You have a large sphere (like a globe, perhaps) of radius r that is ? xed in position. on top of this you place a small sphere (like a marble) of mass m and radius r where r < < r. assume that the small sphere is placed almost exactly on the top of the large sphere at rest so that it is just barely out of balance and begins to roll without slipping or sliding down the side of the larger sphere. it continues to roll down the sphere until it loses contact at some very speci? c point.
suppose we de? ne the angle ? as the angle between the line to vertical and the line from the center of the large sphere. suppose we de? ne the special angle ? = ? c corresponding to the point where the small sphere loses contact with the large sphere. what is this angle ? c? give your answer in terms of the given parameters.