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

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

$A$ car changes speed from $18\,km/h$ to $36\,km/h$ in $5\,s$. The diameter of its wheel is $0.8\,m$. The angular acceleration of the wheel is ........ $rad/s^2$.

$A$ 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?

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

$A$ body is revolving with a uniform speed $v$ in a circle of radius $r$. The tangential acceleration is