Statics/Geometric Properties of Solids

Mass Moments Of Inertia Of Common Geometric Shapes

Slender Rod

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

Thin Rectangular Plate

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

$I_y = \frac {1}{12} mc^2$

$I_z = \frac {1}{12} mb^2$

Rectangular Prism

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

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

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

Thin Disk

$I_x = \frac {1}{2} mr^2$

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

Circular Cylinder

$I_x = \frac {1}{2} ma^2$

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

Circular Cone

$I_x = \frac {3}{10} ma^2$

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

Sphere

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

further reading

• Mechanics/Rigid Bodies