Hollow or solid cylinder

Fig. 38 shows a hollow cylinder of length and inner and outer radii and .We choose as the most convenient volume element a thin cylindrical sheet of radius , thickness and length . The volume of this shell is very nearly equal to that of flat sheet of thickness , length , and width .Then

.

The moment of inertia is given by

Volume

Hence

and the moment of inertia is

If the cylinder is solid letting outer radius be we find that the moment of inertia of a solid cylinder of radius is

If the cylinder is very thin, and , are nearly equal, if represents this common radius

(76)

Note, that the moment of inertia of cylinder does not depend on the length . It depends only on the radial distribution of mass, not on distribution along the axis.