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B In circular motion, What does it mean s = r.θ?

  1. Aug 9, 2018 #1
    In the circular motion, What does it mean by this equation s = r.θ?
     
  2. jcsd
  3. Aug 9, 2018 #2
    S=rø is the formula for arc length, or angular displacement (ø rad).

    R is the radius
    Ø is the angle measure in radians.
     
  4. Aug 9, 2018 #3

    Delta²

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    arctheta.png

    The scheme is not perfect but I think you get the idea...

    If you want to know how this equation is proved:

    Due to symmetry of the circle we can assume that the arc length ##s## will be directly proportional to the angle ##\theta##. So it will be

    ##s=k\theta## (1) for some constant k.

    But we know for angle ##2\pi## corresponds arc length ##2\pi r##. So if we apply equation (1) for those pair of data we get

    ##2\pi r=k (2\pi)## from which we can deduce that the constant k is actually the radius of the circle, ##k=r##.
     
    Last edited: Aug 9, 2018
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