A friction less turntable with rotational inertia 40 kg*m^2/rad^2 spins clockwis

Question

A friction less turntable with rotational inertia 40 kg*m^2/rad^2 spins clockwise at 10 rotations per minute. A rock, m kg, falls straight down onto the turntable and sticks to it. The turntable's speed slows down to 9 rotations per minute. Why does the turntable slow down? Explain using diagrams and sentence explanations. Your friend in physics class says that if the rock suddenly were to fall off the table, the turntable would speed back up to 10 rotations per minute. His logic goes like this: the turntable's moment of inertia would return to its original value(That is, before the rock was dropped on it), and because the rock-table system is isolated, with no outside net force acting on it, angular momentum would have to be conserved. So because the moment of inertia has dropped, the angular velocity of the table must increase. Thoroughly critique your friend's reasoning. List at least one thing they get correct and one thing they are wrong about in the course of your answer, explain what will actually happen to the turntable's speed and why

Explanation / Answer

(a)

From the law of conservation of the angular momentum,

I*w=I'*w'

if the moment of inertia of the system is increased, then the angular speed decreases.

after mass falling on the turn table, then the moment of inertia of the turn table-mass system increases. so, the angular speed of the turn table decreases.

(b)

The concept of your friend is correct.

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