A hollow sphere of radius R lies on a smooth horizontal surface. It is pulled by a horizontal force acting tangentially from the highest point. Find the distance travelled by the sphere during the time it makes one full rotation.

A uniform wheel of radius R is set into rotation about its axis at an angular speed ω. This rotating wheel is now placed on a rough horizontal surface with its axis horizontal. Because of friction at the contact, the wheel accelerates forward and its rotation decelerates till the wheel starts pure rolling on the surface. Find the linear speed of the wheel after it starts pure rolling.

A thin spherical shell lying on a rough horizontal surface is hit by a cue in such a way that the line of action passes through the center of the shell. As a result, the shell starts moving with a linear speed u without any initial angular velocity. Find the linear speed of the shell after it starts pure rolling on the surface.

A solid sphere of mass 0.50 kg is kept on a horizontal surface. The coefficient of static friction between the surfaces in contact is 2/7. What maximum force can be applied at the highest point in the horizontal direction so that the sphere does not slip on the surface?

A solid sphere is set into motion on a rough horizontal surface with a linear speed u in the forward direction and an angular speed u/R in the anticlockwise direction as shown in figure (10-E 16). Find the linear speed of the sphere (a) when it stops rotating and (b) when slipping finally ceases and pure rolling starts.