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Homework Help: What is the moment of inertia of the plate about z axis?

  1. Sep 19, 2010 #1
    1. The problem statement, all variables and given/known data

    What is the moment of inertia of the plate about z axis?


    2. Relevant equations



    3. The attempt at a solution

    Consider the isosceles triangle to be a part of a square of side l/root(2)
    Its mass will be 2M
    We know that its moment of inertia about the centre perpendicular to the plane is 2M(l^2/2)/6=Ml^2/6
    Applying parallel axes theorem, moment of inertia about z axis will be Ml^2/6 + 2M(l^2/4)
    which is 2/3 (Ml^2)
    Moment of inertia of the triangle will be half of it i.e. Ml^2/3
    but the answer is Ml^2/6
    Please explain if there is any other easier approach.
    So the moment of inertia of the triangle will be half of it i.e. Ml^2/12
     

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  3. Sep 19, 2010 #2

    rl.bhat

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    What is the moment of inertia of the plate about z axis?

    What is the shape of the plate and the point of suspension?
     
  4. Sep 19, 2010 #3
    I am sorry I did not post the full question. Here it is.

    The figure shows an isosceles triangular plate of mass M and base L. The angle at the apex is 90°. The apex lies at the origin and the base is parallel to X-axis
     
  5. Sep 19, 2010 #4

    ehild

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    The moment of inertia of the triangle is not half that of the square. See the picture: the points of the upper triangle are farther than those of the lower triangle.

    It is easy to get the moment of inertia by integrating (x^2+y^2)dm for the triangle.

    ehild
     

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  6. Sep 19, 2010 #5
    The base of the triangle is fixed ( it is of length l). Since the apex angle is 90 degrees and it is isosceles, You get a square when it is rotated about l. So there is no chance of upper triangle being bigger or smaller.
     
  7. Sep 19, 2010 #6

    ehild

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    How is the moment of inertia defined for an extended body?

    ehild
     
  8. Sep 20, 2010 #7
    here the extended body is a square. So its moment of inertia is same as that of a square.
     
  9. Sep 20, 2010 #8

    ehild

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    You did not understand me. Forget for the moment that this triangle is half of a square. It is just a set of elementary masses, organized in a certain shape. How would you get the moment of inertia of a set of point masses?

    ehild
     
  10. Sep 22, 2010 #9
    By using the equation ∫x^2 dm
     
  11. Sep 22, 2010 #10

    ehild

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    What do you mean on x? If x is the horizontal axis, a rod along the y axis has zero moment of inertia?



    ehild
     
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