Two particles $A$ and $B$ are moving as shown in figure. At this moment of time, find the angular speed of $A$ relative to $B$.

We know that

$$\begin{gathered} {\left[v_{AB}\right]}_y=v_{Ay}-v_{By} \\ =v_A\sin {\theta }_A-v_B\sin {\theta }_B \end{gathered}$$

and

 $$\begin{gathered} \omega =\frac{{\left[v_{AB}\right]}_y}{AB} \\ \omega =\left[\frac{v_A\sin {\theta }_A-v_B\sin {\theta }_B}{r}\right] \end{gathered}$$ \

                                                in clockwise direction

As there is no separation between the velocity component along $x-$axis, thus there is no specific rotation due to ${\left(v_{AB}\right)}_x={v_A\cos \theta }_A-{v_B\cos \theta }_B$.