A solid sphere of mass m and radius r spins about a horizontal axis with a period T. It is hung by a thread attached to that horizontal axis at the edge of the sphere as shown. In both the Top view and the Side view, the arrow indicates the direction a spot on the surface of the sphere is observed to move as the sphere spins.
a) Find the size and direction of the angular momentum of the sphere spinning about its axis relative to the string and the axis of rotation.
b) Find the size of the torque acting on the sphere about the string.
c) Find the direction of the torque relative to the direction of the angular momentum.
d) Can a torque in this direction change the size of the angular momentum? What shape does the tip of the angular momentum vector make if you follow it over time?