# Moment of Inertia of an Annulus

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Annulus are two circles that have the same center.

### Annulus, Solid Plane formula

$$\large{ I_z = \frac {\pi}{2} \; \left( r_2{^4} - r_1{^4} \right) }$$

$$\large{ I_x = I_y = \frac {\pi}{4} \; \left( r_2{^4} - r_1{^4} \right) }$$

$$\large{ I_x = I_y = \frac {\pi}{64}\; D^4 - \frac {\pi}{64} \;d^4 }$$

Where:

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

$$\large{ d }$$ = inside diameter

$$\large{ D }$$ = outside diameter

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

$$\large{ r_1 }$$ = radius

$$\large{ r_2 }$$ = radius