<Tr> <Td> A filled circular sector of angle θ in radians and radius r with respect to an axis through the centroid of the sector and the center of the circle </Td> <Td> </Td> <Td> I x = (θ − sin ⁡ θ) r 4 8 (\ displaystyle I_ (x) = \ left (\ theta - \ sin \ theta \ right) (\ frac (r ^ (4)) (8))) </Td> <Td> This formula is valid only for 0 ≤ θ (\ displaystyle \ theta) ≤ π (\ displaystyle \ pi) </Td> </Tr> <Tr> <Td> A filled semicircle with radius r with respect to a horizontal line passing through the centroid of the area </Td> <Td> </Td> <Td> I x = (π 8 − 8 9 π) r 4 ≈ 0.1098 r 4 (\ displaystyle I_ (x) = \ left ((\ frac (\ pi) (8)) - (\ frac (8) (9 \ pi)) \ right) r ^ (4) \ approx 0.1098 r ^ (4)) I y = π r 4 8 (\ displaystyle I_ (y) = (\ frac (\ pi r ^ (4)) (8))) </Td> <Td> </Td> </Tr> <Tr> <Td> A filled semicircle as above but with respect to an axis collinear with the base </Td> <Td> </Td> <Td> I x = π r 4 8 (\ displaystyle I_ (x) = (\ frac (\ pi r ^ (4)) (8))) I y = π r 4 8 (\ displaystyle I_ (y) = (\ frac (\ pi r ^ (4)) (8))) </Td> <Td> I x (\ displaystyle I_ (x)): This is a consequence of the parallel axis theorem and the fact that the distance between the x axes of the previous one and this one is 4 r 3 π (\ displaystyle (\ frac (4r) (3 \ pi))) </Td> </Tr> <Tr> <Td> A filled quarter circle with radius r with the axes passing through the bases </Td> <Td> </Td> <Td> I x = π r 4 16 (\ displaystyle I_ (x) = (\ frac (\ pi r ^ (4)) (16))) I y = π r 4 16 (\ displaystyle I_ (y) = (\ frac (\ pi r ^ (4)) (16))) </Td> <Td> </Td> </Tr>

Moment of inertia of a right angle triangle