Question

A rod of mass $m$ and length $l$ is connected with a light rod of length $l$. The composite rod is made to rotate with angular velocity $\omega$ is shown in the figure. Find the total kinetic energy.

Answer 1

Total kinetic energy
$K_{total}=K_{translational}+K_{rotational}$
$=\frac{9}{8}m{\omega }^2{l}^2+\frac{1}{24}m{\omega }^2{l}^2=\frac{7}{6}m{\omega }^2{l}^2$.