Question

Polar Coordinates and Planetary Motion Question

Answer 1

At the point (1,2) velocities in the direction _____ will give \(\Large \frac{dr}{dt} = 0\). Velocities in the direction ______ will give \(\Large \frac{d\theta}{dt} = 0\)

Answer 2

So I have R the position vector as <1,2>
Which makes r \(\large \sqrt{5}\)

so I have

\[\large u_r = \frac{R}{r} = \frac{<1,2>}{\sqrt{5}}\]

Answer 3

\[\large u_r = \frac{1}{\sqrt{5}} , \frac{2}{\sqrt{5}}\]

Answer 4

The velocity is the derivative of the position vector so I have

\[\large \frac{dR}{dt} = \frac{dr}{dt}u_r + r\frac{d\theta}{dt}u_\theta\]

Answer 5

So in order to make dr/dt = 0 we have

\[\large v = r\frac{d\theta}{dt}u_\theta\]

Answer 6

This was a question I found somewhere and have no idea where to go with it...just seemed interesting to do, if I could do it >.< lol