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I've got a question. How do we get this expression for the velocity:

[itex]\dot\vec{r}=\dot{r}+\frac{l^2}{m^2r^2}[/itex], where l is the angular impulse of force

I thought we could do it like this:

[itex]{\vec{l}}^2=l^2=(\vec{r}\times{m\dot\vec{r}})^2=m^2|\vec{r}|^2|\dot\vec{r}|^2-(\vec{r}\bullet{m\dot\vec{r}})^2=

m^2r^2{\dot\vec{r}}^2-(\vec{r}\bullet{m{\dot\vec{r}})^2[/itex]

We can't simply write:[itex]{\dot\vec{r}}^2={\dot{r}}^2[/itex], since then l=0. But why? Which rule forbids that equality. Similarly we can't treat the scalar product above as we would wish to. So how should one proceed in this case?

Thanks

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# Homework Help: Expression for velocity

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