A sphere of mass m rolls on a plane surface. Find its kinetic energy at an instant when its center moves with speed u.

A uniform rod pivoted at its upper end hangs vertically. It is displaced through an angle of 60⁰ and then released. Find the magnitude of the force acting on a particle of mass dm at the tip of the rod when the rod makes an angle of 37⁰ with the vertical.

A cylinder rolls on a horizontal plane surface. If the speed of the center is 25 m/s, what is the speed of the highest point?

A string is wrapped over the edge of a uniform disc and the free end is fixed with the ceiling. The disc moves down, unwinding the string. Find the downward acceleration of the disc.

A small spherical ball is released from a point at a height h on a rough track shown in figure (10-E13). Assuming that it does not slip anywhere, find its linear speed when it rolls on the horizontal part of the track.