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
The opposite reaction of a rotating force is another rotating force, as opposed to a straight one.
No matter where the rotating force is acting on and its relation to the center of mass of the ship, the rotating force does not create any levering action to push the ship, so it doesn’t behave like a straight force that the reaction may produce different angular moments depend on where the force is acting on.
Instead it only produce an angular opposite moment, twisting the ship the other way. Twisting at any point is all twisting, all the same.
Think of two gears turning against one another, except you have a large gear with a hole (where the wheel of the ship is)turning against a smaller gear on the inside of that hole, only in this case the rotation forces would travel through the floor/other materials
Newton’s Third Law, equal and opposite reactions. In order to rotate, the wheel has to apply a force to *something*. The only other something it can apply a force to is the ship. As motors turn the wheel one direction, it applies a force to the rest of the ship, which forces the rest of the ship to turn in the opposite direction with equal force.
This happens on Earth, too, if you try to turn. You have to apply a force to *something*, which is the Earth. It’s just that the force needed to spin you around when applied to the entire planet doesn’t do much of anything, so the Earth doesn’t move a noticeable amount.
It’s possible that the wheel could equal-and-opposite reaction spin itself by exhausting some gas into space. The gas goes off in one direction, and the wheel is moved in the opposite direction. This would *not* force the body of the ship to spin…except that friction still exists and the main body would tend to spin *with* the wheel instead of opposite.
There’s also [gyroscopic precession](https://www.youtube.com/watch?v=ty9QSiVC2g0) where torque is applied 90° from the rotation. But that only happens when a force is applied to the spinning object.
The center of mass of the combined ship+wheel system must stay in one place (or continue in its orbit) unless an external force acts on it.
For your question, intuition might say the ship would rotate around wherever the wheel is, but think what that implies about how the ship’s center of mass moves. When the rotation starts, say the ship’s CoM moves North. What external force made that happen? As the rotation continues, the CoM stops going North and is now moving East. Again, what external force made that happen?
The only way to keep the CoM where it needs to be is for the rotation to have that as its center.
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.
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