I_{XX} ,I_{YY}‘ and I_{ZZ} as the mass moment of inertia about x, y and z (Remember that l_{x}, l_{y}

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 , I_{XX} +I_{YY} =Pt (I_{X} +I_{Y})

=pt I_{Z}

I_{XX} +I_{YY} =I_{ZZ}

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, dI_{xx} + dI_{yy} = dI_{zz} exactly holds good.

**SOLVED EXAMPLES**

**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.

I_{YY} =ʃ x^{2} dm = m /L x 1/3 x L^{3} = mL^{2} /3