Here's the question you clicked on:
Ishaan94
Why can't I use Center of Mass in Moment of Inertia?
coz if it lies on the axis of rotation mostly
Hmm I guess that is because we chose the axis of rotation to be on center of mass, but my question was why can't I find the co-ordinates of center of mass and then apply I=mr^2. I know we get different results but I wanted to get a clear picture.|dw:1325251564371:dw| Rotation axis is assumed to be along the z-axis, or out of (perpendicular) your computer screen.
no this is wrong assumption!!!
If you want to find co-ordinates of a symmtrical body, it is easy. but to find the C.O.M. of a unsymmtrical body, then you have to consider the body to be made up of finite no. of particles......by the way in which standard do you read????
and also intranslational motion(linear or st. line) the mass of a body is the property due to which a body opposes the motion and in rotational motion the moment of inertia opposes the rotation of a body.....any confusion then tell me...
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?
Sorry Typo, Second Paragraph; Second line \[I = \sum_{i=1}^{n}m_{i} \vec{r_{i}}^2\]