Question 1: A uniform, solid metal disk of mass 6.80 kg and diameter 27.0 cm han

Question

Question 1:

A uniform, solid metal disk of mass 6.80 kg and diameter 27.0 cm hangs in a horizontal plane, supported at its center by a vertical metal wire. You find that it requires a horizontal force of 4.29 N tangent to the rim of the disk to turn it by 3.40 , thus twisting the wire. You now remove this force and release the disk from rest.

Part A

What is the torsion constant for the metal wire?

Part B

What is the frequency of the torsional oscillations of the disk?

Part C

What is the period of the torsional oscillations of the disk?

Explanation / Answer

Part A

Torque,

= k

F r = k

(4.23)(0.12) = k (3.34 * /180)

k = 9.760 Nm
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Part B

I = ½ m r²

I = ½ (6.5)(0.12)²

I = 0.0468 kg m²

f = 1/(2) (k/I)

f = 1/(2) (9.760/0.0620)

f = 1.997 Hz

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Part C

T=1/f

T=1/1.997=0.501s

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