
A diver having a moment of inertia of about an axis through its centre of mass rotates at an angular speed of about this axis. If he folds his hands and feet to decrease the moment of inertia to what will be the new angular speed?


Important Questions on Rotational Mechanics




A kid of mass stands at the edge of a platform of radius , which can be freely rotated about its axis. The moment of inertia of the platform is . The system is at rest when a friend throws a ball of mass and the kid catches it. If the velocity of the ball is 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 ball 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 as seen by his friend. Find the angular velocity with which the platform will start rotating.

A kid of mass stands at the edge of a platform of radius , which can be freely rotated about its axis. The moment of inertia of the platform is . The system is at rest when a friend throws a ball of mass and the kid catches it. If the velocity of the ball is 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 with the kid is rotating in anticlockwise direction at an angular speed . The kid starts walking along the rim with a speed relative to the platform also in the anticlockwise direction.
Suppose the platform is brought to rest with the ball 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 as seen by his friend. Find the angular velocity with which the platform will start rotating.

A uniform rod of mass and length is struck at an end by a force perpendicular to the rod for a short time interval . Calculate
(a) the speed of the centre of mass.
(b) the angular speed of the rod about the centre of mass.
(c) the kinetic energy of the rod.
(d) the angular momentum of the rod about the centre of mass after the force has stopped to act. Assume that is so small that the rod does not appreciably change its direction while the force acts.

