Moment of Inertia of a Rectangle

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

moment of inertia Rectangle 1moment of inertia Rec Plane 9rectangle, Solid Plane, z Axis formula

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

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

(Eq. 3)  \(\large{ I_{z1} = \frac {1}{12} m  \left( 4l^2  + w^2 \right) }\)         

rectangle, Solid Plane, x Axis formula

(Eq. 4)  \(\large{ I_x = \frac {1}{12} lw^3 }\)         

(Eq. 5)  \(\large{ I_x = \frac {1}{12} m  l^2 }\)         

(Eq. 6)  \(\large{ I_{x1} = \frac {1}{3} lw^3 }\)              

(Eq. 7)  \(\large{ I_{x1} = \frac {1}{3} m  w^2 }\)         

rectangle, Solid Plane, y Axis formula

(Eq. 8)  \(\large{ I_y = \frac {1}{12} l^3w }\)         

(Eq. 9)  \(\large{ I_{y1} = \frac {1}{3} l^3w }\)         

rectangle, Hollow Core Plane, x Axis formula

(Eq. 10)  \(\large{ I_x =  \frac {lw^3}{12} - \frac {l_1w_1{^3}  }{12}  }\)         

rectangle, Hollow Core Plane, Y Axis formula

(Eq. 11)  \(\large{ I_y = \frac {l^3w}{12} - \frac {l_1{^3} w_1}{12} }\)         

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