$A$ 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?

$A$ particle is rotating in a circular path and at any instant its motion can be described as $\theta = \frac{5t^4}{40} - \frac{t^3}{3}$. The angular acceleration of the particle after $10 \text{ s}$ is . . . . . . $\text{rad/s}^2$.

$A$ car wheel rotates at $1200$ revolutions per minute. On pressing the accelerator,it rotates at $4500$ revolutions per minute in $10 \ s$. The angular acceleration of the wheel is ...

$A$ 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).

An object moves along a circle with normal acceleration proportional to $t^\alpha$,where $t$ is the time and $\alpha$ is a positive constant. The power developed by all the forces acting on the object will have time dependence proportional to

$A$ 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 $.5$)