A force Fθ = 3mr˙θ˙
Consider a particle that feels an angular force only, of the form Fθ = 3mr˙θ˙. Show that r˙ = ± Ar4+B, 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. (As in Problem 3.23, there's nothing all that physical about this force. It simply makes the F = ma equations solvable.)