A uniform circular board of mass `M` and radius `R` is fixed on a horizontal plane and free to rotate along a vertical axis through its center. A man of mass `m` walks round the edge of the board without slipping, when he has walked completely round the board to his starting point, find the angle turned by the board.

A man of mass m stands on the edge of a horizontal unifom disc of mass M and radius R whichis capable of rotating freely about a stationary vertical axis passing through its center. At a certain moment the man starts moving along the edge of the disc, he shifts over angle theta relative to the disc and then stops. Find the angle through which the disc rotates.

A man of mass m_(1) stands on the edge of a horizontal uniform disc of mass m_(2) and radius R which is capable of rotating freely about a stationary vertical axis passing through its centre . The man walks along the edge of the disc through angle theta relative to the disc and then stops . find the angle through which the disc turned the time the man stopped . [(2m_(1)theta)/(2m_(1) + m_(2))]

A circular ring of mass m and radius r is rotating in a horizontal plane about an axis vertical to its plane. What will its rotational kinetic energy? (Angular speed of ring is w)

A homogeneous cylinder of mass M and radius R is pulled on a horizontal plane by horizontal force F acting through its mass centre. Assuming rolling without slipping what is the angular acceleration of the cylinder ?

A man of mass m_1 stands on the edge of a horizontal uniform disc of mass m_2 and radius R which is capable of rotating freely about a stationary vertical axis passing through its centre. At a certain moment the man starts moving along the edge of the disc, he shifts over an angle varphi^' relative to the disc and then stops. In the process of motion the velocity of the man varies with time as v^'(t) . Assuming the dimensions of the man to be negligible, find: (a) the angle through which the disc had turned by the moment the man stopped, (b) the force moment (relative to the rotation axis) with which the man acted on the disc in the process of motion.

A rod of mass M and length L lying horizontally is free to rotate about a vertical axis through its end. A horizontal force F on the rod at the other end, the force always remains perpendicular to the rod. Find the angular velocity of the rod when it has turned an angle pi//2 .