Show magnitude of velocity vector in polar coordinates

  • Thread starter leonne
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  • #1
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Homework Statement


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

Homework Equations





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?

Thanks
 

Answers and Replies

  • #2
kuruman
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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.
 
  • #3
191
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cool thanks for info ill try it out tomorrow
 

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