Question

A particle is moving parallel to x-axis as shown in fig. such that they component of its position vector is constant at all instants and is equal to 'b'. Find the angular velocity of the particle about the origin when its radius vector makes an angle $\theta$ with the x-axis.

Answer 1

$|\overrightarrow{r}|\sin \theta =b$

$|\overrightarrow{r}|=\frac{b}{\sin \theta }$

$\omega =\frac{V\sin \theta }{|\overrightarrow{r}|}=\frac{V\sin \theta }{\left(\frac{b}{\sin \theta }\right)}=\frac{V{\sin }^2\theta }{b}$