Motion in Plane Polar Coordinates

We describe motion using:

• Radial coordinate: $r$
• Angular coordinate: $\theta$

Position Vector

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

Velocity

$$ \vec{v} = \dot{r} \hat{r} + r\dot{\theta} \hat{\theta} $$

Acceleration

$$ \vec{a} = (\ddot{r} - r\dot{\theta}^2)\hat{r} + (r\ddot{\theta} + 2\dot{r}\dot{\theta})\hat{\theta} $$