= Acceleration in cylindrical coordinates
{title2=$\mathbf a=(\ddot r-r\dot\theta^2)\mathbf e_r+(r\ddot\theta+2\dot r\dot\theta)\mathbf e_\theta+\ddot z\mathbf e_z$}
Differentiate the <position vector> $\mathbf r=r\mathbf e_r+z\mathbf e_z$ using $\dot{\mathbf e}_r=\dot\theta\mathbf e_\theta$, $\dot{\mathbf e}_\theta=-\dot\theta\mathbf e_r$, and fixed $\mathbf e_z$. The first <derivative> is the <velocity> $\dot r\mathbf e_r+r\dot\theta\mathbf e_\theta+\dot z\mathbf e_z$; differentiating once more gives the displayed <acceleration>. In particular, $r$ times the azimuthal <acceleration> is $d(r^2\dot\theta)/dt$.
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