The $M.I.$ of a body about a given axis is $1.2 \ kg \cdot m^2$ and initially the body is at rest. In order to produce a rotational kinetic energy of $1500 \ J$,an angular acceleration of $25 \ rad/s^2$ must be applied about that axis for a time duration of $....... \ s$.

$A$ wheel of moment of inertia $10 \ kg \cdot m^2$ is rotating at $10$ rotations per minute. The work done in increasing its speed to $5$ times its initial value will be .......... $J$.

The Moon revolves around the Earth in an orbit of radius $R$ with a time period of revolution $T$. It also rotates about its own axis with a time period $T$. If the mass of the Moon is $M$ and its radius is $r$,the total kinetic energy of the Moon is:

$A$ thin uniform rod $AB$ of mass $m$ and length $l$ is hinged at one end $A$ to the ground level. Initially,the rod stands vertically and is allowed to fall freely to the ground in the vertical plane. The angular velocity of the rod when its end $B$ strikes the ground is ($g$ = acceleration due to gravity).

$A$ uniform rod of mass $M$ and length $L$ is pivoted at one end and is free to rotate in a vertical plane. The rod is released from rest in a horizontal position. What is the angular velocity of the rod when it reaches the vertical position?

$A$ thin rod of length $L$ and mass $M$ is held vertically with one end on the floor and is allowed to fall. Find the velocity of the other end when it hits the floor,assuming that the end on the floor does not slip.