A uniform rod of length \( 2 a \) is held with one end resting on a smooth horizontal table maki...

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A uniform rod of length \( 2 a \) is held with one end resting on a smooth horizontal table making an angle \( \alpha \) with the vertical. Show that when the rod is released, its angular velocity when it makes an angle \( \theta \) with the vertical is given by
\[
\omega=\left[\frac{6 g(\cos \alpha-\cos \theta)}{\left(1+3 \sin ^{2} \alpha\right)}\right]
\]
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