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Re: Relativity



My claim for angular velocity independence of the Lorentz contraction is
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')

I may be wrong (wouldn't be the first time) but it looks to me
like these expressions build in from the very beginning the
condition that the rotation have no effect on the shape
of the disk since you are assuming that an observer in a state of
translational (but not rotational) rest with respect to the disk sees
a circular disk. If that is true, then it is not surprising that we
end up concluding that the rotation has no effect when the observer
is *not* at translational rest either -- we are basically deriving
what we assumed to be true to begin with -- that rotation has no
effect of the apparant "circularity" of the disk.

It is not clear to me that this should be valid. It would certainly
not be true if we replaced the disk with a discrete set of small
boxes travelling in circles -- the individual boxes would be
Lorentz-distorted. Isn't the disk just a limiting case? Glue all the
boxes together and (assuming the flywheel doesn't blow up as Leigh
and others suggested) wherever they are Lorentz-contracted the disk
must get pinched.



Q.E.D.

David Bowman
dbowman@gtc.georgetown.ky.us


Paul J. Camp "The Beauty of the Universe
Assistant Professor of Physics consists not only of unity
Coastal Carolina University in variety but also of
Conway, SC 29528 variety in unity.
pjcamp@coastal.edu --Umberto Eco
pjcamp@postoffice.worldnet.att.net The Name of the Rose
(803)349-2227
fax: (803)349-2926