A bicycle wheel of radius 28 cm is mounted at the middle of an axle 50 cm long. The tire and rim weigh 30 N. The wheel is spun at 12 rev/s, and the axle is then placed in a horizontal position with one end resting on a pivot.

(a) What is the angular momentum due to the spinning of the wheel? (Treat the wheel as a hoop.)

(b) What is the angular velocity of precession?

(c) How long does it take for the axle to swing through 360o around the pivot?

(d) What is the angular momentum associated with the motion of the center of mass, that is, due to the precession? In what direction is this angular momentum?