$$
\begin{align}
\overline{a} & = \frac{d\overline{v}}{dt} = \frac{dx}{dt}\overline{i} + \frac{dy}{dt}\overline{j} = v_{x}\overline{i} + v_{y}\overline{j} \\
a & = \ddot{x} + i \ddot{y} = \ddot{r}e^{i\theta}+2\dot{r}\dot{\theta}e^{i(\theta+\pi/2)}+r\ddot{\theta}e^{i(\theta+\pi/2)} - r\dot{\theta}^{2}e^{i\theta} \\
\overline{a} & = \frac{d\overline{v}}{dt} = \dot{s}\overline{t} = \ddot{s}\overline{t} + \dot{s} \frac{d\overline{t}}{dt} = \ddot{s}\overline{t} + \frac{\dot{s}^{2}}{\rho}\overline{n}\\
\rho d\alpha & = ds \to d\alpha = \frac{ds}{\rho} \\
\frac{d\overline{t}}{dt} & = \frac{ds}{\rho dt}\overline{n} = \frac{\dot{s}}{\rho}\overline{n}
\end{align}
$$
$$||{"id":1453782121083}||$$
$\frac{1}{\rho}$ => curvatura