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 relation `J = –alphatheta` , where J is the restoring couple and q the angle of twist).

Explanation

Hint: The time period of a torsional pendulum is given by `T=2pisqrt(l/(alpha))`. where I is the moment of inertia about the axis of rotation. In our case `I=1/2MR^(2)`, where M is the mass of the disk and R its radius. Substituting the given values, `alpha=2.0Nmrad^(-1)`