Moment of Inertia of a Rectangle
rectangle, Solid Plane, z Axis formula
(Eq. 1) \(\large{ I_z = \frac {1}{12}\; m \; \left( l^2 + w^2 \right) }\)
(Eq. 2) \(\large{ I_z = \frac {1}{12} \;l\;w \; \left( l^2 + w^2 \right) }\)
(Eq. 3) \(\large{ I_{z1} = \frac {1}{12}\;m \; \left( 4\;l^2 + w^2 \right) }\)
rectangle, Solid Plane, x Axis formula
(Eq. 4) \(\large{ I_x = \frac {1}{12}\; l\;w^3 }\)
(Eq. 5) \(\large{ I_x = \frac {1}{12}\; m \; l^2 }\)
(Eq. 6) \(\large{ I_{x1} = \frac {1}{3}\; l\;w^3 }\)
(Eq. 7) \(\large{ I_{x1} = \frac {1}{3}\; m \; w^2 }\)
rectangle, Solid Plane, y Axis formula
(Eq. 8) \(\large{ I_y = \frac {1}{12}\; l^3\;w }\)
(Eq. 9) \(\large{ I_{y1} = \frac {1}{3}\; l^3\;w }\)
rectangle, Hollow Core Plane, x Axis formula
(Eq. 10) \(\large{ I_x = \frac {l\;w^3}{12} - \frac {l_1\;w_1{^3} }{12} }\)
rectangle, Hollow Core Plane, Y Axis formula
(Eq. 11) \(\large{ I_y = \frac {l^3\;w}{12} - \frac {l_1{^3} w_1}{12} }\)
Where:
\(\large{ I }\) = moment of inertia
\(\large{ l }\) = length
\(\large{ l_1 }\) = length
\(\large{ m }\) = mass
\(\large{ w }\) = width
\(\large{ w_1 }\) = width