# Moment of Inertia of a Cylinder

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

### Hollow Cylinder formula

$$\large{ I_z = m \; r^2 }$$

### Solid Cylinder formula

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

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

### Hollow Core Cylinder formula

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

$$\large{ I_x = I_y = \frac {1}{12} \;m \; \left( 3 \; \left( r_2{^2} + r_1{^2} \right) + l^2 \right) }$$

Where:

$$\large{ I }$$ = moment of inertia

$$\large{ l }$$ = length

$$\large{ m }$$ = mass

$$\large{ r }$$ = radius

$$\large{ r_1 }$$ = radius

$$\large{ r_2 }$$ = radius