Gyroscope 1 2 3 4 5 6 A disk with mass m = 6.1 kg and radius R = 0.41 m hangs fr
ID: 1996967 • Letter: G
Question
Gyroscope
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A disk with mass m = 6.1 kg and radius R = 0.41 m hangs from a rope attached to the ceiling. The disk spins on its axis at a distance r = 1.3 m from the rope and at a frequency f = 18.3 rev/s (with a direction shown by the arrow).
1)
What is the magnitude of the angular momentum of the spinning disk?
kg-m2/s
2)
What is the torque due to gravity on the disk?
N-m
3)
What is the period of precession for this gyroscope?
s
4)
What is the direction of the angular momentum of the spinning disk at the instant shown in the picture?
up
down
left
right
5)
What is the direction of the precession of the gyroscope?
it does not precess
clockwise as seen from above (looking down the rope)
counterclockwise as seen from above (looking down the rope)
Explanation / Answer
a) Li = I w
Li = 1/2 M R2 * 2 pi * angular frequency
Li = 1/2 M R2 * (2 pi * angular frequency)
= 1/2 * 6.1 * 0.412 * 2 pi * 18.3 = 58.95 kg.m2/s
b) T = m g d
= 6.1 * 9.8 * 1.3 = 77.71 N.m
c) Period of precession = 2 pi Li / m g d
= 2 pi * 58.95 / (77.71 )
= 4.76
5) clockwise
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