Question

A coin is placed on a flat turntable, a distance 18.6 cm from the center of rotation. The coefficient of static friction between the turntable and the coin is 0.8. At what maximum angular speed may the turntable be rotating before the force of friction is not able to keep the coin at the same distance from the axis? Hint: if you think a critical piece of information is missing, assign it a letter, and see if it cancels in the end.

Answer 1

Concept used- When a coin is placed on a rotating table, it will keep rotating along the same table at the place where it is kept as long as centripetal force on the coin due to static friction, limiting friction is not lesser than the centrifugal force on the coin

Step-by-step solution :

Let the max angular speed for rotation be .

Given that the radius at which the coin is kept = r = 18.6 cm = 0.186 m

Now for the coin to keep rotating on the desired path, as per our concept, we need to have :

so equating both the sides, we get :

putting the values, we get :

or-

Final answer -

Hence the maximum permissible angular velocity is 6.492 radian per second to keep the coin rotating at the same spot