A small metal cylinder rests on a circular turntable that is rotating at a constant speed.

Question

The small metal cylinder has a mass of 0.20kg, the coefficient of static friction between the cylinder and the turntable is 0.080, and the cylinder is located 0.15m from the center of the turntable.

Take the magnitude of the acceleration due to gravity to be 9.81 m/s^2.

What is the maximum speed v_max that the cylinder can move along its circular path without slipping off the turntable?

Answer 1

Refer to the following figure that shows the free-body diagram:
http://img340.imageshack.us/img340/4175/tiffanyc.jpg
F is the centrifugal force pushing the cylinder outwards, where
F=mv²/r
and v the tangential speed.
μN=μmg is the frictional force resisting the movement.
By equating
mv²/r = μmg
and solving for v, you will find
v=√(μgr)
I believe it evaluates to 0.3 m/s.
Check my thinking and calculations.

Answer 2

b n

Answer 3

The answer is 0.3429.