Precession: A certain gyroscope consists of a uniform disk with a 52 cm radius m

Question

Precession:

A certain gyroscope consists of a uniform disk with a 52 cm radius mounted at the center of an axle that is 12 cm long and of negligible mass. The axle is horizontal and supported at one end. If the disk is spinning around the axle at 108 rev/min,

a.) what is the precession rate? _____rad/s

b.) How much time will the gyroscope take to complete one precession? _____s

c.) During this one precession, how many rotations will the disk have completed around its own center of mass? _____rotations

Explanation / Answer

R = 52 cm = 0.52 m
r = 12 cm = 0.12 m
? = (108 rev/min)(2? rad/rev)(1min/60 s) = 11.309 rad/s
Precession Rate = gr / [(R^2)?] = (9.81 m/s^2)(0.12m) / [(0.52 m)^2 (11.309 rad/s)
Precession Rate = 0.3849 rad/s

b)time taken =1/0.3849=2.598s

c)no of rotations =(108/60)*2.598=4.676 revolutions

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