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.

 

   

 

moment of inertia Rod 1Moment of Inertia of a Thin Rod Formula, End Axis

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

Where:

\(\large{ I }\) = moment of inertia

\(\large{ l }\) = length

\(\large{ m }\) = mass

 

Moment of Inertia of a Thin Rod Formula, Center Axis

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

Where:

\(\large{ I }\) = moment of inertia

\(\large{ l }\) = length

\(\large{ m }\) = mass

 

Tags: Equations for Inertia Equations for Moment of Inertia