Introduction to Classical Mechanics · Problem 3.23

Using F = ma — Morin

Physics — Mechanics · angular_force

Problem

A force

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

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

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

. Show that

\dot{r} = \sqrt{A \ln r + B}

, where

A

and

B

are constants of integration, determined by the initial conditions. (There's nothing all that physical about this force. It simply makes the

F = ma

equations solvable.)