NUMERICALS

A body of mass $1\mathrm{kg}$ is revolved in a horizontal circle by attaching to one end of 1 metre long string. If the frequency of revolution is $20 \mathrm{rev}/\mathrm{s}$, find about the axis of rotation, the angular momentum of the body.

A body of mass $1\mathrm{kg}$ is revolved in a horizontal circle  by attaching to one end of 1 metre long string. If the frequency of revolution is $20 \mathrm{rev}/\mathrm{s}$, find about the axis of rotation, the  rotational kinetic energy of the body.

A disc of diameter $0.4 \mathrm{m}$ and of mass $10 kg$ is rotating about its axis at the rate of $1200 \mathrm{rev}/\min$ find the angular momentum and rotational kinetic energy of the disc

A disc of diameter $0.4\mathrm{m}$   and of mass $10 \mathrm{kg}$ is rotating about its axis at the rate of $1200 \mathrm{rev}/\min .$ find the angular momentum and rotational kinetic energy of the disc

A wheel is rotating at a rate of $1000 \mathrm{rpm}$ and its kinetic energy is ${10}^6\mathrm{J}$ Determine the moment of inertia of the wheel about its axis of rotation.

A person taking in his hands spheres each of mass $2 \mathrm{kg}$  is standing on a table revolving with an angular velocity of $10 \mathrm{rad}/\mathrm{s}$. His arms are extended and each sphere is at a distance of $1\mathrm{m}$from the axis of rotation, if the moment of inertia of the person and the table about the axis of rotation be $1 {\mathrm{kgm}}^2$ then what will be the kinetic energy of rotation of the whole system. If the person pulls his arms so that each sphere is now $0.3 \mathrm{meter}$ from the axis of rotation then what will be the new kinetic energy. Explain the difference.

A ball tied to a string takes $4\mathrm{s}$ to complete one revolving along a horizontal circle. If by pulling the cord, the radius of the circle is reduced to half, how much time will the ball take to complete one revolution?

Moment of inertia of a ring is $3{\mathrm{kgm}}^2$ .It is rotated for $30 \mathrm{s}$ by a force of  $6 \mathrm{Nm}$, Calculate the work done.