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To simplify that rotating disk problem consider a circular disk spinning at*******
high relativistic rim speed v about its axis which is stationary in the
observer's frame of reference. Angular velocity w = v/R, where R = radius
of disc, and (c - v)/c << 1) Every arc segment on the rim will be Lorentz
contracted. We can divide the rim into, say, 360 equal length arc segments,
each little different from a straight line translating lengthwise at a
speed v. It is difficult for me to see how these arc segments can appear to
be Lorentz contracted since they must still add up to the circumference of
the disk, 2 pi R. The radius won't change, and even if it could, it would
have to shrink by the same ratio as the rim of the wheel, an unlikelyhood
given that its speed is less than that of the rim.
Leigh