Mass Moments Of Inertia Of Common Geometric Shapes

Slender Rod

$I_{y} = I_{z} = \frac{1}{12} m L^{2}$

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

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

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

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

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

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

$I_{x} = \frac{1}{2} m r^{2}$

$I_{y} = I_{z} = \frac{1}{4} m r^{2}$

$I_{x} = \frac{1}{2} m a^{2}$

$I_{y} = I_{z} = \frac{1}{12} m (3 a^{2} + L^{2})$

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

$I_{y} = I_{z} = \frac{3}{5} m (\frac{1}{4} a^{2} + h^{2})$

$I_{x} = I_{y} = I_{z} = \frac{2}{5} m a^{2}$