THE MOMENT OF INERTIA OF A CONE 241 



Hence the moment of inertia of the elementary disc about the 



axis OY = 7 TcmK 4 8x + mnli 2 x 2 &r. 

 4 



For the whole cylinder I OY = jTtmR 4 I , dx + TcmR 2 1 { a? dx 



J- J- 



7 TimR 4 / + TwR 2 1 - 

 4 



7 TcmR 4 / +~ 

 4 12 



~2 



M 



(R 2 P} 



\T + 12/ 



130. The Cone. Considering an elementary slice of thickness 

 8f/ situated at a distance y from the base of the cone. 



FIG. 71. 



If x is the radius of the slice, 

 Then 



and 



I 



Mass of the slice 



x 

 h-y 



R 



h 



x = _ (h - y) 



Moment of inertia of the slice about OY = -TWW^ 8t/ 



m 



