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Moment of Inertia of a Rectangle

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moment of inertia Rec Plane 9

Moment of Inertia of a Rectangle Formulas, Solid Plane, z Axis

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

\( I_z \;=\; \frac {1}{12} \;l\;w \; \left( l^2  + w^2 \right)  \) 

\( I_{z1} \;=\; \frac {1}{12}\;m \; \left( 4\;l^2  + w^2 \right) \) 
Symbol English Metric
\( I \) = Moment of Inertia \(lbm\;/\;ft^2-sec\) \(kg\;/\;m^2\)
\( l \) = Length \( in \) \( mm \)
\( m \) = Mass \( lbm \) \( kg \)
\( w \) = Width \( in \) \( mm \)

    

Moment of Inertia of a Rectangle Formulas, Solid Plane, x Axis

\( I_x \;=\; \frac {1}{12}\; l\;w^3 \) 

\( I_x \;=\; \frac {1}{12}\; m \; l^2 \)  

\( I_{x1} \;=\; \frac {1}{3}\; l\;w^3 \) 

\( I_{x1} \;=\; \frac {1}{3}\; m \; w^2 \)
Symbol English Metric
\( I \) = Moment of Inertia \(lbm\;/\;ft^2-sec\) \(kg\;/\;m^2\)
\( l \) = Length \( in \) \( mm \)
\( m \) = Mass \(\large{ lbm }\) \(\large{ kg }\)
\( w \) = Width \( in \) \( mm \)

  

Moment of Inertia of a Rectangle Formulas, Solid Plane, y Axis

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

\( I_{y1} \;=\; \frac {1}{3}\; l^3\;w \) 
Symbol English Metric
\( I \) = Moment of Inertia \(lbm\;/\;ft^2-sec\) \(kg\;/\;m^2\)
\( l \) = Length \( in \) \( mm \)
\( w \) = Width \( in \) \( mm \)

   

moment of inertia Rectangle 1

Moment of Inertia of a Rectangle Formula, Hollow Core Plane, x Axis
\( I_x \;=\; ( l\;w^3\;/\;12 ) - ( l_1\;w_1{^3}  \;/\; 12 )  \) 
Symbol English Metric
\( I \) = Moment of Inertia \(lbm\;/\;ft^2-sec\) \(kg\;/\;m^2\)
\( l \) = Length \( in \) \( mm \)
\( l_1 \) = Length \( in \) \( mm \)
\( w \) = Width \( in \) \( mm \)
\( w_1 \) = Width \( in \) \( mm \)

 

Moment of Inertia of a Rectangle Formula, Hollow Core Plane, Y Axis
\( I_y \;=\; ( l^3\;w\;/\;12 ) -  ( l_1{^3} w_1\;/\;12 ) \) 
Symbol English Metric
\( I \) = Moment of Inertia \(lbm\;/\;ft^2-sec\) \(kg\;/\;m^2\)
\( l \) = Length \( in \) \( mm \)
\( l_1 \) = Length \( in \) \( mm \)
\( w \) = Width \( in \) \( mm \)
\( w_1 \) = Width \( in \) \( mm \)

 

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Tags: Moment of Inertia Rectangle

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