I though I understood this concept but the more I learn advanced topics like torque, momentum, work, the more I realize that I have fundamentally misunderstood it. My original, theoretical line of thinking was that COM was that point on object or somewhere outside it where equal amount of mass was distributed that surrounded it from all sides of the space. I though that since there was equal mass on all sides around that point of COM, that this was the reason why you have transnational motion instead of torque (since there is equal parts to supply inertia all around it, so that if inertia is overcome the whole object moves in unison) or that this was reason why when you balance object on COM it doesn't not fall under influence of gravity. Now after much research I have come to realize that this is not the case. In fact, I saw example where cutting an object along COM need not divide it into equal parts.
So now with this stated, my question then becomes that what exactly is COM? How come it is deemed as if all the mass of the object is concentrated in that single point? I mean, COM ( if you try to locate it physically on a object) is still an atom/atoms of certain mass and position, so all the mass is not really concentrated in it, is it? Also why is COM considered as that special point whre putting force on it produces translation motion instead of torque? Has it got to do with the distribution of force through the rest of body of an object? Is COM that point where if you apply force, that is equally distributed to rest of the atoms of the body of the object, no matter how far those atoms are from the COM? Conversely, does applying force on any other point on the object beside COM mean that that force is not equally distributed to the rest of the body, which then produces torque instead of transnational motion?
I know these are lot of question, but if anyone can provide some theoretical, intuitive explanation, instead of mathematical, I would greatly appreciate it.