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My claim for angular velocity independence of the Lorentz contraction isI may be wrong (wouldn't be the first time) but it looks to me
for the circular outer edge of the disk. For this outer edge we write a pair
of parametric equations describing this circle in the (primed) frame in which
the center of the circle is at rest. We label each point on the rotating
circle with a value of theta (where 0 <= theta < 2*pi) the Cartesian
coordinates of these points are given as:
x' = R*cos(theta + omega*t') and y' = R*sin(theta + omega*t')
Q.E.D.
David Bowman
dbowman@gtc.georgetown.ky.us