Two circular discs, one with a diameter of 100.0mm and the other with a diameter

Question

Two circular discs, one with a diameter of 100.0mm and the other with a diameter of 200.0mm (a 2 / 1 ratio) are placed next to each other. No physical connection (chain, belt etc) exists between the two. Each disc has a single mark on the outer edge and rotation is started with the two marks aligned with each other, the marks re-aligning each time the smaller disc rotates 2.0 times. The 2 / 1 speed ratio is precisely maintained during start up, run time and stopping. The outer surface speed of the larger disc is 0.5% light speed. Rotation of both discs starts and is maintained for 20 years. Assuming the number of rotations of the smaller disc is an even number from start to stop. Will the two marks still align once the rotation is stopped? Either my understanding of time dialation is wrong or the two marks would not align. Thanks! Jack Chapman Anderson, SC

Explanation / Answer

Length contraction for rotating wheels is a funny thing: The circumference shrinks, but not the diameter. Look upBell's Rocket Paradox for insight. But here, unless I missedsomething, the outer layers of both have the same velocity and moreimportantly, the angular velocity of the small disk is maintainedat twice that of the larger disk. Since the mechanism to spinthe disks is uneffected by any relativity concerns (yeah right),why would they be different? Or is there something I missingin how you stated the problem?

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