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I think this is analogues for the Woodward effect, but macroscopic:

We assume a spacecraft consisting of a broomstick, a donut and lots of gear for storing and transfering mechanical energy. Take the donut, spin it till the outer edge moves at relativistic speed (We assume a tough glazing), and push it along the broomstick, brake it's spin and then the donut, move donut forward along broomstick, repeat. Since the donut is heavier when it's being accelerated backwards then when it's braked/accelerated forward, there should be a net momentum. Since nothing leaves the broomstick, this has to be wrong. But where?

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your broomstick will also revolve with relativistic speed due to momentum conservation and become heavier. – Yrogirg Jan 9 '13 at 13:36
I could have 2 counterrotating donuts to pick up the torque – mart Jan 9 '13 at 13:44
up vote 9 down vote accepted

The reason the donut is heavier when it's spinning is that it contains more kinetic energy, and this energy has mass. (Or at least, it does if you use the word "mass" to mean "relativistic mass" rather than "rest mass", which is somewhat out-dated language, but I'm going to keep using it anyway.) The question is, where does that energy go when the donut is not rotating?

You could store it in a battery or something, but then the energy will have just as much (relativistic) mass when it's stored in the battery as it does when it's stored in the donut's rotation. Moving energy in between the battery and the donut is exactly like transferring mass from one to another. With a little thought, you should be able to see that no matter how you move the donut and the battery along the broomstick's length while transferring energy from one to the other, there's no way you can make the centre of gravity of the whole system move. In this respect, transferring energy between the battery and the donut is no different from transferring water from one container to another.

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thx ... On one level I think energy = mass, sure why not, on another level I can't wrap my head around this. Maybe I'll turn this into a question. – mart Jan 9 '13 at 15:00
There's plenty of information that might help on Wikipedia's mass-energy equivalence page - I hope that helps. – Nathaniel Jan 9 '13 at 15:16

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