Re: A Spinning disc in space

A sharp question, but no, the outside of the disc 
wouldn't go faster than the speed of light.

Assuming the disc is a strong, rigid material, what one would
find as one tried to spin it up at the center would be that it
would become harder and harder to accelerate the disk, as the
outer parts approached the speed of light, and increasingly
"resisted" the acceleration (it takes an infinite amount of 
energy to accelerate a massive particle to the speed of light).

In actual fact, there is no such thing as a truly rigid body,
because the "rigidity" is mediated by forces (electromagnetic)
which are also subject to the speed limit of the speed of light.
So when you twist on the center of the disk, the force will
take a non-zero amount of time to be transmitted to the outside
of the disk; in the meantime, the center will have rotated,
and thus the outer edge of the disk will lag behind the inner
edge:  the disk will be sheared, or twisted, and cannot remain
a rigid body.

(If you've ever heard the relativistic "paradox" of the pole
vaulter running through a barn, the situation is similar:
the pole hits the wall, but it is not a rigid body, and the
back end of the pole keeps going forward while the front end
has "already stopped".)

-Aaron