A small coin is placed on a horizontal gramophone record that is rotating at a constant angular speed . The coefficient of static friction between the coin and the record is _s . If the acceleration due to gravity is g , what is the maximum distance from the centre at which the coin can be placed without slipping?

Step-by-step solution

For a coin on a horizontal rotating record, the normal force is N = mg . The necessary centripetal force for the coin to move in a circle of radius r is provided by static friction, so f = m ^2 r . To prevent the coin from slipping, the required friction must not exceed the limiting static friction: f _s N m ^2 r _s mg Solving for r , we get the maximum distance: r _s g ^2 Thus, the maximum distance from the centre is _s g ^2 . Answer: _s g ^2