Moment of Inertia of a Sphere

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

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

moment of inertia Sphere

moment of inertia Hollow Sphere

Tags: Equations for Moment of Inertia