A rigid body can be divided into smaller mass elements of masses m1
. The weight of the rigid body must be equal to the sum of the weights of these small mass elements. The weights of these mass elements produce gravitational torque on the body. We can always find a point, such that the total gravitational torque about the point on the body due to these mass elements is zero.
The centre of gravity of a rigid body is defined as that point where the total gravitational torque on the body is zero. When torque is calculated about the centre of gravity, weights of some mass elements produce clockwise torque and of others produce anti-clockwise torque, making the net turning effect zero. Hence the weight of a rigid body can’t produce any net torque about its centre of gravity. Torque due to the weight of a body about any point can be calculated by assuming the whole weight of the body concentrated at its centre of gravity.
We can balance a rigid body by applying an upward force equal to its weight and passing through its centre of gravity. The bird shown is designed in such a way that its centre of gravity is located at the tip of its beak. Hence, we are able to balance the bird by applying an upward force at the tip of its beak.
Centre of mass and centre of gravity are two different concepts. If the acceleration due to gravity is the same for all particles of a rigid body, then the centre of gravity coincides with its centre of mass.
For bodies of small size, the methods used to find the centre of mass can also be used to find the centre of gravity.