Question

Define centripetal acceleration. Derive an expression for the centripetal acceleration of a particle moving with uniform speed 'v' along a circular path of radius 'r'. Give the direction of this acceleration.

Answer 1

rate of change of tangential velocity is called as the centripetal acceleration.

$F=\frac{m{v}^2}{r}$

centripetal acceleration is given by,

$a_c=\frac{F}{m}$

$=\frac{\frac{m{v}^2}{r}}{m}$

$\therefore a_c=\frac{v^2}{r}$