A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle of $30^{\circ}

Question

A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle of $30^{\circ}$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in $\mathrm{rad} \mathrm{s}^{-1}$ ) will be ( $g=10 \mathrm{~m} / \mathrm{s}^{-2}$ )

Professor PC Thomas Classes · Answer

Conservation of energy: $mg\frac{L}{2}\sin(30^{\circ}) = \frac{1}{2} I \omega^2$. $I = mL^2/3$. Solves to $\omega = \sqrt{30}$ rad/s.