Help with Angular Velocity True-False Question

[MattAstros]

Homework Statement

A physics student is sitting on a rotating platform. He is holding a heavy weight in each of his outstretched hands. At request of his physics instructor(!) he carries out various manoeuvres to try to change his angular velocity. Which of the following scenarios are described correctly?

Relevant Equations

L=Iomega

1)Starting at rest, he brings the weights into his chest. His angular velocity increases.
2)A friend throws a third weight so that the student catches it in one of his outstretched hands. No matter what the direction of the throw, the student's angular velocity decreases.
3) Starting with angular velocity ωgw, he transfers both the weights to one outstretched hand. His angular velocity (after the manoeuvre is complete) has reversed.
4) A friend throws a third weight so that the student catches it in one of his outstretched hands. No matter what the direction of the throw, the student's angular velocity reverses.
5)Starting with angular velocity ωgw, he drops the weights. His angular velocity increases.
6)Starting with angular velocity ωgw, he drops the weights. His angular velocity reverses.
7) Starting with angular velocity ωgw, he drops the weights. His angular velocity does not change.
8) Starting with angular velocity ωgw, he transfers both the weights to one outstretched hand. He then stretches his other hand back out to its original position. His angular velocity (after the manouvre is complete) has increased.
9) Starting with angular velocity ωgw, he brings the weights into his chest. His angular velocity increases.
10) Starting at rest, he brings the weights into his chest. His angular velocity does not change.

I tried:
1)T 2)T 3)F 4)F 5)T 6)F 7)F 8)F 9)T 10)F
1)T 2)T 3)F 4)F 5)T 6)F 7)F 8)F 9)T 10)T
1)F 2)T 3)F 4)F 5)T 6)F 7)F 8)F 9)T 10)F
1)F 2)T 3)F 4)F 5)T 6)F 7)F 8)F 9)T 10)T

I can't figure which one(s) is/are wrong.

 

[haruspex]

which one is wrong.

Only one?

Was there a diagram? I am assuming the student is in the centre of the platform and that the arms are stretched out in opposite directions.

Please provide your reasoning for each.

 

[MattAstros]

Only one?

Was there a diagram? I am assuming the student is in the centre of the platform and that the arms are stretched out in opposite directions.

Please provide your reasoning for each.

There wasn't a diagram provided with the question, but yes the student is indeed in the center of the platform and the arms are stretched out. I should have wrote "which one(s)"

For the 1st and the 10th I'm mostly stuck on the "starting at rest" part. Thinking of the student as a point mass, I think if the student brings the weights into his/her chest I reasoned that the center of mass wouldn't change, therefore I wouldn't change which would mean that the angular velocity would stay the same.

For the 2nd one, since the added weight would increase I, I assumed it would decrease the angular velocity.

For the 3rd, 4th, and the 6th one, I couldn't see how the velocity would reverse, so just went with false.

For the 5th one, since dropping the weights decreases I, that would result in the angular velocity increasing in order to conserve the angular momentum, which would also mean that the 7th is false.

For the 8th one, I thought that since the center of mass shifts outward, it would increase I and decrease the angular velocity.

For the 9th, that would decrease I and increase the angular velocity.

 

[haruspex]

For the 2nd one, since the added weight would increase I, I assumed it would decrease the angular velocity.

For the 5th one, since dropping the weights decreases I, that would result in the angular velocity increasing in order to conserve the angular momentum

In both of these, you are ignoring the angular momentum that the weights may bring with them (2) or take away with them (5).

 

[MattAstros]

In both of these, you are ignoring the angular momentum that the weights may bring with them (2) or take away with them (5).

Oh I see it now, makes a lot of sense. Thanks a lot for your help! :)

 

[MattAstros]

In both of these, you are ignoring the angular momentum that the weights may bring with them (2) or take away with them (5).

I tried 1F 2F 3F 4F 5F 6F 7F 8F 9T 10T, but got it incorrect. So for 2, the angular velocity would depend on the direction the weights are thrown from right? As for 5, it would not change right so 7 would be true?

 

[haruspex]

Because you had 1) as T and F on different tries I failed to notice this:

the center of mass wouldn't change, therefore I wouldn't change

What is the formula for MoI of a point mass about some axis?

for 2, the angular velocity would depend on the direction the weights are thrown from right?

Yes.

As for 5, it would not change right so 7 would be true?

Yes.

 

[Delta2]

I agree with you on 3,4,6,8,9 . For 5 and 7 i think you got it the other way around( I see @haruspex helped you already with that).

Now for 1 (and implicitly for 10) how do you interpret the phrase "starting from rest". I interpret it as starting with angular velocity zero. So when he does the manouvre his moment of inertia change (for this i would consider the weights as point masses and not the body of the student). But because his initial angular velocity is zero (and therefore his initial angular momentum is zero too), what do you think is his final angular velocity at the end of the manouvre?

I also think that 2 is F because it depends on the direction of the throw.

 

[haruspex]

2 is F because it depends on the direction of the throw.

... and magnitude.

 

[MattAstros]

What is the formula for MoI of a point mass about some axis?

It's mr^2

 

[MattAstros]

I agree with you on 3,4,6,8,9 . For 5 and 7 i think you got it the other way around( I see @haruspex helped you already with that).

Now for 1 (and implicitly for 10) how do you interpret the phrase "starting from rest". I interpret it as starting with angular velocity zero. So when he does the manouvre his moment of inertia change (for this i would consider the weights as point masses and not the body of the student). But because his initial angular velocity is zero (and therefore his initial angular momentum is zero too), what do you think is his final angular velocity at the end of the manouvre?

I also think that 2 is F because it depends on the direction of the throw.

I interpreted it the same way. I believe the angular velocity at the end of the manouvre would also be zero. So it wouldn't increase or decrease but would stay the same?

 

[Delta2]

So it wouldn't increase or decrease but would stay the same?

Yes I think that's correct.

 

[haruspex]

It's mr^2

So if you have two point masses distance 2r apart, what would you do to change I without changing the centre of mass?