Question

A rigid body is made of three identical uniform thin rods each of length $L$ fastened together in the form of letter $H$. The body is free to rotate about a fixed horizontal axis $AB$ that passes through one of the legs of the $H$. The body is allowed to fall from rest from a position in which the plane of $H$ is horizontal. What is the angular speed of the body, when the plane of $H$ is vertical.

Answer 1

Here $KE=mg\times \frac{l}{2}+mg\times l=\frac{3}{2}mglI=\frac{1}{3}m{l}^2+m{l}^2=\frac{4}{3}m{l}^{2}K.E=\frac{1}{2}{I\omega }^2=\frac{3}{2}mgl=\frac{1}{2}\times \frac{4}{3}m{l}^2{\omega }^2\Rightarrow \omega =\frac{3}{2}\sqrt{\frac{g}{l}}$