A uniform disc of mass and radius is pivoted smoothly at its centre of mass. A light spring of stiffness is attached with the disc tangentially as shown in the figure. Find the angular frequency in rad/s of torsional oscillations of the disc. (Take and )

A uniform disc of mass and radius is pivoted smoothly at its centre of mass. A light spring of stiffness is attached with the disc tangentially as shown in the figure. Find the angular frequency in rad/s of torsional oscillations of the disc. (Take and )

1 Answer

127 votes

**(2)**

If we twist (rotate) the disc through a small clockwise angle , the spring will be deformed (compressed) by a distance .Hence, the spring force will produce a restoring torque

Restoring torque where

This gives

It means after removing the external (applied) torque, the restoring torque rotates the disc with an angular acceleration which will bring the spring disc system back to its original state

Newton’s law of rotation (or torque equation): Applying Newton’s second law of rotation, we have

Where

This gives

Then

Comparing the above equation with , we have

After substituting the values we get

127 votes

127