Reaching speed of light

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Rotate a long bar in space and reach c

Sorry this is very naive, but it's bugging me. If you had a straight solid stick attached on one end and rotating around that attachment at a certain rpm, there would be a length at which the end of the stick would theoretically reach, with that rpm, the speed of light. Well, doesn't seem possible - what specifically would be the limitations that would prevent the end of the stick to reach the speed of light? What would happen?

simply as a practical matter, it's doubtful you could find a material strong enough to withstand the tension to supply the necessary centripetal force. — JustJeff, Jan 17 '11 at 00:53
Voted to close as duplicate: the question has the same answer. — Sklivvz, Jan 17 '11 at 01:06
Maybe we should all just admit once and for all that relativity applies to everything in the universe except really long sticks ;-) — Greg P, Jan 17 '11 at 16:30

score 1 · Answer 1 · answered Jan 17 '11 at 01:02

In order for the bit of matter of mass $m$ at the very end of the stick to continue moving in a circular path of radius $R$ at a speed approaching the speed of light, it would need to be pulled toward the center with a force whose magnitude is

$|F| = |p|\frac{|V|}{R} = \frac{1}{\sqrt{1-(v/c)^2}}\frac{mv^2}{R}$

(the centripetal force you learn about in introductory physics). That force becomes infinitely large as the speed v approaches the speed of light, very rapidly, and eventually exceeds the strength of any interatomic or intermolecular forces that might be trying to hold the object together.

obviously something's going to stop you from getting to c, but what about getting to interesting fractions of c, say, just enough for relativistic effects to become noticable? — JustJeff, Jan 17 '11 at 01:10

score 0 · Answer 2 · answered Jan 17 '11 at 01:11

Something else to consider is that if you begin with a rigid rod rotating about an axis penetrating its center of mass at a constant angular velocity, and then gradually extend the length of the rod by adding mass to the end(s) of the rod, by doing so you are increasing the rod's moment of inertia. The expression for rotational kinetic energy is 1/2*I*omega^2, where I is the moment of inertia of the rod, given a specific choice of axis. For one of the ends to reach the speed of light would require infinite mass to be added to the ends, and hence, an infinite amount of energy. This seems to be a physically unattainable situation.

Reaching speed of light

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