THE MOMENT OF INERTIA OF A SPHERE 243 



If x is the radius of this slice, 



Then x - \/R 2 t/ 2 where R is the radius of the sphere. 



Mass of the slice = irma; 2 %. 



Moment of inertia of the slice about the axis OY = - irmx* dy 



I 



FIG. 72, 



TCTHf^" 



For the whole sphere I OY = x* dy 



2 J-E 



-E 



-E 



itrn 16R 5 



- -- 



a 





 15 



= -MR 2 , where M is the mass 



5 



of the sphere. 



If the sphere is hollow, R 2 and R : being the external and in- 

 ternal radii respectively. The moment of inertia can be taken 



