$A$ fan rotating with an angular speed of $600 \, rev/min$ comes to rest after $60$ revolutions when switched off. The time taken to come to rest is ........ $(sec)$.

$A$ merry-go-round makes $120$ revolutions per minute. $A$ child sitting on it starts crying,so the merry-go-round is slowed down with a retardation of $2 \ rad \ s^{-2}$. How long will it take for the merry-go-round to come to a stop? How many revolutions will it make before coming to a stop?

$A$ wheel rotates with a uniform angular acceleration of $2.0 \ rad/s^2$. If the wheel starts from rest,the number of revolutions completed in the first $10 \ s$ will be approximately:

$A$ particle moves along a circle of radius $\left( \frac{20}{\pi} \right) \, m$ with constant tangential acceleration. If the velocity of the particle is $80 \, m/s$ at the end of the second revolution after motion has begun,the tangential acceleration is

$A$ particle starting from rest moves in a circle of radius $r$. It attains a velocity of $V_{0} \; m/s$ in the $n^{\text{th}}$ round. Its angular acceleration will be

$A$ particle starting from rest moves along the circumference of a circle of radius $r$ with constant angular acceleration $\alpha$. The magnitude of the average velocity,in the time it completes a small angular displacement $\theta$,is: