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.

Cube, Solid, Center axis formula

\(\large{ I_h = \frac {1}{12}  m  \left( l^2  + w^2 \right) }\)

\(\large{ I_l = \frac {1}{12}  m  \left( h^2  + w^2 \right) }\)

\(\large{ I_w = \frac {1}{12}  m  \left( l^2  + h^2 \right) }\)

Where:

\(\large{ I }\) = moment of inertia

\(\large{ h }\) = height

\(\large{ l }\) = length

\(\large{ m }\) = mass

\(\large{ w }\) = width

moment of inertia Cube

Tags: Equations for Moment of Inertia