# Moments and Couples

## The moment of a Force or Torque

The moment of a force is the perdendicular force *F* acting at a distance, *d* and causes an object to rotate.

The moment of a force, also known as the torqueTis defined as the forceFacting at a perpendicular distanced.

*T* = *F d*(1)

The dimension of moment is [M L^{2} T^{-2}] which is the same as energy, however there is no direct relationship between the two. The SI unit of a moment is the Newton meter (Nm).

A special case of moments is where two anti-parallel forces separated by a distance *d* cause an object to rotate. This is known as a couple.

## Couples

If two opposite moments act to cause an object to rotate, such as when your two hand are at the 'quarter-past-three' position on a car steering wheel, it is called a couple. The moment of a couple is called the torque. It is quite often said of engines and applys to the ability of the engine to turn the wheels, or wrongly by Jeremy Clarkson from *'Top Gear'* as in, "This engine has a lot of torques."

The torque is a psuedo-vector quantity. That is, it has magnitude and it has a direction that is projected perpendicular to the plane of the vectors **F** and **r**. The direction of the vector from the plane follows a right-handed corkscrew rule or equivalently the right-hand screw rule.

The magnitude of the torque of a couple can be found by finding the net torque from clockwise and anti clockwise moments acting on an arbitrary point of rotation.

*T* =*F*(*x* + *d*)

*T* =*F x*

Equating, *F x* +*F d* = *F x*.

Net Torque. *T* = *F d*