Q: A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω. Its centre of mass rises to a maximum height of

Sol: $\large m g h = \frac{1}{2}I \omega^2$

$\large m g h = \frac{1}{2} (\frac{m l^2}{3}) \omega^2$

$\large h = \frac{l^2 \omega^2}{6 g}$