The existence of Centre of Mass?

Question

We all must have used or at least heard of the concept of Centre of Mass at some point of life . But this is defined to be a imaginary point where Mass of the body is " supposed to be concentrated " , which means it is not possible in reality , while we have plenty of experiments where people find approximately the same point . Even it's immensely used in Newtonian physics , but why ? how do somebody think of it theoretically ? .... Please help me understand it fundamentally

Answer 1

The problem is the definition you think it has, which is:

this is defined to be a imaginary point where Mass of the body is " supposed to be concentrated "

I note Wikipedia also state this at the start, but it's a terribly poor choice of words.

Center of mass is defined more formally as a point about which the body naturally rotates. If force acts on a line through that point the body will not change angular momentum, but if a force acts on a line not containing that point it will have to change angular momentum.

We do not consider that the mass is concentrated at a point, but that we can consider the body in an abstract way as having this center of rotation, without needing to treat each part of the object separately.

In Newtonian gravity, it's also the point, for spherically symmetric bodies, which we can treat all the mass as concentrated to get the same gravitational effect on bodies outside the object. However we are not saying all the mass is concentrated there, just that the mathematics works out conveniently that way.

Answer 2

Think of an object's centre of mass as the point that can represent the object as a whole, when the shape and exact details aren't important.

Maybe you have often in classical mechanics seen physicists idealize objects as points. E.g. think of throwing a hammer. If you wish to investigate it's trajectory through the air, then you wouldn't care about the fact that the hammer also spins around itself while flying (ignoring wind resistance here). You would rather simply think of the hammer as a single point that is moving.

And which point should you then choose to represent the hammer with? Well, as it turns out, while almost all points on the hammer are on rotation while also flying through the air, there is one single point about which all the other points are spinning. That point is solely flying through the air following the smooth trajectory with no rational effects. So, let's choose that point to represent the hammer.

And this point is the hammer's centre of mass. The point that all mass in the hammer "averaged down to".