A rod of mass 2kg and length $2 \mathrm{m}$ is rotating about its one end O with an angular velocity $\mathrm{\omega }=4$ rad/s. Find angular momentum of the rod about the axis rotation.

In pure rotational motion of a rigid body, component of total angular momentum about axis of rotation is given by

$$\begin{gathered} \mathrm{L}=\mathrm{I\omega }=\left(\frac{{\mathrm{ml}}^2}{3}\right)\mathrm{\omega } \\ \left({\mathrm{I}}_0=\frac{{\mathrm{ml}}^2}{3}\right) \end{gathered}$$

Substituting the values we have,

$$\begin{gathered} \mathrm{L}=\frac{\left(2\right)(2{)}^2}{3}\left(4\right) \\ =\frac{32}{3} \mathrm{kg}-{\mathrm{m}}^2/\mathrm{s} \end{gathered}$$

Direction of this component is perpendicular to paper in word (in right hand rule), as the rotation is clockwise.