Moment-of-inertia uncertainty for an annulus

For axial moment of inertia $I=m(a^2+b^2)/2$, linear sensitivity to mass and outer/inner radius is $dI=(a^2+b^2)dm/2+mada+mbdb$. Independent standard uncertainties give ${\sigma }_I^2=[(a^2+b^2){\sigma }_m/2{]}^2+(ma{\sigma }_a{)}^2+(mb{\sigma }_b{)}^2$. Correlated measurements instead require the full covariance quadratic form. For deterministic bounds, add the absolute linear contributions rather than their squares.