תאוצה בקורדינטות פולריות

\vec{r}=r\hat{r}

\frac{d\hat{r}}{dt}=\dot{\theta}\hat{\theta}\qquad\frac{d\hat{\theta}}{dt}=-\dot{\theta}\hat{r}

\vec{v}=\frac{d\vec{r}}{dt}=\frac{d\left(r\hat{r}\right)}{dt}=\frac{dr}{dt}\cdot\hat{r}+\frac{d\hat{r}}{dt}\cdot r=\dot{r}\hat{r}+r\dot{\theta}\hat{\theta}

\vec{a}=\frac{d\vec{v}}{dt}=\frac{d\left(\dot{r}\hat{r}+r\dot{\theta}\hat{\theta}\right)}{dt}=\ddot{r}\hat{r}+\dot{r}\dot{\theta}\hat{\theta}+\dot{r}\dot{\theta}\hat{\theta}+r\ddot{\theta}\hat{\theta}-r\dot{\theta}^{2}\hat{r}=\left(\ddot{r}-r\dot{\theta}^{2}\right)\hat{r}+\left(2\dot{r}\dot{\theta}+r\ddot{\theta}\right)\hat{\theta}