A gramophone record is revolving with an angular velocity $\omega$. A coin is placed at a distance…
A gramophone record is revolving with an angular velocity $\omega$. A coin is placed at a distance $\mathrm{r}$ from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if
$\mathrm{r}=\mu g \omega^2$
$\mathrm{r} < \frac{\omega^2}{\mu g}$
$r \leq \frac{\mu g}{\omega^2}$
$r \geq \frac{\mu g}{\omega^2}$
Solution
When the disc spins the frictional force between the gramophone record and coin is $\mu \mathrm{mg}$
The coin will revolve with record, if
$\begin{aligned}
F_{\text {frictional }} & \geq F_{\text {centripetal }} \\
\mu m g & \geq m \omega^2 r \\
\frac{\mu g}{r} & \geq \omega^2
\end{aligned}$