**Mass on Turntable (A Mass on a Turntable: Conceptual)**

**Solution Below:**

A small metal cylinder rests on a circular turntable that is rotating at a constant speed as illustrated in the diagram.

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

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

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

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

^{2}.Part A

What is the maximum speed v

Express your answer numerically in meters per second to two significant figures.

_{max}that the cylinder can move along its circular path without slipping off the turntable?Express your answer numerically in meters per second to two significant figures.

Remember that centripetal force is equal to mv^{2}/r. The maximum velocity is where the centripetal force equals the frictional force:

F_{friction} = F_{c}

mgF_{s} = mv^{2}/r

0.20 * 9.81 * 0.080 = 0.20 * v^{2} / 0.15

0.015696 = 1.333v^{2}

v^{2} = 0.1177

v = 0.34 m/s

You might notice that the mass isn’t even important. Because it’s on both sides of the equation, it just cancels out, and you don’t even need it.

0.34 m/s