= Velocity in polar coordinates
{title2=$\mathbf v=\dot r\widehat{\mathbf r}+r\dot\theta\widehat{\boldsymbol\theta}$}
For a differentiable path in <plane polar coordinates> with $r>0$, the moving <unit vectors> are $\widehat{\mathbf r}=(\cos\theta,\sin\theta)$ and $\widehat{\boldsymbol\theta}=(-\sin\theta,\cos\theta)$. Differentiating the <position> $\mathbf r=r\widehat{\mathbf r}$ and using $\dot{\widehat{\mathbf r}}=\dot\theta\widehat{\boldsymbol\theta}$ proves the displayed <velocity>. Its signed radial and transverse <vector components> are $\dot r$ and $r\dot\theta$. A second differentiation gives the <acceleration in polar coordinates>. The complex representatives of the two moving <unit vectors> are $e^{i\theta}$ and $ie^{i\theta}$.
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