.MOMENT OF INERTIA OF RECTANGULAR PRISM 289 



Let PT be a tangent to the circle. 



1 PT ~ *OX 



Then 



For a circular ring, I ox = I OY = - I oz 



128. The Rectangular Prism. Consider an elementary slice of 

 thickness St/, cut by planes parallel to the base. 



FIG. 69, 



Mass of slice = mob y where m is the mass of unit volume. 

 Moment of inertia of the slice about the axis OY 



J_ 

 "12 



For the whole prism I OY = r^ mab(a 2 + b 2 ) dy 



12 J 



= -^ mabc(a 2 + b 2 ) 



M(a 2 +6 2 ), where M is the 



121 



mass of the prism. 



