Question

two particles $1$ and $2$ move with velocities $\overline{v_1}$ and $\overline{v_2}$ making the angles ${\theta }_1$ and ${\theta }_2$ with the line joining them, respectively. Find angular velocity of $2$relative to $1$.

Answer 1

Let us find the relative velocity between the particles perpendicular to the line joining them the velocity of $1$ relative to velocity of $2$ is

${\overline{v}}_{12}={\overline{v}}_1-{\overline{v}}_2$

Then ${\overline{v}}_{{12}_y}=$${\overline{v}}_{1_y}-{\overline{v}}_{2_y}$$=-v_1\sin {\theta }_1\hat{j}-v_2\sin {\theta }_2\hat{j}$

hence , ${\omega }_{1}2=\frac{|{\overline{v}}_{{12}_y}|}{l}$

Substituting $|{\overline{v}}_{{12}_y}|$,we have

${\omega }_{12}=\frac{v_1\sin {\theta }_1+v_2\sin {\theta }_2}{l}$