$A$ solid cylinder of mass $M$ and radius $R$ is placed in a horizontal position. Two strings are wrapped around the cylinder. Find the tension in the strings and the acceleration of the cylinder as the strings unwind.

$A$ thin but rigid semicircular wire frame of radius $r$ is hinged at $O$ and can rotate in its own vertical plane. $A$ smooth peg $P$ starts from $O$ and moves horizontally with constant speed $v_0$,lifting the frame upward as shown in the figure. Find the angular velocity $\omega$ of the frame when its diameter makes an angle of $60^{\circ}$ with the vertical.

For a rigid body in rotational motion,if the linear velocity of a particle at a distance of $2 \ cm$ from the fixed axis of rotation is $10 \ cm \ s^{-1}$,what is the angular velocity of a particle at a distance of $4 \ cm$ from the axis of rotation?

$A$ ball of mass $m$ is released from inside a smooth wedge of mass $m$ as shown in the figure. What is the speed of the wedge when the ball reaches point $B$?

Explain that angular velocity is a vector and its direction is given by the right-hand screw rule.

One end of a rod of length $L$ is on a horizontal plane. It is inclined at an angle $\alpha$ to the horizontal plane. When released,its angular velocity after coming to the horizontal plane is: