The moment of inertia of a hoop or thin hollow cylinder of negligible thickness about its central axis is a straightforward extension of the moment of inertia of a point mass since all of the mass is at the same distance R from the central axis.
For mass M = kg,
internal radius a = cm
and external radius b = cm,
the moment of inertia I = kg m2.
This may be compared with a solid cylinder of equal mass where I(solid) = kg m2, or with a thin hoop or thin-walled cylinder where I(thin) = kg m2.
The moment of inertia of a hollow circular cylinder of any length is given by the expression shown.