A uniform, solid metal disk of mass 6.50 kg and diameter 24.0 cm hangs in a horizontal plane, supported at its center by a vertical metal wire. You find that it requires a horizontal force of 4.23 N tangent to the rim of the disk to turn it by 3.34o, 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 are the frequency and period of the torsional oscillations of the disk? (c) Write the equation of motion for ?(t) for the disk.
Solution Step 1 of Given data, Mass, m= 6.5 kg Diameter, d=24 cm Radius, r = d/2=12 cm =0.12 m Applied force, F=4.23 N 0 Angular displacement, = 3.34 0 Using 360 = 2 rad = 0.0582 rad