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Show magnitude of velocity vector in polar coordinates

  1. Sep 20, 2010 #1
    1. The problem statement, all variables and given/known data
    In Cartesian coordinates the magnitude of the velocity vector squared is
    |v|^2=V*V= Vx^2 +Vy^2 =(dx/dt)^2+(dy/dt)^2
    Show that in polar coordinated
    |v|^2= Vr^2 +V@ ^2

    2. Relevant equations

    3. The attempt at a solution
    Not really sure what the question is asking me to do, but i am guessing to convert (dx/dt)^2+(dy/dt)^2 into polar? or do i need to do it for all of it?

    Well I got dy/dt=(dr/d@) sin@+rcos@ and dx/dt=(dr/d@) cos@-rsin@

    Is this right? Were do i go after this?

  2. jcsd
  3. Sep 20, 2010 #2


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    Science Advisor
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    Gold Member

    It is not right.
    If x = r cosθ, then
    (dx/dt) = (dr/dt) cosθ - r sinθ (dθ/dt). That's the chain rule of differentiation.

    Find a similar expression for (dy/dt), square each expression then add.
  4. Sep 20, 2010 #3
    cool thanks for info ill try it out tomorrow
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