The centripetal force of a body …

In order to maintain uniform circular motion of a particle, a force is needed because uniform circular motion is an accelerated motion. The force is known as the centripetal force. Thus, centripetal force is the force required in order to make an object move along a circular path with uniform speed. The force acts along the radius and is directed towards the centre of circular path.

We know that centripetal acceleration of a particle moving with a constant speed v along a circle of radius r is given by
{tex}a _ { c } = \frac { v ^ { 2 } } { r }{/tex}
Hence, according to Newton's second law of motion, for a particle of mass m, we have
The centripetal force F = ma_c = {tex}\frac { m v ^ { 2 } } { r }{/tex}
As v = r{tex}\omega{/tex}, where {tex}\omega{/tex} is the angular velocity of the particle, then
F = {tex}\frac { m } { r } ( r \omega ) ^ { 2 } = m r \omega ^ { 2 }{/tex}