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Old Jun 16th 2013, 01:22 PM   #1
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Question about angular momentum?

If a ball was spinning on its own axis at a speed close to that of light, how would you calculate the relativistic mass gained? You couldn't just plug in its velocity because the inner part of the ball has a slower velocity than the outermost part! How would you do this?
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Old Jun 16th 2013, 09:16 PM   #2
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Originally Posted by muon321 View Post
If a ball was spinning on its own axis at a speed close to that of light, how would you calculate the relativistic mass gained? You couldn't just plug in its velocity because the inner part of the ball has a slower velocity than the outermost part! How would you do this?
This one I can do! (I'm still working on your other problem.)

First, what do you mean that "a ball was spinning on its own axis at a speed close to that of light."? What is close to the speed of light?

We have the energy of the ball since there is no overall momentum associated with it, so E(tot) will be the energy that the rotating ball has by spinning. (You also have the mass term in the E^2 formula.) There are no SR associated limits on how fast the ball can spin so (theta) is unconstrained. On the other hand none of the points of the ball can travel faster than c so, say, a point on the equator of the ball lags a bit from the points inside the ball. Since the points interior to the ball have smaller angular speeds, and thus smaller linear speeds, the points on the equator of the ball have the highest speeds.

A simpler example of this which is a bit more transparent is where you have a very long pole and you rotate it so that the far end of the pole is traveling at a relativistic speed. The bar must bend according to the person swinging the pole. This is true for any kind of pole, flexible or not. This is one of the "objectional" results that some people use to say SR is ridiculous.

Does that answer your question or do you need more?

-Dan
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