A wheel of moment of inertia 0.10 kg-m² is rotating about a shaft at an angular speed of 160 rev/minute. A second wheel is set into rotation at 300 rev/minute and is coupled to the same shaft so that both the wheels finally rotate with a common angular speed of 200 rev/minute. Find the moment of inertia of the second wheel.

A boy is seated in a revolving chair revolving at an angular speed of 120 revolutions per minute. Two heavy balls form part of the revolving system and the boy can pull the balls closer to himself or may push them apart. If by pulling the balls closer, the boy decreases the moment of inertia of the system from 6 kg-m² to 2 kg-m², what will be the new angular speed?

A boy is standing on a platform which is free to rotate about its axis. The boy holds an open umbrella in his hand. The axis of the umbrella coincides with that of the platform. The moment of inertia of “the platform plus the boy system” is 3.0 × 10^-3 kg-m² and that of the umbrella is 2.0 × 10^-3 kg-m². The boy starts spinning the umbrella about the axis at an angular speed of 2.0 rev/s with respect to himself. Find the angular velocity imparted to the platform.

A kid of mass M stands at the edge of a platform of radius R which can be freely rotated about its axis. The moment of inertia of the platform is I. The system is at rest when a friend throws a ball of mass m and the kid catches it. If the velocity of the ball is u horizontally along the tangent to the edge of the platform when it was caught by the kid, find the angular speed of the platform after the event.

Suppose the platform of the previous problem is brought to rest with the bail in the hand of the kid standing on the rim. The kid throws the ball horizontally to his friend in a direction tangential to the rim with a speed u as seen by his friend. Find the angular velocity with which the platform will start rotating.