This may be a silly question, but I just want to clarify something.
Say we have two spinning spheres, each spinning about an axis going through their own center of mass:
All of the conservation of angular momentum problems I have done have been simple problems where the two objects spin about the same axis. How would you find the angular momentum of this system?
Do you find the angular momentum of the system by using an axis going through the center of mass of the system as your reference axis and use the parallel axis theorem to find the new moments of inertia of the spheres? Can you calculate the angular momentum by considering either of the axis going through a sphere as the reference axis and then use the parallel axis theorem on the other sphere to calculate its new moment of inertia? Can you pick any random axis and use the parallel axis theorem? Or do you simply add the angular momentum of the obects about the axis they are rotating?