Confused in a thought-experiment

[JukuJohannes]

Hello!
I am kinda confused in a thought experiment that my teacher gave me for thinking about.
It is about circular motion. The question is that if you spin a rod and the point A, close to the center, is moving with a speed which is approaching to 'c', then what happens to the rest of the rod, which is further than point A from the center.

I mean, the rest of rod should move even faster, but it would require a speed which would exceed the light barrier, but it would be a violation of STR or ...?

 

[Vanadium 50]

The rod is not infinitely rigid, and as such will flex in such a way as to insure it never travels faster than light.

 

[JukuJohannes]

The rod is not infinitely rigid, and as such will flex in such a way as to insure it never travels faster than light.

Even in the case of idealized material?

 

[Vanadium 50]

If you use something with magical properties, you can get anything you like. But to have the tip moving faster than light, the speed of sound in the rod has to be greater than the speed of light. Which requires magic.

 

[cosmo123]

Actually that's a pretty tricky thing to think about. Id be inclined to think that the outer parts would be traveling slower than youd expect because of how velocities add together in special relativity, but that would cause the rod to continuously flex around the centre so that couldn't work. If the rod is spinning at a constant rate, the rod would only flex outwards, not side to side, not really helping the situation I think what would happen is that as you sped up the rod it would break and fly off. I don't think such a material can exist where this would work.

 

[JukuJohannes]

So depending on the properties of 'real material,' it would stretch until some point, until the force of inertia would overrun materials' flexibility, as the diameter of the rod decreases due the stretching, and then the rod would be torn apart?

 

[HallsofIvy]

In relativity even "idealized material" cannot be completely rigid. We've seen this many times in this guise: take a rigid pole extending from the Earth to the moon and move it forward one millimeter at, say, 1 mm/sec, well below the speed of light. Yet the end on the moon moves forward at the same time thus sending a signal ("I pushed the pole at this end!") instantaneously. Since a signal cannot be sent faster than the speed of light, such a rigid pole cannot exist.

 

[Bob S]

Suppose you had a disk, such as a computer HD or CD, that was strong enough to survive spinning at relativistic speeds. Suppose you spun it such that the rim velocity were 0.99c. What would the circumference be, as seen by a stationary observer? What would the radius be, as seen by the observer? What would pi be?

 

[belliott4488]

I wouldn't have thought the rigidity of the material would be the limiting factor, since that just delays acceleration of the outer parts of the rod (or disc) - assuming that torque is being applied from the center of rotation - but eventually the outer parts "catch up" with the inner parts and move at the same angular rate. (??)

Rather, I would have thought that the limiting fact would be the torque needed to achieve near-lightspeed tangential velocities. Just as ever increasing force is needed to accelerate a mass to near-lightspeed linear velocities due its increasing mass, I would have thought that the inertia of of the rod/disc would would increase and require ever increasing torques.

I'm not sure how to calculate this, however, since relativistic rotational dynamics frightens me.

 

[darkhorror]

What if you didn't have a single rod but instead had a bunch spaceships next to each other? Then each spaceship tries to stay next the two spaceships on ether side?

 

[Phrak]

To be concise, relativity theory and perfectly rigid objects are inconsistant premises. You can't propose both, in general, without contradictory results.

 

[HallsofIvy]

I wouldn't have thought the rigidity of the material would be the limiting factor, since that just delays acceleration of the outer parts of the rod (or disc) - assuming that torque is being applied from the center of rotation - but eventually the outer parts "catch up" with the inner parts and move at the same angular rate. (??)

Rather, I would have thought that the limiting fact would be the torque needed to achieve near-lightspeed tangential velocities. Just as ever increasing force is needed to accelerate a mass to near-lightspeed linear velocities due its increasing mass, I would have thought that the inertia of of the rod/disc would would increase and require ever increasing torques.

I'm not sure how to calculate this, however, since relativistic rotational dynamics frightens me.

Since rotary motion necessarily requires acceleration, not just velocity, you are moving from "Special Relativity" to "General Relativity". The geometry of space changes here and the circumference of a circle is no longer just a constant multiple of the radius.

 

[HallsofIvy]

What if you didn't have a single rod but instead had a bunch spaceships next to each other? Then each spaceship tries to stay next the two spaceships on ether side?

I don't see how this changes anything. Except, of course, it makes it obviously "flexible" now!