- #1

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**1. Problem**

Consider a particle that feels an angular force only of the form:

F_θ = 3mr'θ'. Show that r' = ± (Ar^4 + B)^(1/2), where A and B are constants of integration, determined by the initial conditions. Also, show that if the particle starts with θ' ≠ 0 and r' > 0, it reaches r = ∞ in a finite time.

## The Attempt at a Solution

So I understand the first part of the question and can easily show r' = … using θ' = L/mr^2, where L is the angular momentum. Now my issue is with the second part. I know I probably should set up an integral to evaluate from r_0 to r = ∞. I tried starting at F_θ = 3mr'θ' = m(dθ'/dt). I think this equation is correct (although may not be what I should be using). From here I would separate variables, as 3r'dt = (1/θ')dθ'. But this doesn't seem to be right. I'm really stuck here. Any ideas ?