# Disk spinning at the speed of light [duplicate]

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Of course, I mean that the edge of the disk is traveling at the speed of light. This is a question that popped into my head a few years ago when I was learning about some basic relativity in high school.

According to what I learned, if an object were to move at near-light-speed, it would be "compressed" along the direction of movement (for a stationary observer), but I'm asking myself what would happen if a disk were to spin along its axis. Would its circumference also get compressed?

Even though there is no such material that would resist the extreme centrifugal forces of this spinning disk, I think that a stationary observer would see this disk shrink as it approaches the speed of light.

But if the disk shrinks, a point on its circumference wouldn't travel so fast anymore (because of the reduced radius), so I'm guessing that the maximum speed of such a point is lower than speed of light.

I'm pretty sure I am way off the tracks as far as relativity is concerned, but I made some calculations back then, and using some help from Wolfram|Alpha I came to the conclusion that if my assumptions are correct (that the disk would shrink, and high-school geometry still applies), the maximum speed of a point on the circumference of the disk would be exactly c/2, before requiring an infinite amount energy to increase its speed any further.

So... what would in fact happen?

## marked as duplicate by Qmechanic♦May 9 '14 at 15:37

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## 1 Answer

The Ehrenfest paradox asserts that for a spinning disc rotating at relativistic speed near the edge, the ratio of the diameter to the circumference is no longer pi.

The proposed "resolutions" of this paradox have always seemed unconvincing to me.

Like the pole and barn paradox, absolute rigidity or strength of materials is not really part of the problem, as far as I am concerned.