Moment of inertia of solid cylinder about its axis : In the given diagram a cylinder (solid) of mass M, radius R and length l is shown. Suppose ZZ’ axis is its geometrical axis about which we have to calculate the moment of inertia. For the purpose, the whole length of the cylinder may be supposed to be made of many dish elements of various masses. Such type of one, Therefore, moment of inertia of the whole cylinder,element is shown in the figure. Moment of inertia of this dish element about ZZ’ axis.
dI = \(\frac{1}{2}\)dmR2
Therefore, moment of inertia of the whole cylinder
I = ΣdI = Σ \(\frac{1}{2}\)dmR2
or I = \(\frac{1}{2}\)R2Σdm
or I = \(\frac{1}{2}\)MR2
where M = mass of the cylinder.
