Question

Calculate the Moment of inertia of a uniform rod about an axis passing through its CM and normal to its length.

Answer 1

Let us choose an elementary mass dM at position x on x-axis. Its distance is also x from axis. Its moment of inertia dI_z about Z-axis is given by 

The total MI will be obtained by inetragion over the whole rod (from x= –L/2 to x= L/2). Thus

This is the MI of rod about CM-axis, normal to rod.