Speed of a long rod. Exceeding the speed of light?

Question

If I have a rod that is 2 light-years long, when I rotate it at the centre with angular velocity of 1 rad/s, what is the speed of the end of the rod.

Answer 1

Zero. The rod snaps.

Answer 2

Very close to zero.  Here's why:  When you impel a system to do something, you are applying force to a part of it.  It's not a single particle.  First off, the force will travel through the rod at the speed of sound in the material.  In most solids this will be on the order of 1 to 10 miles per second.  You could theoretically get the rod spinning if you rotated it slowly enough.  Now, let's consider what would happen if we took away these normal considerations and considered the rod a single particle.  First, you'd still have to wait for the speed of light delay to reach the end of the rod.  Beyond that, you CAN'T rotate the rod at 1r/s.  In rotating the rod, you're causing the ends to rotate at a certain speed.  f=ma and m' = m° ÷ √1-V²/C² still applies.  As you approach the speed of light, f→∞, so you'll never be able to exceed a rotation rate of 1 radian per 12 years.

Answer 3

in theory you could surpass the speed of light, but the rod is a giant lever. if the rod has any mass at all, the amount of energy required to move it that fast would approach infinity.