For a circular cross-section of radius
, Eq.(B.11) tells us
that the squared radius of gyration about any line passing through the
center of the cross-section is given by
Using the elementrary trig identity
, we readily
derive
The first two terms of this expression contribute zero to the integral from 0 to
Thus, the radius of gyration about any midline of a circular cross-section of radius
For a circular tube in which the mass of the cross-section lies
within a circular annulus having inner radius
and outer
radius
, the radius of gyration is given by