Moment of Inertia of a Cube

This calculation is for the moment of inertia of a cube.  For the purposes of this calculation, a cube can have three equal sides or it can have three non-equal sides.  The moment of inertia is calculated three different ways, about the center of the I_height, I_width and about the end I_length directions: Z-axis, Y-axis and X-axis, respectively.

 

Moment of Inertia of a Cube formulas
\( I_h \;=\; \frac {1}{12} \; m \; ( l^2  + w^2 ) \)  \( I_l \;=\; \frac {1}{12} \; m \; ( h^2  + w^2 ) \)  \( I_w \;=\; \frac {1}{12} \; m \; ( l^2  + h^2 ) \)
Symbol	English	Metric
\( I \) = Moment of Inertia	\(lbm \;/\; ft^2-sec\)	\(kg \;/\; m^2\)
\( h \) = Height	\( in \)	\( mm \)
\( l \) = Length	\( in \)	\( mm \)
\( m \) = Mass	\( lbm \)	\( kg \)
\( w \) = Width	\( in \)	\( mm \)