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Transforming Cartesian to Polar Coordinates

  1. Nov 19, 2015 #1
    1. The problem statement, all variables and given/known data
    I am currently trying to calculate the moment and products of inertia of a ring rotating about the x axis at the moment the ring lies in the xy plane. The problem is that the notations I have from textbook are denoted for Cartesian coordinates. i.e. Ixx=∑i mi(yi2+zi2), and Ixy=∑imixiyi. How can I convert these to polar coordinates?
    image.jpeg

    2. Relevant equations
    x=rcosθ, y=rsinθ, z=?

    3. The attempt at a solution
    I'd assume that the moment of inertia would become Ixx=∑mr2dθ.

    but since the problem is for a ring with linear mass density, I am also wondering must I exclude certain coordinates?

    thank you in advance.
     
  2. jcsd
  3. Nov 19, 2015 #2

    DrClaude

    User Avatar

    Staff: Mentor

    You can find descriptions of how to calculate such moments of inertia at http://hyperphysics.phy-astr.gsu.edu/hbase/ihoop.html
    Be careful that for continuous objects, not point masses, you have to use density instead of masses and integrals instead of sums.

    For symmetry reasons, you have that Ixy = 0, Ixz = 0, etc., and also Ixx = Iyy.
     
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