If the speed $(v)$ and radius $(r)$ of a particle performing uniform circular motion are both doubled,find its new centripetal acceleration.

$A$ particle is moving on a circular path with a constant speed $v$. Its change of velocity as it moves from $A$ to $B$ in the figure is

$A$ fan is making $600$ revolutions per minute. If after some time it makes $1200$ revolutions per minute,then the increase in its angular velocity is

State the $SI$ units of angular velocity and angular acceleration.

If the direction of motion of an object performing uniform circular motion is reversed,what will be the effect on the direction of the centripetal force?

If a body moving in a circular path maintains a constant speed of $10 \,ms^{-1}$, then which of the following correctly describes the relation between acceleration $(a)$ and radius $(r)$?