Introduction to Classical Mechanics · Problem 3.68

Oscillations — Morin

Physics — Mechanics · polar-coordinates-force

Problem

A force

F_\theta = 3m\dot{r}\dot{\theta}

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

F_\theta = 3m\dot{r}\dot{\theta}

. Show that

\dot{r} = \pm\sqrt{Ar^4 + B}

, where

A

and

B

are constants of integration, determined by the initial conditions. Also, show that if the particle starts with

\dot{\theta} \neq 0

and

\dot{r} > 0

, it reaches

r = \infty

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.)