$A$ billiard ball is hit by a cue at a point distance $h$ above the centre. It acquires a linear velocity $v_0$. Let $m$ be the mass and $r$ be the radius of the ball. The angular velocity acquired by the ball is

$A$ string is wound around the rim of a mounted flywheel (disc) of mass $20 \, kg$ and radius $20 \, cm$. $A$ steady pull of $25 \, N$ is applied on the cord. Neglecting friction and the mass of the string,the angular acceleration of the wheel in $rad/s^2$ is

$A$ wheel of radius $0.4 \ m$ can rotate freely about its axis as shown in the figure. $A$ string is wrapped around its circumference,and a weight of $4 \ kg$ is suspended from it. Due to the torque,an angular acceleration of $8 \ rad \ s^{-2}$ is produced. The moment of inertia of the wheel is = $...... \ kg \ m^2$ $(g = 10 \ ms^{-2})$

One end of a rod is hinged at $O$. The other end is suspended by a string attached to the ceiling as shown in the figure. If the string is suddenly cut,find the angular acceleration of the rod.

$A$ circular disc of radius $2 \ m$ is rotating at $240 \ rpm$. If a torque is applied to the disc, it slows down at a rate of $\pi \ rad/s^2$. How long will it take to stop? How many revolutions will the disc complete before coming to rest?

$A$ stationary horizontal disc is free to rotate about its axis. When a torque is applied on it,its kinetic energy as a function of $\theta,$ where $\theta$ is the angle by which it has rotated,is given as $K\theta^2.$ If its moment of inertia is $I,$ then the angular acceleration of the disc is