# Relationship between linear and angular velocity?

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?

• Feb 23, 2021 at 13:27

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 $$w(t)=\frac{d\theta}{dt}$$