quality:correction
Compound pendulum

For example, a rigid uniform rod of length ℓ {\displaystyle \ell } pivoted about one end has moment of inertia I O = 1 3 m ℓ 2 {\textstyle I_{O}={\frac {1}{3}}m\ell ^{2}}. The center of mass is located at the center of the rod, so r C M = 1 2 ℓ {\textstyle r_{\mathrm {CM} }={\frac {1}{2}}\ell } Substituting these values into the above equation gives T = 2 π 2 3 ℓ g {\textstyle T=2\pi {\sqrt {\frac {{\frac {2}{3}}\ell }{g}}}}. This shows that a rigid rod pendulum has the same period as a simple pendulum of two-thirds its length.