Question

Define centripetal force and derive an expression for it.

Answer 1

Centripetal force : 

The net force which can change only the direction of the velocity of a body is called “centripetal force.” 

Derivation : 

Newton’s second law says that the net force on a moving body produces an acceleration in it, which is directed along the net force. 

So in uniform circular motion, a net force acts towards the centre, called as centripetal force. According to Newton’s second law of motion,

F_net = m x a_c

F_c = m x a_c 

F_c = m x v²/R  ( We know that a_c = v² /R)

∴ Centripetal force F_c = mv²/R

Here R is the radius of the circle.