$A$ 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 ........ $(sec)$.

Angular displacement $(\theta)$ of a flywheel varies with time as $\theta = at + bt^2 + ct^3$. The angular acceleration is given by:

$A$ fan starts from rest and makes $10$ revolutions in the first $3$ seconds. Assuming constant angular acceleration,how many revolutions will it make in the next $3$ seconds?

$A$ disc starts from rest and acquires an angular velocity of $240 \ rpm$ in $10 \ s$. The angular acceleration is ...... $rad/s^2$ (assuming it is constant).

If the equation for the displacement of a particle moving on a circular path is given as $\theta = 2t^3 + 0.5$,where $\theta$ is in radians and $t$ is in seconds,then the angular velocity of the particle after $2$ seconds will be ....... $rad/sec$.

$A$ wheel rotates with an angular acceleration of $3 \ rad \ s^{-2}$ and an initial angular velocity of $2 \ rad \ s^{-1}$. What will be its angular displacement after $2 \ s$?