Dude! it's not that, we aren't calculating moment of inertia here for real, I don't know how to get that for unsymmetrical bodies. I know moment of inertia is analogous to mass in translation motion. What do you want me to do, draw the exact figure and get the exact co-ordinates and I didn't give you exact co-ordinates either \(\vec{r_{cm}}\) is a variable position vector. The drawing I posted it's just to give you guys Idea of what am I asking.
What I was trying to ask is, the moment of inertia is defined as \(I = \sum_{i=1}^{n} m_{i} /vec{r_{i}}^2\) now why can't I get the center of mass of the body and it's position and use it in the equation. We do know that center of mass behaves as if whole of mass is concentrated on that point, so we don't have to take mass of a very small element now, I know I am going wrong because if we do it like this we don't get the moment of inertia, the actual moment of inertia of the body, Because if chose the axis of rotation to pass through center of mass (for geometrical and symmetrical objects, I am not including unsymmetrical because it makes things complicated) we get zero as the answer.
So now after channelizing through my doubts and questions, what I have always wanted to ask is why is moment of inertia defined as \(I = \sum_{i=1}^{n}m_{i} \vec{r_{i}}^2\). What got experimental physicist or theoretician to take the moment of inertia as it's current definition. I get center of mass, it is basically centroid of a region or a body, but what does moment of inertia represents graphically?