Statics/Geometric Properties of Solids

Mass Moments Of Inertia Of Common Geometric Shapes

Slender Rod

$I_y=I_z=\frac{1}{12}m{L}^2$

Thin Rectangular Plate

$I_x=\frac{1}{12}m(b^2+c^2)$

$I_y=\frac{1}{12}m{c}^2$

$I_z=\frac{1}{12}m{b}^2$

Rectangular Prism

$I_x=\frac{1}{12}m(b^2+c^2)$

$I_y=\frac{1}{12}m(a^2+c^2)$

$I_z=\frac{1}{12}m(a^2+b^2)$

Thin Disk

$I_x=\frac{1}{2}m{r}^2$

$I_y=I_z=\frac{1}{4}m{r}^2$

Circular Cylinder

$I_x=\frac{1}{2}m{a}^2$

$I_y=I_z=\frac{1}{12}m(3a^2+L^2)$

Circular Cone

$I_x=\frac{3}{10}m{a}^2$

$I_y=I_z=\frac{3}{5}m(\frac{1}{4}{a}^2+h^2)$

Sphere

$I_x=I_y=I_z=\frac{2}{5}m{a}^2$