Moment of Inertia of an Annulus

on 25 March 2018. 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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