This may sound like a trivial question, but I am wondering: is it possible for there to be multiple centers of mass? And if it isn't, why?
For example, take some arbitrary 3-Dimensional object, floating around in space, perfectly still.
Let's define a $Y$ axis and an $X$ axis that go through the object.
You prod the right side of the object with a stick, so that it rotates entirely around the $Y$ axis. Every part will be in motion except the center of mass, around which the entire system will rotate.
Now you stop the object from spinning, make sure its still in space once again, and now prod it with a stick near the top, so that it rotates around the $X$ axis instead.
What assures that the point that will remain still, the point that the entire system will spin around, the center of mass, will be the same as when the object was rotating around its $Y$ axis?
*Edit: My question was said to be a possible duplicate of the question linked below. I don't really see how, but then again, I'm really confused by rotation (as you can see by a different question I have called Why do things spin) If someone could please explain why its a duplicate in their answer, that would be awesome as well! Thank you!*