A bicycle wheel of radius 32 cm is mounted at the middle of an axle 49 cm long.

Question

A bicycle wheel of radius 32 cm is mounted at the middle of an axle 49 cm long. The tire and rim weigh 42 N. The wheel is spun at 13 rev/s, and the axle is then placed in a horizontal position with one end resting on a pivot. What is the magnitude of the angular momentum due to the spinning of the wheel? (Treat the wheel as a hoop.) What is the angular speed of precession? rad/s How long does it take for the axle to swing through 360 degree around the pivot? What is the magnitude of 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? up up or down, depending on the direction of in part (a) down

Explanation / Answer

(a) L = I w; I = MR2 L = (42/9.81) * 0.32^2* (26*pi) J.s = 35.809 J.s (b) wp = MgD/L wp = (42* 0.245/35.809) rad/s = 0.28735 rad/s (c) T = 2p/wp T = 2*pi/0.28735 s = 21.86 s (d) Lp = MD^2wp Lp = 0.0738 J.s; up or down, depending on the direction of L

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