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

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.