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# Relativity/special relativity-Rotating disk

Question
It seems that there are some paradoxes involving rotating disk and special relativity, How the paradoxes could be resolved and is there an explanation of how the rotating disk would look like if it undergoes some distortions due to the Lorentz contraction ?

Yossi, this is a famous problem in relativity that has been studied by many famous physicists. Their conclusions are often hard to understand, but the essence of today's thinking about it is that there is no such thing as a rigid body.

A simpler problem to help you get a feeling for what happens can be found in the Bell Spaceship Problem.  Bell says, let us imagine two spaceships travelling head-to-tail but connected by a thin string. Let the entire system start from rest with respect to a platform, start the ships' engines at the same time, and let them go moving identically with respect to that platform.  When they get to a speed c/2, although the distance between the ships is constant with respect to the platform, it is not constant with respect to the ships.

With respect to a third spaceship moving inertially near the ships (or say the lead ship)at the c/2 point the distance between the ships will be greater than its initial length. The string must stretch and will break at some point, in spite of the fact that the distance between the ships is constant with respect to the launch platform.

See Wikipedia, Bell's Spaceship Paradox. It really is not a paradox but a valid result of relativity.  The string does break.  Many physicists have got this wrong in the past, but most now agree.

This shows that the spinning disk will be deformed by its spinning. Real materials will fail, perhaps flying apart. All this is just relativity.  Real engineering will involve mechanical properties of the disk material, but that is a separate question.
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Relativity

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#### Uncle Ben

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I can answer questions regarding Einstein's Theory of Relativity, particularly in Special Relativity. I will not answer homework questions or mathematical problems that require special symbols.

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I have taught physics at the college level, undergraduate and graduate, for many years including Special Relativity. I have taught at Johns Hopkins, Case-Western, and MIT. I have also served as a staff member of the Commission on College Physics, which was supported by the National Science Foundation to recommend improvements in the curriculum of college physics departments in the US. I am also the author of a textbook titled Vector Calculus, which was used at MIT in the teaching of electromagnetic theory and relativity. My research interests were mainly in solid state physics, especially the properties of metals at low temperatures. I am listed in the publication known as American Men of Science.

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