Moment of Inertia of a Thin Rod

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 I_c and about the end I_e.

 

Moment of Inertia of a Thin Rod Formula, End Axis
\( I_e \;=\; \frac{1}{3} \; m \; l^2 \)     (End Axis) \( I_c \;=\; \frac{1}{12} \; m \; l^2 \)     (Center Axis)
Symbol	English	Metric
\(\large{ I }\) = Moment of Inertia	\(lbm \;/\; ft^2-sec\)	\(kg \;/\; m^2\)
\(\large{ l }\) = Length	\( in \)	\( m \)
\(\large{ m }\) = Mass	\( lbm \)	\( kg \)