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Objects with mass can't move at/faster than the speed of light. But recently I have been doing angular velocity and came up with a very interesting scenario. I'm sure many people thought about this before but I couldn't find a good explanation for this.

Basically, imagine there was an extremely long and unbreakable stick, and you started spinning it in circles, with one of its edges always in the same spot. Like in the picture below:

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Where the red point is one of the ends of the stick which is rotating on that spot.

If point A on the stick moved extremely close to the speed of light from A1 to A2, what would happen to point B from point B1 to B2? Since A and B have the same angular momentum, why would B not travel at the speed of light?

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Basically, imagine there was an extremely long and unbreakable stick, and you started spinning it ...

There is no such thing as an unbreakable stick. Or equivalently, there is no infinitely hard material, because that would lead to an infinite speed of sound.

The stick will break long before it reaches the speed of light. Actually it will break before it reaches the speed of sound, because the rotational angular velocity cannot propagate outwards through the stick infinitely fast, but only with the speed of sound.

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