Velocity in plane polar coordinates

  • Thread starter marcom
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  • #1
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Main Question or Discussion Point

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
 

Answers and Replies

  • #2
470
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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##.
 
  • #3
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Thanks!
 

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