Polar radius ($r=\sqrt{x^2+y^2}$)

In planar polar coordinates $(r,\theta )$, the polar radius $r\ge 0$ is the Euclidean distance to the origin. It satisfies $x=r\cos \theta$ and $y=r\sin \theta$. For a differentiable plane curve with parameters $r(t),\theta (t)$, the orthogonality of radial and angular directions gives squared speed ${\dot{r}}^2+r^2{\dot{\theta }}^2$.