If a wheel starting from rest is rotating with an angular acceleration of $\pi \ rad \ s^{-2}$,then the number of rotations made by the wheel in the first $6 \ s$ is:

$A$ car is moving at a speed of $72 \, km/h$. The diameter of its wheels is $0.25 \, m$. If the wheels stop after completing $20$ revolutions upon applying brakes,the angular retardation produced by the brakes is ....... $rad/s^2$. (in $.5$)

$A$ body rotating with uniform angular acceleration covers $100 \pi \text{ rad}$ in the first $5 \text{ s}$ after the start. Its angular speed at the end of $5 \text{ s}$ (in $\text{rad/s}$) is .........$\pi$.

$A$ particle revolves with constant angular acceleration $\pi \, rad/s^2$. If the particle starts from rest,how many revolutions will it make in the first $10 \, s$?

$A$ particle moves from point $P_1$ to $P_2$ along a circular path with constant speed $v$. If the angle subtended by the arc $P_1P_2$ at the center is $90^{\circ}$,what is the change in velocity?

When a ceiling fan is switched on,it makes $10$ rotations in the first $3\,s$. How many rotations will it make in the next $3\,s$? (Assume uniform angular acceleration)