My question regarding centre of mass is less of a mathematical type and is more a conceptual one. As I have been taught that COM is a point (maybe within or outside the body) where crudely speaking all the mass of the body can be said to be concentrated and hence Newton's laws of motion can be applied as they are applicable only for point sized objects.
Then they taught me the derivations of COM of various objects and other related terminologies. This is where the trouble began. Till date I haven't been able to figure how am I to apply this concept (besides using it to apply Newton's laws of motion). Besides what do it means when we say velocity, acceleration or displacement of COM?
The confusion and bafflement intensified even more as they began using this concept in spring block problems to find maximum extension of the spring, maximum velocity of blocks, etc. The prof told us that the spring and the block system will perform both oscillatory and translational motion, the latter of which can be attributed to the velocity of COM (external force on the system of block and spring was 0).
So that means the velocity of centre of mass gives information only about the translational motion of the body or put it in another words does the body move with the velocity of COM? What about the oscillatory motion? Is that not manifested in the velocity of COM? Maybe, my whole notion of COM is screwed up.
I would love to have an explanation from beginning if anyone pleases to do so. Any help would greatly be appreciated.