The angular velocity of a particle is given by $\omega = 1.5t - 3t^2 + 2$. How much time in $sec$ does it take for the angular acceleration to become zero?

$A$ flywheel rotates with a uniform angular acceleration. Its angular velocity increases from $20\pi \, rad/s$ to $40\pi \, rad/s$ in $10 \, s$. How many rotations did it make in this period?

$A$ wheel is rotating at $900 \, r.p.m.$ about its axis. When the power is cut-off,it comes to rest in $1 \, minute$. The angular retardation in $rad/s^2$ is:

$A$ 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?

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)

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