# 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.

## Solid Sphere formula\(\large{ I = \frac {2}{5} \; m \; r^2 }\) ## Hollow Sphere formula\(\large{ I = \frac {2}{3} \; m \; r^2 }\) ## Hollow Core Sphere formula\(\large{ I = \frac {2}{5} \; m \; \left( \frac { r_2^5 \;-\; r_1{^5} } { r_2{^3} \;-\; r_1{^3} } \right) }\) Where: \(\large{ I }\) = moment of inertia \(\large{ m }\) = mass \(\large{ r }\) = radius \(\large{ r_1 }\) = radius \(\large{ r_2 }\) = radius |