A particle is subjected to a radial force: $\vec{F}=f(\vec{|r|}) \hat{e_r}$.
How do we show that $\vec{F}×\vec{L}=-mf(r)[-\vec{r}\dot r+r \dot {\vec{r}}]$
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2 Answers
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Hint.
$\vec{F} \times (\vec{r}\times \vec{p})=\vec{r}(\vec{F}\cdot\vec{p})-\vec{p}(\vec{F}\cdot \vec{r})$ by BAC-CAB rule, aka the vector triple product.
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You will find that hard to solve because the cross product is not well defined in spherical coordinates.
That means any cross product you come across in spherical coordinates you will want to convert to cartesian coordinates, then once you've done the cross product revert the answer back to polar.
It is usually a bit tedious.
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$\begingroup$ Can you suggest the start like I don't know how to start and where to go $\endgroup$ Sep 29 at 7:55