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A disk with mass m = 6.3 kg and radius R = 0.46 m hangs from a rope attached to

ID: 1620772 • Letter: A

Question

A disk with mass m = 6.3 kg and radius R = 0.46 m hangs from a rope attached to the ceiling. The disk spins on its axis at a distance r = 1.54 m from the rope and at a frequency f = 19.7 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

(1)

angular moment of disk,

L = lw

where l = (1/2)mR^2

w = 2*pi*f

L = (1/2)*mR^2*2*pi*f

L = (6.3*(0.46)^2*3.14*19.7

L = 82.4 kg.m^2/s

(2)

torque due to gravity,

T = mgr = 6.3*9.8*1.54

T = 97 N.m

(3)

rate of precession = T / L

f = 97 / 82.4 = 1.153

period od precession for this gyroscope,

t = 2*pi / f = 2*3.14 / 1.153

t = 5.45 s

(4)

From the right hand rule, the  direction of the angular momentum of the spinning disk is RlGHT.

(5)

direction of the precession of the gyroscope is clockwise.

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