Coordenadas Polares

$\displaystyle \vec{r} = {\color{myblue}x} \, {\color{myred}\hat{x}} + {\color{myblue}y} \, {\color{myred}\hat{y}} \quad \quad \quad$	$\textstyle ,$	$\displaystyle \quad \quad \quad \vec{r} = {\color{mygreen}r} \, {\color{myred}\hat{r}}$
$\displaystyle {\color{myblue}x} = {\color{mygreen}r \, {\rm cos} \theta} \quad \quad \quad \quad$	$\textstyle ,$	$\displaystyle \quad \quad \quad {\color{mygreen}r} = {\color{myblue}\sqrt{x^2 + y^2}}$
$\displaystyle {\color{myblue}y} = {\color{mygreen}r \, {\rm sen} \theta} \quad \quad \quad \quad$	$\textstyle ,$	$\displaystyle \quad \quad \quad {\color{mygreen}{\rm tan} \theta} = {\color{myblue}\frac{y}{x}}$

$\displaystyle {\color{myred}\hat{r}}$	$\textstyle =$	$\displaystyle {\color{myred}\hat{x}} \, {\rm cos} \theta + {\color{myred}\hat{y}} \, {\rm sen} \theta$
$\displaystyle {\color{myred}\hat{\theta}}$	$\textstyle =$	$\displaystyle - {\color{myred}\hat{x}} \, {\rm sen} \theta + {\color{myred}\hat{y}} \, {\rm cos} \theta$

Note que, quando consideramos uma trajetória qualquer, tanto o raio quanto o ângulo podem ser funções do tempo.