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## Main Question or Discussion Point

I have read that in polar coordinates, we can form the position vector, velocity, and acceleration, just as with Cartesian coordinates. The position vector in Cartesian coordinates is ##\vec{r} = r_x \hat{i} + r_y \hat{j}##. And any choice of ##r_x## and ##r_y## maps the vector to a position in the plane. How is this done with polar coordinates? Online I have read that the position vector in polar coordinates is ##\vec{r} = |r| \hat{r}##, but I don't see how this can map to any point in the plane. Don't we need an angular description as well? I don't see that in this equation.