Can a rotating rod exceed the speed of light?

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Hey,

There's one thought experiment that I can't seem to wrap my head around.

If we had an extremely long rod (say > 1 lightsecond) and rotate it about one end rapidly enough (say 1 rad/second), would the far end of the rod be moving faster than the speed of light (using v=omega*r)?

What's going on?
 
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What makes you think you could get it up to that speed of rotation?

Consider the last inch of the rod like a little spaceship. It still has mass and inertia. The force applied to it (whether from a rocket exhaust or from a radial force 1/2 light second away) still experiences the same inertia. At some point in gearing up your rotation, you simply would not be able to accelerate the rotation any more.

Also, consider that there is no such thinbg as a rigid material. The force applied at any point on the rod can only be propogated through the material of the rod at a limited speed (significantly less than c). The rod will bend, even if it is an "ideal" material. Eventually, you will have an s-shaped rod one light-second in length. The ends will not be rotating as fast as the centre.
 
Ah OK, I see.
Thanks a lot! :smile:
 
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