Rotation of rigid bodies

In this section we are going to look at the case of rigid bodies whose mass is spread over a definite area. The behaviour of rotating objects is of considerable importance in our lives: the results of our considerations can be applied to rotating car wheels, flywheels, the rotation of high divers and many other things.

A rotating object has kinetic energy associated with it. Flywheels can be used to store rotational kinetic energy; for example, current to energise the electromagnets of the proton accelerator at the Rutherford laboratory in Oxfordshire is provided by a generator this driven by a 5 m diameter flywheel; this allows pulses of electricity to be obtained without putting a sudden large drain on the mains supply.

Rotational energy is also important in stability, which is due to the angular momentum of the body (discussed below); many washing machines have a disc of concrete fixed to the base of the drum to prevent vibrations due to uneven loading with clothes.

If we think of a mass m on a string being swung round in a circle of radius r (Figure 1) then its kinetic energy at any instant is given by:


where w is the angular velocity of the mass. (Think of the action of a hammer thrower: he may swing a 7.5 kg hammer round his head once a second and use the kinetic energy so gained to project it some 80 m when it is released.

Linear and rotational equations

These equations for angular motion can be compared with the similar ones for linear motion.