Question

derive the expression for the centripetal accilaration

Answer 1

The centripetal force in a particle moving in uniform circular motion is given as

F = mv2 / r

here

'm' is the mass of the body

'v' is the velocity of the body

and 'r' is the radius of its orbit

now, according to Newton's Second Law of motion

F = ma

thus, by equating the two relations we get

ma = mv2 / r

here acceleration 'a' is the centripetal acceleration, which would be given as

a = v2 / r

This one is easy and simple if you want to have a diff. one just tell me.