I am having a few doubts while writing relationship between angular speed and linear speed ,in the reference frame of a moving observer .
Suppose at an instant, car A is heading towards car B with velocity 'v'. Car B is moving towards right with velocity 'u' ,i.e along positive x-axis . The instantaneous distance between A and B is 's' .
What is the relationship between the different parameters at this instant ?
The Attempt at a Solution
In the reference frame of car A ,the car B is rotating with angular velocity ω ,and translating with velocity ucosθ-v .
So , uT = sω where uT=usinθ is the tangential speed of car B .
Now,my confusion is angular speed is the time rate of change of angle .But which angle ? Is it θ or α or something else?
If it is θ then $$ s\dotθ = -usinθ $$ . If it is α ,then $$ s\dotα = usinθ $$ .
While dealing with angular speeds,I have difficulty in determining the angle ,whose time rate of change is ω.
I am not sure if what I have written makes sense .
I would be grateful if somebody could reflect his/her thoughts on this .