Question

particle P satisfy the differential equation
(c is a constant vector) dr/dt = c x r . Show that P moves with a constant speed on a circular path

Answer 1

\[\Large \frac{d\mathbf{r}}{dt}=\mathbf{c}\times \mathbf{r}\]

Answer 2

Show that the equation is satisfied by
\[ \vec{r}(t) =a <\cos(\omega t), \sin(\omega t) > \]
where a and omega are constants.

Answer 3

is there other solution that satisfy the equation? if not, why?

Answer 4

and is there any other way to solve this question without explicitly stating the components of r ?

Answer 5

You can first verify that the magnitude of the velocity vector remains constant, and then that the magnitude of the position vector remains constant as well.

Answer 6

give me clue how to verify that the magnitude of the velocity vector remains constant

Answer 7

\[ \frac{d}{dt} v^2 = \frac{d}{dt} |\textbf{v}\cdot \textbf{v}| = 2\textbf{v}\cdot \frac{d \textbf{v}}{dt} \]

Answer 8

oh wow, that worked, how do you see that coming? and last question, showing that it is circular