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This may seem like a dumb question, as I'm not really a physicist, but here it goes.

So, π is the number of diameter distances required to equal the circumference of a 2D disk. Relativity tells us that the faster an object moves, the shorter length of the object.

My question is: if a disk is spinning with angular velocity of say, $c/2$, would the number π be affected or would it remain it's same old 3.14 for a rapidly spinning disk?

Along those lines, how does the Lorentz contraction interact with an object that has varying velocities from the outward edge, to the inward center?

peterh
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Mmm Donuts
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    I realize this does not respond to your main question, only to your choice of wording, but: Up until recently, nine was the number of planets. When Pluto was de-planetized, did the number nine change? – WillO Dec 14 '15 at 03:47
  • @WillO No, neither depend on the other. I realize what you're saying, so the answer is... π remains the same, even though the diameter and circumference may change? How does the edge contract relative to the diameter though? – Mmm Donuts Dec 14 '15 at 03:50
  • http://physics.stackexchange.com/q/155537/60080 possible duplicate – QCD_IS_GOOD Dec 14 '15 at 04:02
  • I do not believe you can answer this question without specifying how the disk got started spinning in the first place. Consider two different points on the circumference. Did they start spinning at the same time according to someone sitting on one of those points? Or at the same time according to someone sitting in the "stationary" frame? Those are going to have different implications for how the circumference is distorted according to various observers. – WillO Dec 14 '15 at 04:10
  • @WillO The question appears to assume the stationary frame, especially given no mention of sitting on the disc. – SevenSidedDie Dec 14 '15 at 04:54
  • @SevenSidedDie: I do not agree with you. The question says that the disk is spinning, which does seem to mean that we're supposed to answer from the viewpoint of the stationary frame --- that much I agree with. But that doesn't tell me exactly how the spinning commenced (and what it looked like from the stationary frame), and I'm not sure we can answer without knowing that. – WillO Dec 14 '15 at 05:53
  • @WillO Sorry Will, excuse my lack of understanding but... What exactly do you mean by, 'how the spinning commenced'? – Mmm Donuts Dec 14 '15 at 17:19
  • @Kris: See my earlier comment. – WillO Dec 14 '15 at 17:51
  • @Kris: Was a force applied to a point on the circumference, so that that point accelerated and then the signal propagated around the disk? Or were forces applied to all of the points on the circumference at the same time? And if so, the same time according to whom? Etc. – WillO Dec 14 '15 at 17:57
  • @WillO I see what you mean. Let's suppose this is a thought experiment. The disk is indestructible and is spun up by a theoretical drill. The angular velocity reaches c/2 and an outside observer is measuring the circumference. – Mmm Donuts Dec 14 '15 at 18:13
  • Related: http://physics.stackexchange.com/q/8659/2451 and links therein. See also Ehrenfest paradox on Wikipedia. – Qmechanic Dec 08 '16 at 06:52
  • Possible duplicate of "Understanding the “$\pi$ ” of a rotating disk" (pse/q/121889). – user12262 Dec 08 '16 at 17:56

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The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity.

Shivahari Subedi
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