Question

A coin is placed at the edge of a horizontal disc rotating about a vertical axis throught its axis with a uniform angular speed $2\text{rad/s}$. The radius of the disc is $50\text{cm}$. Find the minimum coefficient of friction between disc and coin so that the coin does not slip $(g=10{\text{ms}}^{-2})$

Answer 1

$f_l=\mu mg$,
friction will provide the necessary centripetal force.
$f=m{\omega }^{2}r$
$f\le f_l\Rightarrow m{\omega }^{2}r\le \mu mg$
$\Rightarrow \mu \ge \frac{{\omega }^{2}r}{g}=\frac{2^2\times 50/100}{10}$
$\Rightarrow \mu \ge 0.2$