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 Translational kinetic energy.

Answer 1

Translational kinetic energy of rod,
$K_{translational}=\frac{1}{2}m{v}_c^2$
Velocity of centre of mass $v_c=\omega \left(\frac{3}{2}l\right)$
Hence $K_{translational}=\frac{1}{2}m{\left[\frac{3\omega l}{2}\right]}^2=\frac{9}{8}m{\omega }^2{l}^2$.