# Converting between cartesian and polar coordinates

1. Nov 30, 2009

### henryc09

1. The problem statement, all variables and given/known data

Particle is moving with velocity v= ui along the line y=2. What is its v in polar coordinates

2. Relevant equations

3. The attempt at a solution
I think I'm being really stupid here but not entirely sure where to start. If you integrate to find position you have it as = ut + c i + 2j and then in polar coordinates is this

r=$$\sqrt{}(ut+c)^2 + 4$$r^? But then if you were to differentiate that the velocity would depend on the initial position which can't be right. I'm obviously doing something wrong and haven't got my head round this topic yet, any help would be appreciated.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Dec 1, 2009

### ehild

$$r=\sqrt{(ut+c)^2 + 4}$$

The polar angle is:

$$\phi=\arctan(\frac{2}{ut+c})$$

The speed in polar coordinates:

$$v=\sqrt{(dr/dt)^2+( r d\phi /dt)^2 }$$

ehild