Angular Momentum Question?

Question

A student sits on a freely rotating stool holding two weights, each of mass 3.01 kg. When his arms are extended horizontally, the weights are 0.91 m from the axis of rotation and he rotates with an angular speed of 0.759 rad/s. The moment of inertia of the student plus stool is 3.01 kg·m2 and is assumed to be constant. The student pulls the weights inward horizontally to a position 0.296 m from the rotation axis. Find the new angular speed of the student. Find the kinetic energy of the rotating system before and after he pulls the weights inward.

Please explaine how you arrived at the answer.

Answer 1

First, let's compute the moment of inertia for arms extended
3.01+2*3.01*0.91^2
3.01*2.66 kg m^2

with the weights pulled in
3.01+2*3.01*0.296^2
3.01*1.175 kg m^2

using conservation of momentum
3.01*2.66*0.759=3.01*1.175*ω
solve for ω

ω=1.718 rad/sec

Now compare KE
Extended
(.5*3.01*2.66*0.759^2)
2.31 J

Inward
(.5*3.01*1.175*1.718^2)
5.22 J

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