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Converting between cartesian and polar coordinates

  • Thread starter henryc09
  • Start date
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1. Homework Statement

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

2. Homework 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=[tex]\sqrt{}(ut+c)^2 + 4[/tex]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. Homework Statement



2. Homework Equations



3. The Attempt at a Solution
 

ehild

Homework Helper
15,360
1,766
[tex]
r=\sqrt{(ut+c)^2 + 4}
[/tex]

The polar angle is:

[tex]
\phi=\arctan(\frac{2}{ut+c})
[/tex]

The speed in polar coordinates:

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

[/tex]

ehild
 

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