Question about TBR Physics Lecture 4 (re: Angular Momentum/Moment of Inertia)

[prophecygirl]

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Hello everyone,

One of the questions in passage VIII (about angular momentum/moment of inertia) is driving me crazy! Here is the set-up: One student sits on a stool that rotates freely. He holds a 5-kg mass in each hand. Initially, the student has an angular velocity of 5 radians/sec with his arms in his lap.

The question (#53 in the 2008 edition) states that with his arms outstretched, the student drops the weights. This will cause the angular velocity of the student to:

A. increase
B. decrease
C. remain the same
D. A change cannot be determined.

I chose increase (choice A), but the answer says that it is should be choice C (remain the same). The explanation states that dropping the weights does not change the moment of inertia for the system.

I don't understand the answer/explanation at all -- I thought dropping the weights would decrease the mass of the system by 10kg. (I'm assuming that the weights hit the floor since the student had his arms outstretched when he dropped them and is sitting on a rotating stool.) The moment of inertia is proportional to the mass times the radius squared. So the moment of inertia should decrease and therefore the angular velocity should increase, right?

Maybe I'm missing something or reading the question wrong somehow? The only explanation I can think of is that the weights didn't hit the floor and somehow remained part of the rotating system at the same radius from the axis of rotation. But that seems like a huge stretch based on the wording of the question.

Any help would be much appreciated!! 🙂

Thanks in advance!!

 

[Dr Gerrard]

Yeah, I am with you.

I thought conservation of angular momentum.

Decreasing mass decreases moment of inertia, increase angular velocity.

 

[prophecygirl]

Thanks!! 🙂 That makes me feel better -- maybe it's just a mistake...

 

[Dr Gerrard]

But my subject matter on this is not the strongest, so it is very possible that I am wrong.

I hope, for both of our sakes, that I am not though. haha

Especially because TBR is pretty much the leading source in physics, so I am more likely to question my line of thought than theirs.

 

[pandoraaj009]

Ok, this is how I arrived at the answer, and it made sense given their explanation...I'm not supremely confident in my physics skills, so do with that what you will lol..

In the passage, they gave us a few eqns:

torque=r * F
L=I *w ....(w=ang velocity)
and angular momentum was conserved w/ respect to time (b/c it's angular) if the net torque=0
(L)initial=(L) final
L is the angular momentum.

Dropping the weights indicated kinetic energy was not conserved, b/c the change in shape or weight=inelastic coll=only momentum conserved, so we can use the info in the passage to figure it out from here.

I marked C at that point b/c the whole cons of momentum thing, but it actually makes sense: KE is NOT conserved, so any increase in speed will be dissipated as heat/friction and will counteract the gain in angular velocity.

If the cons of E doesn't make sense, you could also look at the eqns....this isn't a definitive way of solving it, but it might help to enhance our thinking here lol.....

the distance terms in all the eqns were squared, except in the KE eqn, but it doesn't enter into this particular question. Since the Interia thing was proportional the the meters^2 times kg, you'd have to mess with the radius to change I. To change the w term, you'd have to change the other two terms, which we have established is not really feasible....

that's the way i thought of it, but it's pretty convoluted. if anyone has any extra insights, i'm curious myself....

 

[prophecygirl]

Thanks!! 🙂 Very interesting -- I hadn't thought of approaching it from a conservation of energy perspective. I'll have to think about that some more.

I'm still struggling with why changing the mass doesn't change moment of inertia -- can you expand on how you thought about that? If the moment of inertia decreases and angular velocity increases, I think the angular moment would still be conserved. I actually thought this was an easy problem before I looked at the answer!

 

[txprodigal]

i'm not sure angular momentum is one of the topics covered by the MCAT according to the official guide?

 

[prophecygirl]

Good question -- you're right, I just checked the AAMC topic list, and it only includes conservation of linear momentum -- not angular momentum. Thanks for pointing that out!

I'm still kinda curious about the answer though... 🙂

 

[Fort]

I don't agree with their explanation. The moment of inertia of the system should change in this scenario.

As soon as the student releases the weights, they won't be rotating about a fixed axis. In fact, they won't be rotating at all, they'll just fly off tangent to your arms at the moment of release.

Moment of inertia is also defined as rotational inertia; since the weights don't rotate about a fixed axis at the moment of release, their contributing moment of inertia to the student spinning in the chair is zero; thus, the total moment of inertia of the system decreases. Angular velocity should increase.

Edit: I don't have TBR physics, but I think what they're getting at is if the student drops the weights, puts his arms back in his lap, then his angular velocity will be 5 rads/s (unchanged), based off the initial conditions from the information in the passage. Seems a little poorly worded, but that's the only way I can justify their answer.

 

[prophecygirl]

Thanks -- your explanation makes perfect sense! I think you're right -- the question was probably just poorly worded.