$A$ boy is standing at the center of a turntable holding two blocks in his hands. The rotational kinetic energy of the system about the axis passing through the center is $K$. When the boy extends his arms,the moment of inertia of the system about the axis of rotation doubles. What will be the new rotational kinetic energy of the system?

$A$ dancer is standing on a rotating platform holding two spheres in her hands. If she drops the spheres to the ground,the dancer's...

$A$ boy stands at the center of a horizontal platform with $2 \ kg$ masses in each hand,held close to his body. The platform rotates about a vertical axis passing through its center at a speed of $2 \ rev/s$. The moment of inertia of the system is $1 \ kg \cdot m^2$. When the boy extends his arms fully with the masses,the moment of inertia becomes $2 \ kg \cdot m^2$. In the second state,the kinetic energy of the system compared to the first state will be:

$A$ particle of mass $m$ moves with a velocity $v$ along the rim of a disc of radius $R$ in the counter-clockwise direction. The disc has a moment of inertia $I$ and is rotating in the clockwise direction with an angular velocity $\omega$. If the particle stops moving,what will be the angular velocity of the disc?

Two discs of same moment of inertia $I$ are rotating about their central axes perpendicular to their planes with angular velocities $\omega_1$ and $\omega_2$. They are brought into contact face to face,such that their axes of rotation coincide. The expression for the loss of energy during this process is:

$A$ rotating table has an angular velocity $\omega$ and a moment of inertia $I_1$. $A$ man of mass $m$ stands at the center of the table. If the man walks a distance $r$ along the radius of the table,what will be his final angular velocity?