Moment of Inertia of a Cube

on . Posted in Classical Mechanics

moment of inertia Cube 2This 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

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

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

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

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 \( in \) \( mm \)

 

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Tags: Moment of Inertia