Sciencepoo said:
How large a wheel would have to be for the outer edge to travel faster than the speed of light if powered by a motor that's around now.
This answer cuts to the chase of what you're asking. It
grants every possible engineering objection - from fuel to speed to material strength*. And yet
the edge will never reach c, let alone exceed it.
*Except one: the theory of relativity itself
prohibits the existence of
infinitely-strong/
infinitely-rigid materials.
Q: Why won't it reach c?
A: Like all things, the wheel is subject to relativity. As the edge approaches relativistic speed, it will length contract, just like anything else. Increasing speed will get the edge closer to c but will never exceed it.
Yes, this will cause the wheel to distort in shape, since the non-relativistic inner parts will not likewise get length-contracted. Yes, it will actually disintegrate - but
not simply because the material is not strong enough to withstand the forces - it will disintegrate because
relativistic effects will distort it.You'll want to read up on
Bell's Spaceship Paradox. That one is two spaceships in a line, but there's a derivative experiment (
link, anyone?), set up like so:
Tie a bunch of spaceships into a circle, nose-to-tail, with pieces of string. Space the ships so the string is taut. Set the spaceships chasing each around the circle at relativistic speeds.
Q: We know the spaceships will shrink in length, but will the strings break?
A: Yes. Any rigid loop, when accelerated to a rotation of relativistic velocity, will be contracted. Its rotational speed will approach, but never reach, c.
!
