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Moment of inertia of a lamina

  1. Oct 2, 2009 #1
    1. The problem statement, all variables and given/known data
    A lamina of unit density consists of the region between the two curves [tex]y=\sqrt{4-x^2}[/tex] and [tex]y=1-4x^2[/tex] and the x axis.
    Find it's moment of inertia about the x-axis.

    2. Relevant equations
    This is the correct answer:
    [tex]2\left \{ \int_{0}^{2}\int_{0}^{\sqrt{4-x^2}}}y^2 dy dx - \int_{0}^{1/2}\int_{0}^{1-4x^2}y^2 dy dx \right \}[/tex]
    which I do understand.

    3. The attempt at a solution
    [tex]2\int_{0}^{2}\int_{1-4x^2}^{\sqrt{4-x^2}}y^2 dy dx[/tex]
    I don't understand why this is wrong.

    Thanks in advance.
  2. jcsd
  3. Oct 2, 2009 #2


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    Science Advisor
    Homework Helper

    Because you only want the moment of inertia BETWEEN the two curves. 1-4x^2 is negative for x>1/2. Sketch a graph of the region you want. You have to split the integral into two parts.
  4. Oct 2, 2009 #3
    Thank you. That makes perfect sense !!
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