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The actual Lorentz-contracted shape of the disk depends only on the
translational velocity of the disk and not on its angular velocity. The shape
is the same as if the disk was not rotating. Thus the disk would become an
ellipse with an eccentricity of v/c where the original rest-radius is the
semimajor axis along the direction transverse to the motion, and the semiminor
axis is (1 - (v/c)^2)^(1/2) times the rest-radius oriented along the motion.
David Bowman
dbowman@gtc.georgetown.ky.us