$A$ rope is wound round a hollow cylinder of mass $5\,kg$ and radius $0.5\,m.$ What is the angular acceleration (in $rad/s^2$) of the cylinder if the rope is pulled with a force of $20\,N$?

$A$ solid cylinder of mass $2\; kg$ and radius $4\; cm$ is rotating about its axis at the rate of $3\; rpm$. The torque required to stop after $2\pi$ revolutions is

$A$ particle of mass $m$ moves in a circular path of radius $r$,under the action of a force which delivers constant power $P$ and increases its speed. The angular acceleration of the particle at time $t$ is proportional to:

In the following figure,$r_1 = 5\,cm$ and $r_2 = 30\,cm$. If the moment of inertia of the wheel is $1500\,kg\cdot m^2$,then its angular acceleration will be (approximately):

$A$ pulley of radius $10 \ cm$ has a moment of inertia of $10^{-3} \ kg \ m^2$ about its geometric axis. $A$ time-varying tangential force $F = (0.5t - 0.3t^2) \ N$ is applied to its rim. The pulley is initially at rest. If $t$ is in seconds,what will be the angular acceleration of the pulley at $t = 3 \ s$ in $rad \ s^{-2}$?

Consider a body shown in the figure,consisting of two identical balls,each of mass $M$,connected by a light rigid rod of length $L$. If an impulse $J = MV$ (where $V$ is the linear velocity of a ball) is imparted to the body at one of its ends,what would be its angular velocity?