A coin is placed on a disc. The coefficient of friction between the...

Normal force acting on the coin is, $N = mg$.

Required friction force to provide centripetal force for the coin is, $f = m{\omega}^{2}r$ and maximum value of static friction force available is, $f = \muN = \mumg$.

For limiting condition, we can write

$⇒ \mumg = mr{\omega}^{2}$

$⇒ \omega = \sqrt{\dfrac{\mug}{r}}$