Acoin of mass m rests on a turntable a distance r from the axis of rotation. the turntable rotates with a frequency of f. what is the minimum coefficient of static friction between the turntable and the coin if the coin is not to slip?

Explanation:

= normal force acting on the coin

Normal force in the upward direction balances the weight of the coin, hence

= frequency of rotation

Angular velocity of turntable is hence given as

= distance from the axis of rotation

= minimum coefficient of static friction

static frictional force is given as

The  static frictional force provides the necessary centripetal force , hence

Centripetal force = Static frictional force

see earlier