Moment of Inertia of an Annulus

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

moment of inertia Annulus 1Annulus 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

 

Tags: Equations for Moment of Inertia