Moment of Inertia of a Rectangle

on . Posted in Classical Mechanics

moment of inertia Rectangle 1moment of inertia Rec Plane 9

 

 

 

 

 

 

 

 

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

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

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

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

Symbol English Metric
\(\large{ I }\) = moment of inertia \(\large{\frac{lbm}{ft^2-sec}}\) \(\large{\frac{kg}{m^2}}\)
\(\large{ l }\) = length \(\large{ in }\) \(\large{ mm }\)
\(\large{ m }\) = mass \(\large{ lbm }\) \(\large{ kg }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

 

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

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

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

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

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

Symbol English Metric
\(\large{ I }\) = moment of inertia \(\large{\frac{lbm}{ft^2-sec}}\) \(\large{\frac{kg}{m^2}}\)
\(\large{ l }\) = length \(\large{ in }\) \(\large{ mm }\)
\(\large{ m }\) = mass \(\large{ lbm }\) \(\large{ kg }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

  

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

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

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

Symbol English Metric
\(\large{ I }\) = moment of inertia \(\large{\frac{lbm}{ft^2-sec}}\) \(\large{\frac{kg}{m^2}}\)
\(\large{ l }\) = length \(\large{ in }\) \(\large{ mm }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)

  

Moment of Inertia of a Rectangle Formula, Hollow Core Plane, x Axis

\(\large{ I_x =  \frac {l\;w^3}{12} - \frac {l_1\;w_1{^3}  }{12}  }\) 
Symbol English Metric
\(\large{ I }\) = moment of inertia \(\large{\frac{lbm}{ft^2-sec}}\) \(\large{\frac{kg}{m^2}}\)
\(\large{ l }\) = length \(\large{ in }\) \(\large{ mm }\)
\(\large{ l_1 }\) = length \(\large{ in }\) \(\large{ mm }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)
\(\large{ w_1 }\) = width \(\large{ in }\) \(\large{ mm }\)

 

Moment of Inertia of a Rectangle Formula, Hollow Core Plane, Y Axis

\(\large{ I_y = \frac {l^3\;w}{12} - \frac {l_1{^3} w_1}{12} }\) 
Symbol English Metric
\(\large{ I }\) = moment of inertia \(\large{\frac{lbm}{ft^2-sec}}\) \(\large{\frac{kg}{m^2}}\)
\(\large{ l }\) = length \(\large{ in }\) \(\large{ mm }\)
\(\large{ l_1 }\) = length \(\large{ in }\) \(\large{ mm }\)
\(\large{ w }\) = width \(\large{ in }\) \(\large{ mm }\)
\(\large{ w_1 }\) = width \(\large{ in }\) \(\large{ mm }\)

 

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Tags: Moment of Inertia Equations