Moment of Inertia of a Rectangle

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

moment of inertia Rectangle 1moment of inertia Rec Plane 9Formulas that use rectangle, Solid Plane, z Axis

\(\large{ I_z = \frac {1}{12}\; m \; \left( l^2  + w^2 \right)  }\)   
\(\large{ I_z = \frac {1}{12} \;l\;w \; \left( l^2  + w^2 \right)  }\)   
\(\large{ I_{z1} = \frac {1}{12}\;m \; \left( 4\;l^2  + w^2 \right) }\)   

 

Formulas that use rectangle, Solid Plane, x Axis

\(\large{ I_x = \frac {1}{12}\; l\;w^3 }\)   
\(\large{ I_x = \frac {1}{12}\; m \; l^2 }\)    
\(\large{ I_{x1} = \frac {1}{3}\; l\;w^3 }\)   
\(\large{ I_{x1} = \frac {1}{3}\; m \; w^2 }\)  

         

Formulas that use rectangle, Solid Plane, y Axis

\(\large{ I_y = \frac {1}{12}\; l^3\;w }\)   
\(\large{ I_{y1} = \frac {1}{3}\; l^3\;w }\)   

  

Formulas that use rectangle, Hollow Core Plane, x Axis

\(\large{ I_x =  \frac {l\;w^3}{12} - \frac {l_1\;w_1{^3}  }{12}  }\)   

       

Formulas that use rectangle, Hollow Core Plane, Y Axis

\(\large{ I_y = \frac {l^3\;w}{12} - \frac {l_1{^3} w_1}{12} }\)   

 

Where:

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

\(\large{ l }\) = length

\(\large{ l_1 }\) = length

\(\large{ m }\) = mass

\(\large{ w }\) = width

\(\large{ w_1 }\) = width

 

Tags: Equations for Moment of Inertia