The concept of **torque** in physics originated with the work of Archimedes on levers. Informally, torque can be thought of as "rotational force". The weight that rests on a lever, multiplied by its distance from the lever's fulcrum, is the torque. For example, a weight of three newtons resting two metres from the fulcrum exerts the same torque as one newton resting six metres from the fulcrum. This assumes the force is in a direction at right angles to a straight lever. More generally, one may define torque as the cross product:

Torque has dimensions of distance × force; the same as energy. However, the units of torque are usually stated as "newton metres" or "foot pounds" rather than joules. Of course this is not simply a coincidence - a torque of 1 Nm applied through a full revolution will require an energy of exactly 2π J — mathematically, *E* = *τ θ*, where *E* is the energy and *θ* is the angle moved, in radians.

A very useful special case, often given as the definition of torque in fields other than physics, is as follows:

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*τ*= moment arm × force

*τ*= distance to centre × force

For example, if a person places a force of 9.8 N (1 kg) on a spanner which is 0.5 m long, the torque will be approximately 4.9 Nm, assuming that the person pulls the spanner in the direction best suited to turning bolts.

Torque is the time-derivative of angular momentum, just as force is the time derivative of linear momentum. For multiple torques acting simultaneously:

Torque on a rigid body can be written in terms of rotational inertia I: **L** = I**ω** so if I is constant,

The measurement of torque is important in automotive engineering, being concerned with the transmission of power from the drive train to the wheels of a vehicle. It is also used where the tightness of screws and bolts is crucial (see torque wrench). Torque is also the easiest way to explain mechanical advantage in just about every simple machine except the pulley.

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