A ring of radius $0.5\, m$ and mass $10 \,kg$ is rotating about its diameter with an angular velocity of $20 \,rad/s.$  Its kinetic energy is .......... $J$

A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity $\omega$. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If $E$ be the initial Kinetic energy of the system, then final Kinetic energy will be $\frac{E}{x}$.The value of $x$ is $....$

A cord is wound round the circumference of wheel of radius $r$. The axis of the wheel is horizontal and moment of inertia about it is $I$. A weight $mg$ is attached to the end of the cord and falls from rest. After falling through a distance $h$, the angular velocity of the wheel will be

Explain work done by torque.

To maintain a rotor at a uniform angular speed of $100\, rad\, s^{-1}$, an engine needs to transmit torque of $100\, Nm$. The power of the engine is

$A$ man, sitting firmly over a rotating stool has his arms streched. If he folds his arms, the work done by the man is