A uniform, solid metal disk of mass 6.30kg and diameter 22.0cm hangs in a horizo

Question

A uniform, solid metal disk of mass 6.30kg and diameter 22.0cm hangs in a horizontal plane, supported at its center by a vertical metal wire. You find that it requires a horizontal force of 4.22N tangent to the rim of the disk to turn it by 3.36?, thus twisting the wire. You now remove this force and release the disk from rest.

a)What is the torsion constant for the metal wire?

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

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

Explanation / Answer

1) torsional constant K = torque/angle = (F*R)/theta = (4.17*0.115)/(3.31*0.01744) = 8.31 Nm /rad

2) MOI I = 0.5*m*R^2 = 0.5*6.6*0.115^2 = 0.0436 kg m^2

f = (1/2pi)*sqrt(K/I) = (1/6.28)*sqrt(8.31/0.0436) = 2.1984 Hz

3) T = 1/f = 0.4549 s

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