# Moment of Inertia of a Cube

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

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 Iheight, Iwidth and about the end Ilength directions: Z-axis, Y-axis and X-axis, respectively.

## Moment of Inertia of a Cube formulas

 $$\large{ I_h = \frac {1}{12} \; m \; \left( l^2 + w^2 \right) }$$ $$\large{ I_l = \frac {1}{12} \; m \; \left( h^2 + w^2 \right) }$$ $$\large{ I_w = \frac {1}{12} \; m \; \left( l^2 + h^2 \right) }$$

### Where:

$$\large{ I }$$ = moment of inertia

$$\large{ h }$$ = height

$$\large{ l }$$ = length

$$\large{ m }$$ = mass

$$\large{ w }$$ = width