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Math Help - moments of inertia

  1. #1
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    moments of inertia

    Hi, I needed some help with an integration problem in polar coordinates:

    The region R is bound by the polar curve r = 1 - cos(theta).

    Set up (do not solve) an iterated integral which gives the moments of inertia about the y axis for the region R. The density is d= x^2 + y^2

    Thanks!!!
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  2. #2
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    Quote Originally Posted by intrepidy View Post
    Hi, I needed some help with an integration problem in polar coordinates:

    The region R is bound by the polar curve r = 1 - cos(theta).

    Set up (do not solve) an iterated integral which gives the moments of inertia about the y axis for the region R. The density is d= x^2 + y^2

    Thanks!!!
    In Cartesian coordinates:

    M_y = \int \int_{R} x \, \rho(x, y) \, dx \, dy.

    Switch to polar coordinates:

    M_y = \int \int_{R} r \cos \theta \, \rho(r, \theta) \, r\, dr \, d\theta = \int_{0}^{2 \pi} \int_{0}^{1 - \cos \theta} r^3 \, dr \, d\theta.
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