I'm trying to solve a problem which includes a spinning object and I want to find it's velocity vector with respect to an object moving in a straight line on the the x axis with constant velocity.
I can represent the spinning object's velocity in cartesian coordinates and subtract from it the velocity of the moving object. But that is a method that doesn't scale if I have a more complex spinning shape. Is there a way to convert the object moving in a straight line to polar coordinates?
What is the x basis vector in polar vector form?
Edit: figured it out. The relation I was looking for was:
$\hat{x}=cos(\theta)\hat{r}-sin(\theta)\hat{\theta}$