- A rough disc is rotating in a horizontal plane with constant angular speed \(\omega\) about a vertical axis through the centre of the disc. A particle \(P\) is placed on the disc at a distance \(r\) from the axis. The coefficient of friction between \(P\) and the disc is \(\mu\).
Given that \(P\) does not slip on the disc, show that
$$\omega \leqslant \sqrt { \frac { \mu g } { r } }$$