74, 75] CALCULATION OF MOMENTS OF INERTIA. 241 



Rectangular Parallelepiped, of dimensions 2 a, 2b, 2c. 



a b c 



A' 



'a b c 



a b c 



'-/// 



a b c 



a b c 



"/// 



a b c 



a b c 



- c r r 



C' = I I 



/ fj *J 



a 6 c 



102) B = C r + A' --= y abc (c 2 + a 2 ), 



C r = ^ f + i?' = |-a&c 

 Thus the radii of gyration a 07 6 , c are 



mo\ 



103) a Q = 



Sphere, with radius E. 



A' = CCCx 2 dxdydz, B f =j f fodxdydz, C 1 = 

 the limits of integration being given by the inequality # a -f y 2 + 2 <R 2 . 

 A' + B' + C' =JJJ(x 2 -f ?/ 2 + 



Changing to polar coordinates, 



R 



A' + B' + C' = xr*dr = ~ 



A=& + C' = ~ 



104) A=B=C=~ 



Ellipsoid, with semi -axes a, fr, 



the limits of integration being given by the inequality 



^ + p- + -# < 1- 



, Dynamics. 16 



