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Fres = -mgsinθ pendulum

  1. Dec 5, 2012 #1
    Okay I hope I can write this so it makes sense what I am thinking.
    For a pendulum you have:

    Fres = -mgsinθ
    And Fres points along the circumference:
    So:
    mRθ'' = -mgsinθ

    I wonna discuss this property that you can just express the acceleration as Rθ''. In a cartesian coordinate frame your acceleration would depend on the characteristic length scale of x. How do you know that the characteristic length scale of Rθ is the same as x? I know it sounds weird, but I hope you understand what Im going at.
     
  2. jcsd
  3. Dec 5, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: pendulum

    I'm not sure what you mean by "characteristic length scale" but I suspect it has to do either with the units of measurement or a specific length in the problem.

    The angle, [itex]\theta[/itex] is "dimensionless" so that "[itex]R\theta[/itex]" has the same units as R. Whatever "length scale" you are using for R also applies to [itex]R\theta[/itex].
     
  4. Dec 5, 2012 #3

    jedishrfu

    Staff: Mentor

    Re: pendulum

    are you asking if X and Y are measured in meters then would r*theta be measured in meters?
     
  5. Dec 5, 2012 #4
    Re: pendulum

    no rather something like this: If we imagine that at some point the x-axis of our coordinate system tangential to the arc then the pendulum will move a distance dx measured in cartesian coordinates. How can we know that dx=rdθ, I mean what is it that says that these differentials are comparable? After all what if we made r bigger?
     
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