A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant a is defined by the relationJ=- alpha theta, where J is the restoring couple and the angle of twist).

A circular disc of mass 10 kg is suspended by a wire attached to its c

1.	A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant a is defined by the relationJ=- alpha theta, where J is the restoring couple and the angle of twist).
Answer» Solution :Here m=10kg ,R=15 cm=0.15m,T = 1.5s Moment of INERTIA of disc, `I= (1)/(2)mR^(2)= (1)/(2) xx 10 xx (0.15)^(2) kgm^(2)` Now `T= 2pisqrt((I)/(alpha))` so, `alpha= (4PI^(2)I)/(T^(2))= 4 xx ((22)/(7))^(2)xx (1)/(2) xx (10xx (0.15)^(2))/((1.5)^(2))= 1.97 Nm//"rad"`