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Show that the kinetic energy of a uniform rod of mass \(m\) is
\[ T  = \frac{1}{6}m(\vec{u}.\vec{u} + \vec{u}.\vec{v}+\vec{v}.\vec{v} )\]
where \(\vec{u}\) and \(\vec{v}\) are the velocities of the two ends.

Woodhouse

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