# Moment of Inertia of a Cylinder

on . Posted in Classical Mechanics

### Moment of Inertia of a Cylinder Formula, Hollow Cylinder

$$I_z = m \; r^2$$
Symbol English Metric
$$I$$ = moment of inertia $$lbm \;/\; ft^2-sec$$ $$kg \;/\; m^2$$
$$m$$ = mass $$lbm$$ $$kg$$
$$r$$ = radius $$in$$ $$mm$$

### Moment of Inertia of a Cylinder Formulas, Solid Cylinder

$$I_z = \frac{1}{2}\; m \; r^2$$

$$I_x = I_y = \frac {1}{12} \;m \; ( 3\;r{^2} + l^2 )$$

Symbol English Metric
$$\large{ I }$$ = moment of inertia $$lbm \;/\; ft^2-sec$$ $$kg \;/\; m^2$$
$$\large{ l }$$ = length $$in$$ $$mm$$
$$\large{ m }$$ = mass $$lbm$$ $$kg$$
$$\large{ r }$$ = radius $$in$$ $$mm$$

### Moment of Inertia of a Cylinder Formulas, Hollow Core Cylinder

$$I_z = \frac {1}{12}\; m \; ( r_1{^2} + r_2{^2} )$$

$$I_x = I_y = \frac {1}{12} \;m \; ( 3 \; ( r_2{^2} + r_1{^2} ) + l^2 )$$
Symbol English Metric
$$\large{ I }$$ = moment of inertia $$lbm \;/\; ft^2-sec$$ $$kg \;/\; m^2$$
$$\large{ l }$$ = length $$in$$ $$mm$$
$$\large{ m }$$ = mass $$lbm$$ $$kg$$
$$\large{ r_1 }$$ = radius $$in$$ $$mm$$
$$\large{ r_2 }$$ = radius $$in$$ $$mm$$

Tags: Moment of Inertia