A thin spherical shell of radius R lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?

Figure (10-E14) shows a rough track, a portion of which is in the form of a cylinder of radius R. With what minimum linear speed should a sphere of radius r be set rolling on the horizontal part so that it completely goes round the circle on the cylindrical part.

Figure (10-E15) shows a small spherical ball of mass m rolling down the loop track. The ball is released on the linear portion at a vertical height H from the lowest point. The circular part shown has a radius R.

(a) Find the kinetic energy of the ball when it is at a point A where the radius makes an angle θ with the horizontal.

(b) Find the radial and the tangential accelerations of the center when the ball is at A.

(c) Find the normal force and the frictional force acting on the ball if H = 60 cm, R = 10 cm, θ = 0 and m = 70 g.

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.