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Moment of Inertia of a Rectangle

      
moment of inertia Rec Plane 9

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

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

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

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

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

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

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

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

\( I_{x1} \;=\; \dfrac {1}{3} \cdot m \cdot w^2 \)

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

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

\( I_{y1} \;=\; \dfrac {1}{3} \cdot l^3\cdot w \) 

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

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

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