Relationship between linear and angular velocity?

Question

Let us assume that car is going straight on a road with no turns, now let a observer observe it. According to the relation v=rω there should be some angular velocity or angular displacement. But where is this angular velocity or displacement?

Answer 1

Draw a line joining the observer and the car. The line clearly changes over time as the car moves. Set up a pair of co-ordinate axes, with the observer at the origin. At any instant $t$, the line that you drew would have some length $r(t)$ and some angular position $\theta(t)$ (the angle it makes with your chosen x-axis).

The relation $v(t)=r(t)w(t)$ is satisfied, where $w(t)=\frac{d\theta}{dt}$