A bicycle wheel of diameter 62cm. and mass m rotates on it\'s axle, two 22cm. lo

Question

A bicycle wheel of diameter 62cm. and mass m rotates on it's axle, two 22cm. long wooden handles,one on each end acts as an axle. You tie a rope to a small hook on the end of one of the handles, and then then spin the bicycle wheel with the flick of your hand. When you release the spinning wheel it precesses about the vertical axis defined by the rope,instead of falling to the ground(as if it were not spinning). Estimate the rate of precession if the wheel rotates at 2.5rev/s. and its axle remains horizontal.

Explanation / Answer

Radius of the wheel, r1 = 31 cm = 0.31 m Length of the wooden handle, r2= 0.25 m Angular velocity, w = 2 Pi * 2.5 = 5 pi rad/s Precession rate = Torque /angular momentum Angular momentum, L = Iw Moment of inertia, I = mr1^2 (this assumes all the mass is at the rim) Torque, T = mg*r2 Precession rate = mgr2 / (mr1^2 w) = g r2/(r1^2 w) = 9.8 * 0.25 / ( 0.31^2 * 5 Pi ) = 1.623 rad/s

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