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Mass Moment of Inertia about x, y, z Axis

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

z = 0 in equation (8.6)

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)

=pt IZ

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.

 

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.

 

dm = m /L dx

IYY =ʃ x2 dm   = m /L x 1/3 x L3 = mL2 /3