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anonymous
 4 years ago
Here's one that was in my head for a few days:
Imagine a solid rotating in space, like a disk or something.
Lets say that the angular velocity of the solid is: \[\ \omega = 0.9c \ rad*s^{1} \] where c is the speed of light.
What is the tangential velocity of the solid at the distance r, lets say 2m from the axis of rotation?
What would happen to the solid?
I can't quite imagine what that would look like.
anonymous
 4 years ago
Here's one that was in my head for a few days: Imagine a solid rotating in space, like a disk or something. Lets say that the angular velocity of the solid is: \[\ \omega = 0.9c \ rad*s^{1} \] where c is the speed of light. What is the tangential velocity of the solid at the distance r, lets say 2m from the axis of rotation? What would happen to the solid? I can't quite imagine what that would look like.

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[r* \sqrt{1v^2/c^2}\] I think

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1In any case, no part of the disk (let's make it a disk) can be traveling at or faster than c. So given a disk of radius R, this put a ceiling on angular velocity \[ \omega < c/R \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but radius should not contract because it is perpendicular to the tangent velocity. If something moves only in x direction it's length along x dimension will contract right, so no contraction in y direction.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0I don't know if this helps, but I remember hearing a similar issue arise over a giant hypothetical pair of scissors opening (say the size of the solar system). If halfway down the scissors is moving at say, 90% the speed of light, then the tip of the scissors should be moving faster than the speed of light. This doesn't happen though, because the impulse of the force opening the scissors cannot move down the blade faster than the speed of light, hence it cannot behave as a perfectly rigid object. I imagine we have a similar situation here. The disk cannot behave as a rigid object if at some radius from the center we have the velocity approach c. The impulse of the forces connecting the atoms in the disk will not convey the motion to the outer edges of the disk immediately, so the disk would warp. As to exactly how it would warp, I'm not sure... Here are some thoughts on an equivalent situation: http://www.physicsforums.com/showthread.php?t=75563

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0In any event, it seems that the Lorentz contraction alone is not sufficient to explain the situation for a number of reasons pointed out in the link above.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thank you. I'll look more into this tomorrow. I'll post anything interesting I find here.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0TuringTest. I've never heard the scissor analogy, as I've never studied relativity, but it reminded me of studying super sonic flows. Gases cannot transmit information through them faster than the speed of sound, that's why we develop a shock wave. This shock wave could be thought of as this "warp." Interesting stuff to think about.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0Here's something I found that seems a bit over my head, but is apparently ontopic. http://en.wikipedia.org/wiki/Born_coordinates I get pretty lost by the time this thing starts talking about Killing vector fields, which have something to do with Riemannian manifolds, which I have not studied. The impression I get from it though is that attempts to create a consistent coordinate system for a relativistic rotating ring (or disk) have been met with stark failure. It seems that they lead to discontinuous or multivalued notions of time. Still, this is debated according to some entries on physicsforums, so if anyone can clear this up a bit I'm all ears.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Apparently this thing is called "Ehrenfest paradox", if anyone is still interested. http://en.wikipedia.org/wiki/Ehrenfest_paradox There's a resolution to this paradox, but it's way out of my league.
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