system
Given the following post, respond as if you're commenting on Reddit:
human
If the near centre of a record rotates in 1 second (1cm/second) what would happen if the record was 1000's of metres wide?

If the record had a big enough diameter, and it was possible to actually turn it, why wouldn't it be going faster than light?
gpt
This is a classic thought experiment in special relativity. The problem it's impossible for a record to be perfectly rigid, and therefore it's impossible to make a large enough record rotate uniformly.

This isn't an issue of just needing strong enough materials - it comes down to the nature of special relativity itself. When you spin an object, you do that by pushing or pulling on some parts of the object, using your hands or a turntable or whatever. That *push* is transmitted through the rest of the object, so that it all spins uniformly. However, this transmission isn't instant. It's transmitted from atom to atom, by atoms pushing and pulling each other to try to get nearby atoms to follow along with the motion. This is actually the same process that allows sound to be transmitted through material. In fact, the speed of this transmission does come out to be the speed of sound in the material. This is always much much slower than the speed of light.

So, if you had a record that was 100,000 km in diameter, and try to rotate it 1 rotation per second, the outer edge won't go faster than the speed of light. The speed of sound in metal is maybe 6 km/s, so by the time the rotation signal has been transmitted atom-to-atom from the inside to the outside, it's been over 4 hours, and the inner edge of the record has rotated tens of thousands of times. If the inner edge has rotated far more than the outer edge, you are tearing apart your record. It's not rotating uniformly - it's breaking.

For a disc to rotate uniformly, you need to transmit the torque instantly across the entire disc. "Instantly" is faster than light. So, if you assume something is rotating perfectly uniformly, you are accidentally assuming you can break the speed of light, and it's not surprising that assuming you can break the speed of light ends up proving you can break the speed of light!