1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
     

    Attached Files:

    • I.jpg
      I.jpg
      File size:
      2.1 KB
      Views:
      265
  2. jcsd
  3. Sep 19, 2010 #2

    rl.bhat

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    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
     

    Attached Files:

  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

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

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



    ehild
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook