## Torque and Moments

The motion of a rigid body is in general a combination of translation and rotation. The two tyopes of motion can be treated independently.

A translation takes place when every particle in a rigid body has the same velocity while a rotation is when every particle in an object moves in a circle about the axis of rotation, which each particle necessarily having a different velocity.

The turning effect of a force F about a point is called the moment of a force or the torque. The torque will increase if

The magnitude of the force increases.

The perpendicular distance from the force to the axis of rotation – x in the diagram below, which shows a rod of length l rotating about an axis at A, the rod being subject to a horizontal force F acting at the other end of the rod - is increased.

We can find the distance x given the length of the rod l and the angle %theta using simple trigonometry. We obtainHence

If the force is perpendicular to the line the body makes with the axis of rotation then %theta = 90 degrees and

The SI unit for torque in Nm. This has the same units as energy – consider the equation– but torque is quite different. The equationto find work done assumes the force acts in the direction of the distance moved. The same equation to find the torque assumes the is perpendicular to the distance of the force from the pivot.