Moment-of-inertia uncertainty for an annulus
= 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 $dI=(a^2+b^2)dm/2+ma\,da+mb\,db$. <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.