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Velocity in plane polar coordinates

  1. Feb 3, 2015 #1
    Hi,
    I have a problem with the following explanation of velocity in plane polar coordinates.
    30sik39.jpg
    I don't understand why the magnitude of Δer is approximately equal to Δθ.

    Thanks
     
  2. jcsd
  3. Feb 3, 2015 #2
    You know from basic geometry that the arc of circumference spanned by ##\Delta \theta## is going to be ##\delta=|\hat{e}_r|\Delta\theta##. However, even if ##\Delta e_r## is actually straight, it is very very small and so it will be close in magnitude to the arc of length. Also since ##\hat{e}_r## has unit magnitude, you find ##\Delta e_r\simeq\delta=\Delta\theta##.
     
  4. Feb 3, 2015 #3
    Thanks!
     
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