Conservation of Angular Momentum Homework Help

AI Thread Summary
A student on a swivel seat holds a spinning bicycle wheel with an initial angular velocity of 12.6 rad/s and reverses its direction, causing the student to rotate. The conservation of angular momentum principle is applied, leading to the equation IWo = IWf + iw, where I represents the moments of inertia. The student initially guessed that the final angular velocity (Wf) would equal -Wo but encountered a calculation error. Additional considerations about the wheel's rotation around the student's axis were mentioned, but more information would be needed to clarify this aspect. The discussion revolves around finding the correct final angular velocity based on the given moments of inertia.
hb94
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Homework Statement


"A student sits on a swivel seat. Initially the student is at rest, holding a spinning bicycle wheel that has an angular velocity of 12.6 rad/s (see figure below). The student turns the spinning wheel upside down, reversing the direction of its angular velocity. This causes the student to begin to rotate. Find the student's final angular velocity. The moments of inertia of the wheel and of the student are 0.340 kg · m2 and 2.25 kg · m2 respectively."
9-p-036.gif



Homework Equations


How do you find the final angular velocity with the given information?


The Attempt at a Solution


Well since initial momentum is equal to final momentum, IWo = IWf +iw, where I is the moment of inertia of the wheel, Wo is the initial angular velocity of the wheel, Wf is the final angular velocity of the wheel, i is the moment of inertia of the girl, and w is the angular velocity of the girl. So, (I(Wo-Wf))/i = w. I guessed that Wf would equal -Wo, but I was mistaken, or I made a calculation error.
Thanks in advance for your help :D
 
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hb94 said:
Well since initial momentum is equal to final momentum, IWo = IWf +iw, where I is the moment of inertia of the wheel, Wo is the initial angular velocity of the wheel, Wf is the final angular velocity of the wheel, i is the moment of inertia of the girl, and w is the angular velocity of the girl. So, (I(Wo-Wf))/i = w. I guessed that Wf would equal -Wo, but I was mistaken, or I made a calculation error.
How do you know?

At any rate, your procedure seems to be correct. One additional thing you could think about is the fact that in the final situation, the wheel is not only spinning around its own axis, but also that axis is revolving around the girl's rotational axis. But in order for you to take that into account, I think they would have to give you more information, so I have my doubts that that is what's causing your problem.
 
Well, I(Wo-Wf)/i = 3.808, and if these are the only factors applied to the problem, then I got the wrong answer.
 
You forgot the units...

What's the right answer supposed to be?
 
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