# Moment of Inertia of a Thin Rod

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

This calculation is for the moment of inertia of a thin rod.  For the purposes of this calculation, a thin rod is one where the diameter of the rod is neglible.  The moment of inertia is calculated two different ways, about the center Ic and about the end Ie.

### Thin Rod, End Axis formula

$$\large{ I_e = \frac {1}{3} \; m \; l^2 }$$

### Thin Rod, Center Axis formula

$$\large{ I_c = \frac {1}{12} \; m \; l^2 }$$

Where:

$$\large{ I }$$ = moment of inertia

$$\large{ l }$$ = length

$$\large{ m }$$ = mass