Question

Consider a body, shown in figure, consisting of two identical balls, each of mass $2\text{kg}$ connected by a light rigid rod. If an impulse, $J=20\text{kg - m/s}$ is imparted to the body at one of its end, then angular velocity will be $\left(\text{in rad/s}\right)$

Answer 1

We know that, when impulse is provided to the free body, then body starts rotating about axis passing through it's centre of mass.
Centre of mass of the given body will lie at middle of light rigid rod connecting the two identical balls.
Let us suppose, angular velocity after impulse is provided is $\omega$.

We know,
Angular impulse = change in angular momentum
$\Rightarrow 20\times \frac{5}{2}=[2\times {\left(\frac{5}{2}\right)}^2\times \omega +2\times {\left(\frac{5}{2}\right)}^2\times \omega ]-[0+0]$
$L=I\omega$ and Angular impulse $=r_{\perp }\times J$
$\Rightarrow 50=25\omega$
$\Rightarrow \omega =2\text{rad/s}$
The angular velocity is $2\text{rad/s}$