{title2=$\mathbf a=(\ddot r-r\dot\theta^2)\widehat{\mathbf r}+(2\dot r\dot\theta+r\ddot\theta)\widehat{\boldsymbol\theta}$}

Differentiating $\mathbf r=r\widehat{\mathbf r}$ twice and using $\dot{\widehat{\mathbf r}}=\dot\theta\widehat{\boldsymbol\theta}$ and $\dot{\widehat{\boldsymbol\theta}}=-\dot\theta\widehat{\mathbf r}$ gives the displayed <acceleration>. For a <central force>, its angular component vanishes, so $r^2\dot\theta$ is constant and expresses <conservation of angular momentum>.


 Acceleration in polar coordinates

ID: acceleration-in-polar-coordinates