# Centre of gravity

Centre of gravity

We have already seen a body is attracted to the earth by the force of gravity. This tatement, however, says nothing about the point of application of the force, so we hall now discuss this. Any particular body, a stone, for example, may be regarded as being made up of a very large number of tiny equal particles of mass m, each of which is pulled towards the earth with a force mg (Fig. 6.5). The earth’s pull on the stone thus consists of a very large number of equal almost parallel forces. These will have a resultant which is equal to the total force of gravity Mg on the stone, and it will act through a point G called the centre of gravity.

The centre of gravity of a body is defined as the point of application of the resultant force due to the earth’s attraction on it.) The centre of gravity of a body also coincides with its centre of mass. A ruler can be made to balance on a finger-tip if the finger is placed immediately below the centre of gravity. Under these conditions the ruler is in equilibrium under the action of two forces; the force of gravity acting vertically downwards and the
equal and opposite reaction of the finger to the weight of the ruler acting upwards. Should the centre of gravity not be exactly above the finger, the force of gravity will have a turning moment about the finger and so cause the ruler to topple over.

Note carefully the distinction we have made above between the force of gravity which acts on the ruler and the weight of the ruler which acts on the finger. The essential point to grasp is that three forces all equal in magnitude are involved in the above discussion, namely: (a) the force of gravity acting on the ruler; (b) the weight of the ruler acting on the finger;
(c) the reaction of the finger acting on the ruler. In this particular case, as indeed for all bodies at rest, or on a support moving with constant velocity, the force of gravity on the body is equal to its weight on its support. We saw, on pages 42-3 that this is not so for a body resting on an accelerating support. Here, the force of gravity on the body is effectively constant, while the weight varies according to the acceleration of the support.