Were one to do this assuming hypothetical material that wouldn't break up under the stress, nor expand due to stress alone - hypothetical like I said - reversing it would cause relativistic expansion + general weirdness at the fast end. Wouldn't that expansion cause the gears to hbe forced apart and rupture, or something? I have a feeling it would somehow not but I can't imagine what would happen. They must expand, yet still remain engaged, which seems contradictory.

Typically when you try to rotate something in a way that makes it move faster than the speed of light it'll just rip itself apart.

Actually I think this typically happens when you reach speeds somewhere on the order of the speed of sound of the material.

The material will break eventually. Other gears provide some structural support against expansion, but that is not what is going to break a gear. IMO the thing that would break it would simply be the mass of the gear; the fast acceleration would tear the gear out of it's axis or break it's teeth.

If it doesn't, at some point the material will give, likely away from the driving gear, and the entire thing will fling itself apart.

Of course it would, which is why I talked about a hypothetical material.

If it did not, though, what would relativity make it do?

I'm not a physicist but it's hard to have a thought experiment where you introduce ideas like ignoring materials strength, because that could be a factor in what relativity would make it do.

Anyway as you approach the speed of light the energy required to accelerate approaches infinity, so you would just not get it there because of the energy requirement.

I think a simpler version of this experiment is a really long rigid rod. What happens if you pick one end of the rod to be the axis and then you try to rotate the rod about the axis? https://physics.stackexchange.com/questions/455189/rotating-...

Also: You'd not be able to apply anywhere close to the amount of torque that'd be needed.

Sorry to be a buzz kill, but AFAIK you can't "reverse" a worm gear.

You can, worm gears that can't be reversed are called self-locking, but depending on setup, it's possibly to drive them in reverse with some effort.

Can't do it with Lego worm gears though. Maybe if you add some machine oil, but otherwise the plastic-vs-plastic friction is just too much.

I wonder how much energy it would take to spin it at all