Spinning disk approaching c, what will happen?

[CuriousG44]

1. a clever engineer solves the high velocity exploding flywheel problem (structure fails) and any other serial problems.
2. therefore a bench top a. torus, b. disk, c. cylinder spinning about its axis with a tip speed approaching c
3. what will happen to space time and gravity or anything else interesting for a, b and c?
4. at what fraction of c will strange things begin?
5. any helpful equations?

 

[Dale]

It will break.

 

[bcrowell]

This may be helpful: http://www.lightandmatter.com/html_books/genrel/ch03/ch03.html#Section3.4 (subsection 3.4.4)

As explained in the link, the disk can't be accelerated from rest. It has to be built rotating.

We recently had an extremely lengthy discussion of this: https://www.physicsforums.com/showthread.php?t=367826&highlight=rotating+disk

 

[russ_watters]

It will break.

...or if it were strong enough it would just continuously slow its acceleration as the torque required for constant acceleration would keep going up.

 

[Dale]

The stress becomes infinite as the rim approaches c, so it does not matter how strong it is, it will break.

 

[russ_watters]

The torque required to keep it accelerating also becomes (actually, approches) infinite as it approaches C, but I guess when the scenario is so far outside of reality, it probably isn't useful to quibble over this. Any real material would break long before reaching relativistic velocity.

 

[Dale]

Yes, I agree on all points.

 

[bcrowell]

...or if it were strong enough it would just continuously slow its acceleration as the torque required for constant acceleration would keep going up.

The stress becomes infinite as the rim approaches c, so it does not matter how strong it is, it will break.

Both of these statements are actually quite a bit weaker than necessary. Perfectly rigid angular acceleration is a kinematic impossibility: http://www.phys.uu.nl/igg/dieks/rotation.pdf So the issues don't just arise as the rim approaches c. Even at low velocities, you can choose one of two things: (1) Born-rigidity, (2) nonzero angular acceleration. You can have one or the other, but not both, and this is the case at all angular velocities. This was all discussed in excruciating detail in this recent thread: https://www.physicsforums.com/showthread.php?t=367826

[EDIT] Oops, I gave a reference to the wrong paper. It should have been Ø. Grøn, Relativistic description of a rotating disk, Am. J. Phys. 43 869 (1975). This is the one that proves that a Born-rigid disk can't be subjected to angular acceleration, because that implies contradictory kinematic requirements.

 

[CuriousG44]

Thank you for your responses and I have read much of what was referenced but, I now see my topic statement steered the responses rather than the question. Therefore, I will hopefully be more clear.

This is a thought experiment. A nonrigid disk in a vacuum made of many fibers of infinite tensile strength oriented in the tensile direction r with a tip speed near c. Please do not focus on accelerating the disk. Magnitude of Angular acceleration = 0 as it has already been accelerated so that the tip speed is near c. Furthermore, I do not care about the physics of the physical disk, I am curious about the spacetime enveloping the disk so, an academic rigid disk of infinite strength is also ok.

For example,
a) Two in plane parallel beams of light. The axis of rotation, of the disk, is within the plane and perpendicular to the beams of light. One beam on top of the disk and one on bottom in close proximity to the disk face and equal distance to their respective face. So my question is, will the disk effect the path of the beams of light and how? Will they be effected near the tip or at the axis or both? Will they be effected in the same way or have the opposite effect? Also will it make any difference if the disk is residing in a gravity field or not?

b) One beam of light parallel and in plane to the axis in close proximity to the disk tip (rim). Will the disk effect the path of the beam of light and how? If so, will reversing angular velocity make any difference? Also will it make any difference if the disk is residing in a gravity field or not?

If you are asking yourself "relative to what" then an observer A on the tip of the disk, B off the disk and C on the face of the disk at the axis. The disk axis is stationery in respect to observer B. Better yet compare the examples to the disk when it is not spinning I guess.

 

[EWSwan]

Given your assumptions, and assuming the fiber tips are moving at very close to c, the whole assembly will then have enough mass/energy to distort spacetime around it, because it will have a very strong gravitational field. Light rays passing near it will be bent toward it. And an observer far away, watching a clock near the object, would see the clock seem to run too slowly. Basically, you would see all of the effects you would expect if you made observations in the vicinity of a black hole, plus some effects due to the rotation itself. You can get a pretty good idea of the conditions from a book like "Gravity" by James B. Hartle, which is an intro (college intro) text on General Relativity, which is what you are asking about.

Some theories would have us believe that other very exotic conditions might begin to come into play, like mapping the spacetime events near the object to other events throughout spacetime. When I say "spacetime event" I mean "some point in space at some moment in time." So these theorists would have us believe that you could send an object along a certain path near this object, and at some point it would cease to exist here, and begin existing somewhere/when else. But I am plenty astonished by the stuff that seems to happen by rotating black holes, so I'll leave the controls of the Way-Back Machine set to here-and-now.

Oh, and yes it would make a difference if you passed a beam of light tangent to the rotation, or along its axis, due to those relativistic rotation effects I mentioned.

 

[Ich]

It seems that you'd get the answers you want by analyzing the Neugebauer-Meinel solution, which is a rigidly rotating disk made of dust. I'm not familiar with this solution, but http://arxiv.org/abs/gr-qc/0301107" might contain something interesting.