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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 torque T is defined as the force F acting at a perpendicular distance d.

T = F d(1)

The moment of a force.
Figure 1. The moment of a force.

The dimension of moment is [M L2 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.


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."

Figure 2. A couple.

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.

Torque is a psuedo-vector quanitity with the direction given by 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