Why does a wheel spinning on a space ship cause the ship to rotate in the opposite direction around the ship’s center, regardless of the location of the wheel?

Question

Intuitively it makes sense when the wheel is located at the center of mass on the ship/axis of rotation, but I can’t wrap my head around how it makes sense when the wheel is located somewhere else

In: Physics

Answer 1

Newton’s Third Law.

If you throw a hammer in space, you will fly in the opposite direction. This is how most aircraft are propelled – by throwing air behind them.

If you rotate a (heavy enough) object in space, likewise, you will rotate in the opposite direction. Consider a turntable with a pole in the middle – spinning the pole while standing on the turntable will cause the turntable to spin. It’s the same thing here.

And it’s not around the ship’s centre. It’s around the wheel’s centre – which is why you want the wheel near the centre of the ship.