Essence of The Paradox
Imagine a disk of radius R rotating with constant angular velocity .
Let us fix the reference frame to the stationary center of the disk. Then the magnitude of the relative velocity of any point in the circumference of the disk is . So the circumference will undergo Lorentz contraction by a factor of .
However, since the radius is perpendicular to the direction of motion, it will not undergo any contraction. So we have . This is paradoxical, since Euclidean geometry tells us it should be exactly equal to .
Read more about this topic: Ehrenfest Paradox
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