# Moment of Inertia of a Circle

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Formulas that use Circle, Hollow Plane

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

### Where:

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

$$\large{ m }$$ = mass

$$\large{ r }$$ = radius

## Formulas that use Circle, Solid Plane

 $$\large{ I_z = \frac {1}{2}\; m \; r^2 }$$ $$\large{ I_z = \frac {1}{2}\; \pi \; r^4 }$$ $$\large{ I_x = I_y = \frac {1}{4} \;m \; r^4 }$$ $$\large{ I_x = I_y = \frac {1}{4}\; \pi \; r^4 }$$ $$\large{ I_x = I_y = \frac {1}{64}\; d^4 }$$

### Where:

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

$$\large{ d }$$ = diameter

$$\large{ m }$$ = mass

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius