A gramophone record is revolving with an angular velocity $\omega$. A coin is placed at a distance $

Question

A gramophone record is revolving with an angular velocity $\omega$. A coin is placed at a distance $r$ from the centre of the record. The static coefficient of friction is $\mu$. The maximum angular velocity $\omega_{max}$ for the coin to revolve with the record without slipping is

Professor PC Thomas Classes · Answer

For the coin to not slip, the required centripetal force must be provided by static friction. $m r \omega^2 \le \mu m g \implies \omega^2 \le \frac{\mu g}{r}$. Therefore, $\omega_{max} = \sqrt{\frac{\mu g}{r}}$.