--- # Group Discussion 4-2 Consider the generic position vector $\vec{R}$ for a particle in 2D space. Find the velocity vector $\vec{V}$ for the particle in Cartesian coordinates ($x$, $y$). ## What happens in plane polar coordinates? $$\vec{R} = r \hat{r} + \phi \hat{\phi}$$ Note: $$\hat{r} = \cos(\phi) \hat{x} + \sin(\phi) \hat{y}$$ $$\hat{\phi} = -\sin(\phi) \hat{x} + \cos(\phi) \hat{y}$$