MEDIUM
JEE Main
IMPORTANT
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A diver having a moment of inertia of 6.0 kg m2 about an axis through its centre of mass rotates at an angular speed of 2 rad s-1 about this axis. If he folds his hands and feet to decrease the moment of inertia to 5.0 kg m2 what will be the new angular speed(rad s-1)?

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Important Questions on Rotational Mechanics

MEDIUM
JEE Main
IMPORTANT
A boy is seated in a revolving chair revolving at an angular speed of 120 revolutions per minutes. 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?
HARD
JEE Main
IMPORTANT
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-1 with respect to himself. Find the angular velocity imparted to the platform?
HARD
JEE Main
IMPORTANT
A wheel of moment of inertia 0.10 kg m2 is rotating about a shaft at an angular speed of 160 rev min-1. A second wheel is set into rotation at 300 rev min-1 and is coupled to the same shaft, so that both the wheels finally rotate with a common angular speed of 200 rev min-1. Find the moment of inertia of the second wheel.
HARD
JEE Main
IMPORTANT
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 v 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.
HARD
JEE Main
IMPORTANT

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 v 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 v as seen by his friend. Find the angular velocity with which the platform will start rotating.

HARD
JEE Main
IMPORTANT

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 v 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 ω. The kid starts walking along the rim with a speed v 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 v as seen by his friend. Find the angular velocity with which the platform will start rotating.

HARD
JEE Main
IMPORTANT

A uniform rod of mass m and length l is struck at an end by a force F perpendicular to the rod for a short time interval t. 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 t is so small that the rod does not appreciably change its direction while the force acts.

HARD
JEE Main
IMPORTANT
A uniform rod of length L lies on a smooth horizontal table. A particle is moving on the table strikes the rod perpendicularly at an end and stops. Find the distance travelled by the centre of the rod by the time it turns through a right angle. Show that if the mass of the rod is four times that of the particle, the collision is elastic.