IXX ,IYY‘ and IZZ as the mass moment of inertia about x, y and z (Remember that lx, ly
and Iz reter to area moment of inertia).
If z dimension of the body is negligible compared to x and y dimensions, we can put
where tis the z dimension (i.e., the figure is plane with t as thickness which is very small
Now , IXX +IYY =Pt (IX +IY)
IXX +IYY =IZZ
Equation (8.8) is true only for a thin flat plate.
Equation (8.8) is important when we deal with a differential mass element of thickness
dz. Thus, in such a case, dIxx + dIyy = dIzz exactly holds good.
Example 8.1. Find out the mass moment of inertia of a slender rod of length Land mass m with respect to an axis which is perpendicular to the rod and passes through one end of the rod.
IYY =ʃ x2 dm = m /L x 1/3 x L3 = mL2 /3