# Moment of Inertia of a Rectangle

on . Posted in Classical Mechanics

### 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 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 $$in$$ $$mm$$