Moment of Inertia of an Annulus

on . Posted in Classical Mechanics

moment of inertia Annulus 1Annulus are two circles that have the same center.

 

Moment of Inertia of an Annulus Formulas, Solid Plane

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

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

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

Symbol English Metric
\(\large{ I }\) = moment of inertia  \(\large{\frac{lbm}{ft^2-sec}}\)  \(\large{\frac{kg}{m^2}}\)
\(\large{ d }\) = inside diameter \(\large{ in }\) \(\large{ mm }\)
\(\large{ D }\) = outside diameter \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi \(\large{dimensionless}\)
\(\large{ r_1 }\) = radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ r_2 }\) = radius \(\large{ in }\) \(\large{ mm }\)

 

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Tags: Moment of Inertia