Now you(orange) spin the blue wheel ( torus) with an $\omega$ in the direction of axis and then let go of the wheel . Now how will you move ? Will you keep moving in the brown circle ? ( Because by conservation of angular momentum you must also have an opposite $\omega '$ of some different value .
Edit1: Okay i have neglected something very basic , gravitational force ,which makes it even harder to imagine what will happen and how angular momentum will stay conserved