Moment of Inertia of a Sphere

This calculation is for the moment of inertia of a sphere.  There are three separate calculations:  a solid sphere, a hollow sphere and a hollow core sphere.  The difference between a hollow sphere and a hollow core sphere is a hollow sphere has a thin shell, or a thickness that is neglible.  Because a sphere is the same dimensions in every dimension, the moment of inertia is the same about every axis.

  

Moment of Inertia of a Sphere Formula, Solid Sphere
\( I = \frac {2}{5} \; m \; r^2 \)
Symbol	English	Metric
\(\large{ I }\) = Moment of Inertia	\(lbm\;/\;ft^2-sec\)	\(kg\;/\;m^2\)
\(\large{ m }\) = Mass	\( lbm \)	\( kg \)
\(\large{ r }\) = Radius	\( in \)	\( mm \)

 

 

Moment of Inertia of a Sphere Formula, Hollow Sphere
\( I = \frac {2}{3} \; m \; r^2 \)
Symbol	English	Metric
\(\large{ I }\) = Moment of Inertia	\(lbm\;/\;ft^2-sec\)	\(kg\;/\;m^2\)
\(\large{ m }\) = Mass	\( lbm \)	\( kg \)
\(\large{ r }\) = Radius	\( in \)	\( mm \)

    

Moment of Inertia of a Sphere Formula, Hollow Core Sphere
\( I = \frac {2}{5} \; m \; \left( \; r_2^5 \;-\; r_1{^5} \;/\; r_2{^3} \;-\; r_1{^3}\;  \right)   \)
Symbol	English	Metric
\(\large{ I }\) = Moment of Inertia	\(lbm\;/\;ft^2-sec\)	\(kg\;/\;m^2\)
\(\large{ m }\) = Mass	\( lbm \)	\( kg \)
\(\large{ r }\) = Radius	\( in \)	\( mm \)
\(\large{ r_1 }\) = Radius	\( in \)	\( mm \)
\(\large{ r_2 }\) = Radius	\( in \)	\( mm \)