240 PRACTICAL MATHEMATICS 



i 

 It is evident that I ( 



and I, 



__ 



12 



12 



129. The Cylinder. Consider an elementary slice of thickness 

 , cut by planes parallel to the base. 



-& 





LL. 



/ ! \ /\ 



/ \ / \ 





B 



Mass of slice = TimR 2 So; 



FIG. 70. 



Moment of inertia of the slice about the axis OX = - TrmR 4 



2 



For the whole cylinder I ox == - TT 



1 



dx 



= - MR 2 where M is the mass. 



30 



If the cylinder is hollow, R 2 and R x being the external and 

 internal radii respectively. 



The moment of inertia o r the elementary disc about the axis 



B = i 



4 



