1. The problem statement, all variables and given/known data When calculating moment of inertia of a disk there is something that really bothers me. I've googled this a lot and everywhere i look they 'assume' that the Δa = Δr*2∏r, formula for rectangle, not circle: (area of circle r+Δr - area of circle r) Δa = ∏(r+Δr)^2 - ∏r^2 = ∏r^2 + 2∏Δr*r + ∏Δr^2 - ∏r^2 = 2∏Δr*r + ∏Δr^2. One link is the same but you get the extra Δr^2. is it even possible to integrate this? the question is why is this allowed? is it because Δr^2 << Δr*r? 2. Relevant equations I = ∫r^2 dm 3. The attempt at a solution I=∫r^2 dm disk with inner diameter D/2, outer diameter D, mass M. r = D/2 => r1 = D/2, r2 = D/4 Δm = M * ΔA / A = M(∏(r+Δr)^2 - ∏r^2)/(∏(r1^2-r2^2)) ... Δm = M (2Δr*r + Δr^2) / (r1^2-r2^2) ΔI = Δm * r^2 = ... = 2Mr^3 Δr/(r1^2-r2^2) + M*r^2 Δr^2/(r1^2-r2^2) I = ∫..... ??