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Moment of inertia about the origin for the lamina

  1. Dec 11, 2016 #1
    1. The problem statement, all variables and given/known data
    find the moment of inertia about the origin for the lamina which the surface of sphere (x^2) + (y^2) +(z^2) = 9 . z>2 . Given that density is a constant . Here's my wroking

    The ans is 16pi (k) , but my ans is different , is my ans wrong ?
    If so , which part is wrong ?
    I have checked thru the working many times, yet , still cant find the error

    2. Relevant equations


    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Dec 14, 2016 #2

    Jonathan Scott

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    Gold Member

    Note that a moment of inertia is about an axis, not a point. In this case I assume you meant the z axis.

    I haven't worked right through your answer, and it contains some errors, for example the expression for ##z## is missing a square root, which however seems to have been assumed below. You then appear to have done a substitution which doesn't seem necessary and makes it more complicated.

    I would do this question by integrating over circular bands of constant ##z##, where the mass of each band is ##2 \pi r## times its width which is ##\sqrt{dz^2 + dr^2}## where obviously you need to express ##dr## in terms of ##dz## before you integrate it. The resulting integral is simple. I make the answer ##16 \pi k## where ##k## is the area density.
     
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