I don't feel I have a good understanding of what the center of mass of an object it, and what its properties are. I know it's the position of all mass elements weighted by their mass and divided by the total mass. I have learnt that the center of mass moves as if it was only subject to external forces. So say you pushed on a box of mass m with a certain force F, then the center of mass of that box should move with an acceleration given by F/m. But since the whole box moves with the same acceleration what is then the so special about this specific point? I also have trouble finding out what exactly the center of mass represents physically. Say it is in the middle of the box, is the center of mass then the point particle situated in the midst of the box or is it a more abstract point?