Classical Mechanics (Kibble & Berkshire) · Problem 2.12

Newton's laws of motion and the law of gravitation — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · general-particle-motion

Problem

A particle

P

moves so that its position vector

\boldsymbol{r}

satisfies the differential equation

\dot{\boldsymbol{r}} = \boldsymbol{c} \times \boldsymbol{r},

where

\boldsymbol{c}

is a constant vector. Show that

P

moves with constant speed on a circular path. [Hint. Take the dot product of the equation first with

\boldsymbol{c}

and then with

\boldsymbol{r}