Classical Mechanics · Central-force motion and scattering
Radial speed contributes no angular momentum
Problem
In plane polar coordinates, a $0.800\,\mathrm{kg}$ particle is at $r=2.50\,\mathrm m$ with $\dot r=-1.20\,\mathrm{m/s}$ and $r\dot\phi=4.00\,\mathrm{m/s}$. Find the signed angular momentum for increasing $\phi$, the areal velocity, and the value each would have if only $\dot r$ changed sign.
Hint
The cross product of $\mathbf r$ with $\dot r\hat{\mathbf r}$ is zero.
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