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Moment of Inertia of a Curved Rod

  1. Apr 14, 2009 #1
    Find the moment of inertia when the wire of constant density shaped like the semicircle
    y=sqrt(r^2-x^2)
    where r is the radius
    is revolved around the x-axis

    I dont even know where to begin =[
     
  2. jcsd
  3. Apr 14, 2009 #2

    berkeman

    User Avatar

    Staff: Mentor

    Welcome to the PF. Start with the definition of the Moment of Inertia. What is it in the general case?

    I'm also having a little trouble visualizing the shape... is there any way you can sketch it?
     
  4. Apr 14, 2009 #3
    the general case for a thin rod is I=\int(mr^2)
    with m=mass and r=radius

    but I don't know what it is for a curved rod. The rod in the problem is a semi circle about the origin in quadrants I and II with radius r
     
  5. Apr 15, 2009 #4
    You have to do the integration from the definition of moment of inertia.

    [tex]
    I\ =\ \int dm\ r^2\
    [/tex]

    Some tips: dm can be expressed in terms of linear density [tex]dm\ = \rho d\theta[/tex], with theta in play due to it being easier in this case to use polar co-ordinates.
     
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