# Moment of Inertia of a Rectangle

on . Posted in Classical Mechanics

## 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 $$\large{ in }$$ $$\large{ mm }$$ 