is the angle between the force vector and the lever arm vector.

The length of the lever arm is particularly important; choosing this length appropriately lies behind the operation of levers, pulleys, gears, and most other simple machines involving a mechanical advantage.

The SI unit for torque is the newton metre (N·m). For more on the units of torque, see below.

Read more about Torque: Terminology, History, Definition and Relation To Angular Momentum, Units, Machine Torque, Relationship Between Torque, Power, and Energy, Principle of Moments, Torque Multiplier

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### Famous quotes containing the word torque:

“Poetry uses the hub of a *torque* converter for a jello mold.”

—Diane Glancy (b. 1941)