<Tr> <Td> Solid ellipsoid of semi-axes a, b, c and mass m </Td> <Td> </Td> <Td> I = (1 5 m (b 2 + c 2) 0 0 0 1 5 m (a 2 + c 2) 0 0 0 1 5 m (a 2 + b 2)) (\ displaystyle I = (\ begin (bmatrix) (\ frac (1) (5)) m (b ^ (2) + c ^ (2)) &0&0 \ \ 0& (\ frac (1) (5)) m (a ^ (2) + c ^ (2)) &0 \ \ 0&0& (\ frac (1) (5)) m (a ^ (2) + b ^ (2)) \ end (bmatrix))) </Td> </Tr> <Tr> <Td> Right circular cone with radius r, height h and mass m, about the apex </Td> <Td> </Td> <Td> I = (3 5 m h 2 + 3 20 m r 2 0 0 0 3 5 m h 2 + 3 20 m r 2 0 0 0 3 10 m r 2) (\ displaystyle I = (\ begin (bmatrix) (\ frac (3) (5)) mh ^ (2) + (\ frac (3) (20)) mr ^ (2) &0&0 \ \ 0& (\ frac (3) (5)) mh ^ (2) + (\ frac (3) (20)) mr ^ (2) &0 \ \ 0&0& (\ frac (3) (10)) mr ^ (2) \ end (bmatrix))) </Td> </Tr> <Tr> <Td> Solid cuboid of width w, height h, depth d, and mass m </Td> <Td> </Td> <Td> I = (1 12 m (h 2 + d 2) 0 0 0 1 12 m (w 2 + d 2) 0 0 0 1 12 m (w 2 + h 2)) (\ displaystyle I = (\ begin (bmatrix) (\ frac (1) (12)) m (h ^ (2) + d ^ (2)) &0&0 \ \ 0& (\ frac (1) (12)) m (w ^ (2) + d ^ (2)) &0 \ \ 0&0& (\ frac (1) (12)) m (w ^ (2) + h ^ (2)) \ end (bmatrix))) </Td> </Tr> <Tr> <Td> Slender rod along y - axis of length l and mass m about end </Td> <Td> </Td> <Td> <P> I = (1 3 m l 2 0 0 0 0 0 0 0 1 3 m l 2) (\ displaystyle I = (\ begin (bmatrix) (\ frac (1) (3)) ml ^ (2) &0&0 \ \ 0&0&0 \ \ 0&0& (\ frac (1) (3)) ml ^ (2) \ end (bmatrix))) </P> </Td> </Tr>

Moment of inertia of a ring of mass