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Movimento bidimensional

$\begin{figure}\centerline{\epsfig{file=cinematica_polar.eps,width=10cm,height=7cm}}\end{figure}$

Nas coordenadas cartesianas, $\bgroup\color{myblue}$\vec{r}(t) = \{ x(t),y(t) \}$\egroup$ . Os versores $\bgroup\color{myblue}$\hat{x}$\egroup$ e $\bgroup\color{myblue}$\hat{y}$\egroup$ permanecem fixos ao longo do movimento:

$\displaystyle \vec{r} (t)$	$\textstyle =$	$\displaystyle x(t) \, {\color{myred}\hat{x}} + y(t) \, {\color{myred}\hat{y}}$
$\displaystyle \vec{v} (t)$	$\textstyle =$	$\displaystyle \frac{d \, \vec{r}(t) } {d t} \, = \, \frac{d\, x(t) }{dt} \, {\c... ...} \, = \, \dot{x} \, {\color{myred}\hat{x}} + \dot{y} \, {\color{myred}\hat{y}}$

Já em coordenadas polares temos $\bgroup\color{myblack}$\vec{r}(t) = \{ r(t), \theta(t) \}$\egroup$ , mas os versores $\bgroup\color{myblack}$\hat{r}$\egroup$ e $\bgroup\color{myblack}$\hat{\theta}$\egroup$ não estão fixos ao longo do movimento:

$\displaystyle \vec{r} (t)$	$\textstyle =$	$\displaystyle r(t) \, {\color{myred}\hat{r}(t)}$
$\displaystyle \vec{v} (t)$	$\textstyle =$	$\displaystyle \frac{d }{dt} \, r(t) \, {\color{myred}\hat{r}(t)} \, = \, \frac{... ..., {\color{myred}\hat{r}(t)} + r(t) \, \frac{d \, {\color{myred}\hat{r}(t)}}{dt}$
	$\textstyle =$	$\displaystyle \dot{r} \, {\color{myred}\hat{r}} + r \, \frac{d {\color{myred}\h... ...{\color{myred}\hat{r}} \; + \; r \, \dot{\theta} \, {\color{myred}\hat{\theta}}$

Luis Raul Weber Abramo 2002-08-08