A person sitting in a smooth groove on a rotating horizontal circular table at the edge by holding a rope joint to the center the moment of inertia of table is I. Mass of person is M. Man now pulls the rope so that he comes to the center .The angular velocity of the table is.

A rotating table completes one rotation is 10 sec. and its moment of ineratia is 100 kg- m^2 . A person of 50 kg. mass stands at the centre of the rotating table. If the person moves 2m. from the centre, the angular velocity of the rotating table in rad/sec. will be:

A child of mass m is standing, on the periphery of a circular platform of radius R , which can rotate about its central axis. The moment of inertia of the platform is I . Child jumps off from the platform with a velocity u tangentially relative to the platform. Find the angular speed of the platform after the child jumps off.

A uniform rope of length l and mass m lies on a smooth horizontal table with its length perpendicular to the edge of the table and a small part of the rope having over the edge. The rope starts sliding from rest under the weight of the over hanging end. The velocity of the rope when the length of the hanging part is . x

A metre stick is pivoted about its centre. A piece of wax of mass 20 g travelling horizontally and perpendicular to it at 5 m/s strikes and adheres to one end of the stick so that the stick starts to rotate in a horizontal circle. Given the moment of inertia of the stick and wax about the pivot is 0.02 kg m^(2) , the initial angular velocity of the stick is :

Figure shows a spool with thread wound on it placed on a smooth plane inclined at angle from horizontal. The spool has mass m, edge radius R , and is wound up to a radius r. its moment of inertia about its own axis is I . The free end of the thread is attached as shown in the figure. So that the thread is parallel to the inclined plane. T is the tension in the thread. Which of the following is correct?

A hemisphere of radius R and mass 4 m is free to slide with its base on a smooth horizontal table . A particle of mass m is placed on the top of the hemisphere . The angular velocity of the particle relative to centre of hemisphere at an angular displacement theta when velocity of hemisphere has become v is

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 as 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.

A particle A of mass 2m is held on a smooth horizontal table and is attached to one end of an inelastic string which runs over a smooth light pulley at the edge of the table. At the other end of the string there hangs another particle B of mass m, the distance from A to the pulley is l. The particle A is then projected towards the pulley with velocity u. (a) Find the time before the string becomes taut, and shown that after the string becomes taut, the initial velocity of A and B is 4u//3 . (b) Find the common velocity when A reaches the pulley (assume that B has not yet reached the ground).

A uniform circular disc of mass m is set rolling on a smooth horizontal table with a uniform linear velocity v. Find the total K.E. of the disc.

A uniform rod PQ of mass m and length t rotates with an angular velocity a while its center moves with linear velocity v = (2omega* f) / 3 on a smooth horizontal surface If the end Q of the rod is suddenly gets stuck at the moment as shown in the figure then angular velocity of the rod will be