Observing a rotating body when approaching it at near light speed

[Meruem]

TL;DR Summary

Will the motion around us become faster when we travel faster?

Summary: Will the motion around us become faster when we travel faster?

When we approach a body rotating on its axis with certain speed v, will we see the body rotating in speed slightly more than the v during our motion ?And what happens assuming that we are approaching the same body in speed of light?

 

[mitochan]

Hello.
Periphery of rotating body has speed ##\mathbf{v}+\mathbf{w}## to us where v is rotating speed which depends on the part, e.g. coming, going, transverse for us and w is our approaching speed to the rotating axis. If v or w is close to light speed we should follow the theory of relativity and its velocity addition rule instead which assure that resulted speed does not exceed light speed.

 

[berkeman]

(Mentor Note -- thread title edited a bit to clarify the OP's question, and thread moved to the Relativity forums)

 

[Orodruin]

Hello.
Periphery of rotating body has speed ##\mathbf{v}+\mathbf{w}## to us where v is rotating speed which depends on the part, e.g. coming, going, transverse for us and w is our approaching speed to the rotating axis. If v or w is close to light speed we should follow the theory of relativity and its velocity addition rule instead which assure that resulted speed does not exceed light speed.

Note that this last bit of information means that the part of the body that rotates in the same direction as the body is moving will have a speed less than v+w whereas the part of the body that rotates in the opposite direction will have a speed larger than w-v.

 

[Ibix]

When we approach a body rotating on its axis with certain speed v, will we see the body rotating in speed slightly more than the v during our motion ?

I take it you mean that the periphery of the object is moving at v in its rest frame.

Your question is slightly ambiguous. Do you mean to ask about what you literally see, or how you would interpret what you see? These are two different things, and sources often use the word "see" for either or both (somewhat sloppily).

What you would actually directly observe is largely the Doppler effect - the faster you go towards it the faster it appears to spin. This is because after the object has completed one revolution it is closer to you than before that revolution, so the light has less distance to travel so the apparent period decreases.

However, if you correct for the changing distance, you will find that the object's rim does not have a constant speed. Furthermore, it is length contracted in its direction of motion, so may be distorting as it rotates. The overall rotation rate will be slower, not faster.

And what happens assuming that we are approaching the same body in speed of light?

It is impossible for a massive body to travel at the speed of light, and it turns out to be self-contradictory to describe the viewpoint of someone traveling at the speed of light. So this question has no answer

 

[olgerm]

I refrase OP's question:
what would happen if I put a spinning cylinder with radius R in a black box and gave it angular speed ##\omega>c/R##.
In classical physics ##v=\omega*R##, where v is speed of edge of the cylinder.
, but in this case speed of edge of cylinder would be faster than speed of light. Therefore non-relativistic approx is not good for this situation. What would actually happened if I really attempted it?

the answer is that angularspeed of body has no limit, but ##v=\omega*R## is not valid in SR?

 

[PeterDonis]

what would happen if I put a spinning cylinder with radius R in a black box and gave it angular speed ##\omega>c/R##.

You can't.

What would actually happened if I really attempted it?

The cylinder would break apart before you were able to reach such an angular speed.

the answer is that angularspeed of body has no limit, but ##v=\omega*R## is not valid in SR?

No, that's not the answer. See above.

 

[olgerm]

I did not think that it would be possible with currently available materials. It is just a thought experiment to describe fundamental physics.
I meant it as idealised situation, where the cylinder is perfectly rigid and strong body. Would the answer in idealised case still be that angularspeed ##\omega## of body has no limit, but v=ω∗R is not valid in SR?

 

[PeterDonis]

I meant it as idealised situation, where the cylinder is perfectly rigid and strong body.

There is no such thing. Relativity limits the strength of materials; roughly speaking, the limit is that the speed of sound in the material cannot exceed the speed of light. That limits all other material properties like tensile strength.

Would the answer in idealised case still be that angularspeed ##\omega## of body has no limit, but ##v=ω∗R## is not valid in SR?

No.