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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?

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    $\begingroup$ 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? $\endgroup$
    – WillO
    Commented Dec 14, 2015 at 3:47
  • $\begingroup$ @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? $\endgroup$
    – Mmm Donuts
    Commented Dec 14, 2015 at 3:50
  • $\begingroup$ physics.stackexchange.com/q/155537/60080 possible duplicate $\endgroup$
    – QCD_IS_GOOD
    Commented Dec 14, 2015 at 4:02
  • $\begingroup$ 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. $\endgroup$
    – WillO
    Commented Dec 14, 2015 at 4:10
  • $\begingroup$ @WillO The question appears to assume the stationary frame, especially given no mention of sitting on the disc. $\endgroup$
    – SevenSidedDie
    Commented Dec 14, 2015 at 4:54

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

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