system
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human
How is it possible for all points on a rotating disc to be moving at the same speed?

This is something that just hit me while I was thinking about planetary rotation. In theory, the length of a day should be different depending on your latitude, since the actual distance covered by any line of latitude changes depending on how close or far you are from the equator. However, everyone everywhere has a 24 hour day, even though the actual distance they're traveling as the earth rotates varies everywhere from 0 at the poles, to the circumference of the Earth at the equator. 

I've heard about this paradox every since I was little, but I've never really gotten an answer to it. If every point on earth's surface is rotating around Earth's axis at the same speed, then how can everyone have the same length of day if the actual distance they're covering is different? Does this mean that any planet rotating at the same speed as earth would have a roughly 24-hour day, completely regardless of its actual size? If latitude x has the same length of day as Earth's equator, then that should mean a planet with an equatorial circumference of x should also have a 24 hour day as long as its rotating at the same speed.

How is this possible?
gpt
Earth and other rocky planets are solid bodies. This means the whole thing rotates at a fixed angular velocity, that is, at the same number of *degrees per minute*. No matter where you are on Earth, you are moving at about 1 degree every 4 minutes.

However your *linear speed* (relative to the centre of the Earth) in mph or m/s or whatever does vary a lot based on where you are. If you're on the north pole or south pole, you aren't actually moving (relative to the centre of the Earth), you're just standing still and spinning on the spot. At the equator, you are moving at 460 m/s. At a latitude of 45°, you're somewhere in the middle, moving at 330 m/s.

This works because as you go further from the equator, you have less distance to cover in your daily circle, so for the same rate of degrees per minute, you go slower in m/s.

If everything rotating at the same rate of m/s, that actually means the Earth would be twisting and breaking. If England or Japan or whatever was moving at 460 m/s, the same as the equator's linear speed, then they would complete their rotation in less time than Ecuador or Kenya. That only works if the Earth is twisting or breaking, and not if it's a solid rigid object.

Note that for stars and gas planets, they *don't* rotate at the same rate of degrees per minute across all latitudes. This is called "differential rotation". Because it's all just gas or plasma, it *can* just twist around without breaking anything. This also happens in galaxies. Galaxies actually have "flat rotation curves" across a large fraction of their radius. These means that the stars are all moving at the same linear speed (about 200 km/s for the Milky Way), but because the stars are all at different radii, they are moving at a different rate of degrees per million years, and the stars in the middle take less time to orbit than the stars further out. Again, that's fine, because a galaxy isn't a single solid object, and it can't really "break".