# Superman's Helicopter

## Main Question or Discussion Point

Hi! I'm sure this has been done before, but here goes.

Superman is flying through the vacuum of space and stumbles across a rod 100,000 kilometers long. This rod is of nonzero mass and is narrow enough for him to hold in his hand. It is infinitely rigid, with an infinitely high shear modulus. It can't be broken by anything and is perfectly uniform.

At any rate, Superman decides to get some exercise. He goes to the center of the rod and lifts the rod over his head. That's not enough exercise for him, however, as there's no gravity in space. So, he lifts the rod over his head and starts twirling it around at 60 rpm.

What happens to the rod? You may assume that Superman can impart an arbitrarily high (though finite) amount of angular momentum to the rod and that the rod never bends or breaks. The thing to keep in mind is that the ends of the rod are going to be whizzing around at 2*pi*50,000 km per second. This happens to be higher than c.

I was thinking of three cases:

1. The rod is infinitely rigid and can't bend or break.
2. The rod can bend but not break (think of it like rope). Presumably the rod bends, but how?
3. The rod can break but not bend (think of it like glass). Presumably the rod breaks, but how? And where?

ACG

P.S. I know. Superman gets dizzy. But he's Superman. He doesn't throw up :)

## Answers and Replies

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I'll have a crack at it.I think the rod will display relatistic changes including a mass increase these changes increasing from the centre outwards.As the rod gains speed and approaches c at its ends, M approaches infinity as does the centripetal force.I believe that even Superman couldn't cope with an infinite force.If it were a real rod the story would be different and I sort of see it bending and breaking but more time is needed sitting under the thinking cap.I shall try it out with a broomstick.

Another thing to keep in mind is the fact that the "signal" that the rod is being spun has to propagate down the length of the rod. There are actually two things to keep in mind here: the speed that the end of the rod is moving at and the speed at which the signal is propagating down the end of the moving rod. I would suspect that the signal never makes it all the way to the point where the rod would be traveling at "c" because when you add the radial component telling it to turn that would exceed c.

Yea, these are all nice assumptions you are making, but they're simple not possible. The thing is, the rod is held together by the particles and forces present inside the rod. This is mostly the Coulomb interaction between the electrons and the atoms. And it's these forces and particles that are also subject to the constraints of relativity.

To be more specific, the Coulomb interaction is the cause of the rigidity of the rod. But this force travels with the speed of light. So once the rod is set in motion, this 'information of movement' takes a finite amount of time to reach the other end of the rod. The end of the rod, opposite of superman, simply doesn't know that the rod is put in motion, until the information reaches this endpoint! The rod will bend and eventually break (or become some sort of spaggethi rod).

So the assumption that the rod is completely rigid is actually not possible. The forces inside the rod, i.e. the Coulomb interaction, are subject to the maximum speed of light as well.

The rod will bend into something that looks like a model of a spiral galaxy. Relativity asserts that there is no such thing as an infinitely rigid rod. Find such a rod and will need a replacement for relativity (or the rod would be truly immovable). Another example is tapping one end of a very long "infinitely rigid" rod. If it really was infinitely rigid, the far end would move instantaneously and a signal would have been transmitted faster than the speed of light.

Dale
Mentor
In addition to the fact that perfect rigidity is incompatible with relativity there is also the following problem.
Superman can impart an arbitrarily high (though finite) amount of angular momentum to the rod
If the angular momentum is finite then the ends of the rod must travel at v<c.