Moment of Inertia of an Annulus

on . Posted in Classical Mechanics

Annulus are two circles that have the same center.

 

moment of inertia Annulus 1

Moment of Inertia of an Annulus Formulas, Solid Plane

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

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

\( I_x = I_y = \frac {\pi}{64}\; D^4 -  \frac {\pi}{64} \;d^4 \) 

Symbol English Metric
\( I \) = Moment of Inertia  \(lbm\;/\;ft^2-sec\)  \(kg\;/\;m^2\)
\( d \) = Inside Diameter \( in \) \( mm \)
\( D \) = Outside Diameter \( in \) \( mm \)
\( \pi \) = Pi \(dimensionless\) \(dimensionless\)
\( r_1 \) = Radius \( in \) \( mm \)
\( r_2 \) = Radius \( in \) \( mm \)

 

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Tags: Moment of Inertia