# Rotating a Professor on a Turntable

Hi

I need you help for two questions.

1. A professor steps onto a stationary turntable while holding a rotating bicycle wheel that is rotating with an angular velocity of 15 rad/s pointing upward. The wheels axis of rotation goes through the axis of the turntable. The rotational inertia of the wheel is 1.5 kg m^2 and the combined rotational inertia of the professor and the turntable about the turntable's axis is 9.0 kg m^2. The professor flips the bicycle wheel so that it is still rotating with the same angular velocity, but pointing downward. How fast will this cause the professor and the turntable to rotate?

2. How much work is required to bring a 2.00-kg mass, 4.00-cm radius uniform sphere from rest to a rotational speed of 30.0 revolutions per second about an axis through its center?

Thank you for your help.

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#### Solution Preview

1)

Moment of inertia of the wheel I1 = 1.5 kg.m^2

Moment of inertia of the professor + turntable I2 = 9.0 kg.m^2

Initial angular velocity of the wheel w1 = 15 rad/s (pointing upward)

Let us assume before flipping the angular velocity of the professor+turntable be 'wo'

Therefore, by the law of conservation of angular momentum,

I1*w1 = ...

#### Solution Summary

The solution uses the laws of the conservation of angular momentum to solve this problem of rotation, explaining the methods in clear, easy-to-follow steps aided by short written explanations.