# Conservation of Anular Momentum

1. Oct 19, 2007

### mit_hacker

1. The problem statement, all variables and given/known data

My Physics Textbook, just like all others I guess shows that example of a acrobat spinning with first his arms wide "open" and then it goes on to show how when he pulls his arms in towards his stomach, his angular velocity increases. The solved example goes on to show numerically that the rotational kinetic energy increases. The textbook then goes on to ask a rather interesting question- "where does this extra energy come from?" Keeping up with the spirit of this forum, I thought of an explanation myself. Can you please help me see if I am correct?

2. Relevant equations

3. The attempt at a solution

When the person pulls his arms in towards his stomach, the distribution of his mass around the axis of rotation changes. Therefore, the moment of inertia which is a measure of how "hard" it is to rotate a body around an axis decreases. Therefore, the same force is able to revolve the person at a faster angular velocity around the same axis.

Even if my above explanation is correct, can you please explain how to resolve this situation and show it is consistent with the Law of Conservation of Energy? I am completely blank there. Thanks!!

2. Oct 19, 2007

### learningphysics

As per your title, it is conservation of angular momentum that's the reason the angular velocity increases...

angular momentum = momentum of inertia * angular velocity...

moment of inertia drops => angular velocity increases.

As far as the energy is concerned... there's only one place the energy can come from... what sources of energy are there in this situation?

3. Oct 19, 2007

### mit_hacker

Still confused!

I still don't know which is that source of energy you're talking about? Are you referring to the chemical energy of the person?

4. Oct 19, 2007

### learningphysics

yes exactly. the chemical potential energy of the person

5. Oct 19, 2007

### mit_hacker

Great! Thanks a ton!!

Thanks a lot for the help!!

6. Oct 19, 2007

no prob. :)