# Mass Moments Of Inertia Of Common Geometric ShapesEdit

## Slender RodEdit

$I_x = 0$

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

## Thin Quarter-Circular RodEdit

$I_x = I_z = mr^2 (\frac {1}{2} - \frac {4}{\pi^2})$

$I_y = mr^2 (1 - \frac {8}{\pi^2})$

## Thin RingEdit

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

$I_z = mr^2$

## SphereEdit

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

## HemisphereEdit

$I_x = I_y = \frac {83}{320} mr^2$

$I_z = \frac {2}{5} mr^2$

## Thin Circular DiskEdit

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

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

## Rectangular PrismEdit

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

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

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

## Right Circular CylinderEdit

$I_x = I_y = \frac {1}{12} m( 3r^2 + h^2)$

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

## Right Half CylinderEdit

$I_x = \frac {1}{12} mh^2 + mr^2( \frac {1}{4} - \frac {16}{9\pi^2})$

$I_y = \frac {1}{12} mh^2 + \frac {1}{4}mr^2$

$I_z = mr^2( \frac {1}{2} - \frac {16}{9\pi^2})$

## Thin Rectangular PlateEdit

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

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

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

## Right Circular ConeEdit

$I_x = I_y = \frac {3}{80} m ({4}{r^2} + h^2)$

$I_z = \frac {3}{10} mr^2$

## Right TetrahedronEdit

$I_x = \frac {3}{80} m (b^2+c^2)$

$I_y = \frac {3}{80} m (a^2+c^2)$

$I_z = \frac {3}{80} m (a^2+b^2)$