(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a particle that feels an angular force only, of the form F[tex]_{\theta}[/tex] = 3m[tex]\dot{r}[/tex][tex]\dot{\theta}[/tex]. Show [tex]\dot{r}[/tex]=[tex]\pm[/tex][tex]\sqrt{Ar^{4}+B}[/tex], where A and B are constants of integration, determined by the initial conditions. Also, show that if the particle starts with [tex]\dot{\theta}[/tex][tex]\neq[/tex]0 and [tex]\dot{r}[/tex]>0, it reaches r=[tex]\infty[/tex] in a finite time.

2. Relevant equations

F[tex]_{r}[/tex]=m([tex]\ddot{r}[/tex]-r[tex]\dot^{\theta}[/tex]^2)=0

F[tex]_{\theta}[/tex]=m(r[tex]\ddot{\theta}[/tex]+2[tex]\dot{r}[/tex][tex]\dot{\theta}[/tex])

3. The attempt at a solution

I've already shown that [tex]\dot{r}[/tex]=[tex]\pm[/tex][tex]\sqrt{Ar^{4}+B}[/tex]. What I need to do now is show that it reaches r=[tex]\infty[/tex] in a finite time. I'm not sure what I need to do here... any thoughts?

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# Homework Help: Motion in a Plane Problem

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