Question

A 50.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 480 kg · m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth.

In what direction does the turntable rotate?

Answer 1

The turntable will rotate counterclockwise when the woman starts walking clockwise on its rim, in order to conserve angular momentum.

Step-by-step explanation:

The question asks about the direction in which a turntable would rotate if a woman starts walking on it in a clock-wise direction. According to the conservation of angular momentum, if a system is free of external torques, the total angular momentum of the system remains constant. In this scenario, the turntable and the woman constitute an isolated system if we can neglect air resistance and friction at the pivot.

When the woman begins walking clockwise, she imparts a clockwise angular momentum relative to the Earth. To conserve the total angular momentum of the system, which was initially zero, the turntable must acquire an angular momentum that is equal in magnitude but opposite in direction to that of the woman's. Hence, the turntable will begin to rotate counterclockwise (as viewed from above), which is the opposite direction to the woman's movement.