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

Step-by-step solution

Let the impulse applied by the cue be J at a height h above the centre of the thin spherical shell of mass M and radius R . The linear velocity v acquired by the centre of mass is given by the linear impulse: J = Mv The angular velocity acquired by the shell is given by the angular impulse about the centre of mass: Jh = I For a thin spherical shell, the moment of inertia about its diameter is I = 2 3 MR^2 . For the shell to not slip on the surface immediately after being struck, the velocity of the point of contact