A uniform, solid metal disk of mass 6.80 kg and diameter 26.0 cm hangs in a hori

Question

A uniform, solid metal disk of mass 6.80 kg and diameter 26.0 cm hangs in a horizontal plane, supported at its center by a vertical metal wire. You find that it requires a horizontal force of 4.15 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.

What is the torsion constant for the metal wire?

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

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

Explanation / Answer

Torque = rF = k

=> 0.13 * 4.15 = k * (3.40 * / 180)

=> Torsion constant, k = 9.09 N-m/rad

Frequency of small oscillations, f = (1/2) * (k/I)1/2 = (1/2) * (2k/mr2)1/2

=> f = (1/2) * [2 * 9.09 / (6.80 * 0.132)]1/2 = 2 Hz

Time period, T = 1/2 = 0.5 s

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