Question

Why can't I use Center of Mass in Moment of Inertia?

Answer 1

coz if it lies on the axis of rotation mostly

Answer 2

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.

Rotation axis is assumed to be along the z-axis, or out of (perpendicular) your computer screen.