# Moment of Inertia of a Cylinder

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Hollow Cylinder formula

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

### Where:

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

$$\large{ m }$$ = mass

$$\large{ r }$$ = radius

## Solid Cylinder formulas

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

### Where:

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

$$\large{ l }$$ = length

$$\large{ m }$$ = mass

$$\large{ r }$$ = radius

## Hollow Core Cylinder formulas

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

### Where:

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

$$\large{ l }$$ = length

$$\large{ m }$$ = mass

$$\large{ r_1 }$$ = radius

$$\large{ r_2 }$$ = radius