242 VI. SYSTEMS OF VECTORS. DISTRIBUT. OF MASS. INSTANT. MOTION. 



The integration is most easily performed by a change of variable. 

 If we put 



x i y i z I 



the integral being taken for values corresponding to points within 

 the sphere 



x' 2 + y' 2 + 2 12 <1. 



Now the moment of inertia of the sphere with respect to a diametral 

 plane is #, hence 



A'=;ita*l>c, B ! =*-xb*ca, C' = ~xc*ab. 



lo lo lo 



105) B=C' + A' = 



106) Q 



Thin Circular Disk normal to Z-axis. 



, C' = 0, 



107) A = B = - 



The moment about the normal to the disk is double that about a 

 diameter. 



Circular Cylinder of radius JR, length 2L 



The moment about the axis of rotation, is ? as for the disk, 



C = ~MR 2 , A = B' = 



C'= fx 



-i 



108) A = B 



