A uniform, solid metal disk of mass 6.60 kg and diameter 21.0 cm hangs in a horizontal plane, supported at its center by a vertical metal wire. You find that it requires a horizontal force of 4.16 N tangent to the rim of the disk to turn it by 3.35 degrees, thus twisting the wire. You now remove this force and release the disk from rest.

(a) What is the torsion constant of the metal wire?

(b) What are the frequency and period of the torsional oscillations of the disk?

(c) Write the equation of motion for the disk.