I believe Veritasium covered this: spinning at relativistic speeds generates centripetal forces that overcome the nuclear force. There is no material you can use to test this paradox, and there can be no such material because your device would atomize - or worse - in the attempt.

Effectively there are g-forces so high that you end up with subatomic particles.

It's mean to be a thought experiment but some people (like Veritasium) can't get around this simple realization.

Like, "I wonder what could be happening inside of a black hole?"

"Oh we would never know, because if we send a camera it would break. Also suppose we MaaaAaAKKeee aa cCAaaMeerra with ThE STROooonngGEEstt Material In the UUunniveersssee, so it wouldn't break, you would find that there's no wifi in there so how would you transmit your findings ;)"

I hate this kind of "smart" people.

(Disclaimer: I am not a physicist.)

I think it's actually a pretty reasonable description? Sounds like it's a paradox because we assume a rigid body, but nothing in real life is a perfect rigid body. So the situation simply becomes a bunch of particles following circular orbits. If you measure distance along one direction (while constantly accelerating in relativistic speed) you get one number; if you measure distance in another direction you get a different number. But that's what relativity does.

In other words, it's similar to the simpler question: "If I have a perfectly rigid rod that can reach the moon, and I push it, then the other end pushes the moon immediately. But speed of information cannot exceed speed of light. How come?" Answer: There's no perfectly rigid rod.

The example you give and its answer follows a line of reasoning that leads you to an interesting conclusion, that's the point of thought experiments.

What I was saying is more akin to answering your example with:

"Oh no you can't! There's not enough steel on Earth to build such thing and even if you had it, it would require an EEeEeeenOOOOrrrMMMoooUUUusss amount of energy to put in place ;)."

That would be quite a moronic interpretation of the problem that completely misses the goal of said thought experiment, which is, well, to make you think.

The difference there is, I think, that the pragmatic argument of "not enough steel" doesn't prove the non-existence; while the argument about "there are no truly rigid bodies" does.

I haven't seen that Veritasium video, but it sounds like it makes the exact same point. It's not that we haven't found a material that's rigid enough; it's that a rigid disk is counter-factual to begin with, even in non-relativistic conditions.

It's one of the reason I dislike physical terms that has words like "ideal" or "perfect" as their part. They subliminally suggest that their properties and behaviours are the "true" ones while the real material things are their imperfect counterparts whose imperfections you can sometime disregard.

Of course, it's exactly the opposite: it's those "ideal" concepts are imperfect approximations of the real things, omitting lots of details which sometimes are not that important but sometimes are absolutely crucial.

My personal favourite example is attaching a perfect source of voltage (zero internal resistance) to a perfect wire (zero resistance). You can't arrive to this scenario starting with the real world entities: both the battery and the wire will have non-zero resistances and depending on their proportions, you end up with approximating either one of those as zero, or none, but never both.

Hence the “perfectly spherical cow” joke.

Relativistic speed rotations means that you are close to trapping light, meaning your force is similar to being very close to the event horizon of a black hole.

And what is one of the properties of gravity wells like black holes? Well, their circumference isn't equal to 2 pi times radius, since the space has enough curvature to not be flat, similar to how circumference isn't 2 pi times radius if your space is a 2d sphere. So the paradox is correct, you would get that effect, at least if you used a black hole to cause the fast rotation. Although I'm not sure if the maths adds up to be the same.

Yes, this is similar to transmitting a message faster than the speed of light by moving a very long perfectly rigid rod; a perfectly rigid rod is not realisable and neither is a perfectly rigid disk.

Relativistic paradoxes are the most insane. Twin paradox, ladder paradox, grandfather paradox, things get so mindbendingly weird at very large, very fast, and very small scales.

I think if you rotate the disk at maximum speed ignoring all material material properties, all points on disk will approach speed of light and you will end up with "spin through" because layers won't be able to maintain same angular speed (needed to consider the thing a disk) with fixed linear speed...

Spin the observer at the centre of the disc, and keep the disc stationary... now what happens?

not a physicist, but remember that accelerated frames break the symmetry.