<Tr> <Td> Thin, solid disk of radius r and mass m . <P> This is a special case of the solid cylinder, with h = 0 . That I x = I y = I z 2 (\ displaystyle I_ (x) = I_ (y) = (\ frac (I_ (z)) (2)) \,) is a consequence of the perpendicular axis theorem . </P> </Td> <Td> </Td> <Td> I z = m r 2 2 (\ displaystyle I_ (z) = (\ frac (mr ^ (2)) (2)) \, \!) I x = I y = m r 2 4 (\ displaystyle I_ (x) = I_ (y) = (\ frac (mr ^ (2)) (4)) \, \!) </Td> </Tr> <P> This is a special case of the solid cylinder, with h = 0 . That I x = I y = I z 2 (\ displaystyle I_ (x) = I_ (y) = (\ frac (I_ (z)) (2)) \,) is a consequence of the perpendicular axis theorem . </P> <Tr> <Td> Thin cylindrical shell with open ends, of radius r and mass m . <P> This expression assumes that the shell thickness is negligible . It is a special case of the thick - walled cylindrical tube for r = r . </P> Also, a point mass m at the end of a rod of length r has this same moment of inertia and the value r is called the radius of gyration . </Td> <Td> </Td> <Td> I ≈ m r 2 (\ displaystyle I \ approx mr ^ (2) \, \!) </Td> </Tr> <P> This expression assumes that the shell thickness is negligible . It is a special case of the thick - walled cylindrical tube for r = r . </P>

Moment of inertia of a rod about a point