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Find the Mass Moment of Inertia about the x,y,z axes

  1. Apr 29, 2013 #1
    1. The problem statement, all variables and given/known data
    The two small spheres of mass m each are connected by the light rigid rod which lies in the x-z plane. Determine the mass moments of inertia of the assembly about the x, y, z axes.

    I have attached an image of the question


    2. Relevant equations



    3. The attempt at a solution

    The answer is given but I don't understand how the answer is reached.

    For Ixx The slender bar of length 2L has no mass moment of inertia about x. Then the other two rods each have a mass moment of inertia of 1/3*ml2 or do these cancel out and it's only the spheres which give the system a mass moment of inertia?

    I think that, for the spheres, the mass moment of inertia should be:

    2*(2/3)mr2 + 2ml2

    Is the first portion, 2*(2/3)mr2, 0 because the radius is negligible small?

    This would leave me with 2mL2

    Any guidance would be appreciated. Thank you.
     

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  2. jcsd
  3. Apr 29, 2013 #2

    SammyS

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    Anyone helping you will want a nice size image of that.

    attachment.php?attachmentid=58355&d=1367294931.png


    How far is each mass from each of the three possible axes of rotation?

    .
     
  4. Apr 29, 2013 #3
    So, I'm only really using the parallel axis theorem?

    For the mass moment of inertia about the x axis, the centers of the slender rods perpendicular to the x-axis are a distance L/2 away and the spheres are each a distance L away.

    But summing these would give me 3mL^2
     
  5. Apr 29, 2013 #4

    SammyS

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    Light rods usually implies that you can ignore the mass of the rods. After all, that mass is not given.
     
  6. Apr 29, 2013 #5
    Ahh, that makes sense now. I think I misread the question, because I was thinking that the slender rods also had mass m.

    But, then isn't it the same case for Iyy? The spheres are still a distance L from the y axis.
     
  7. Apr 29, 2013 #6

    SammyS

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    Not for the y-axis, look again.

    What are the coordinates of the two masses?
     
  8. Apr 29, 2013 #7
    On the x-z plane, the spheres have coordinates (L, L) and (-L, -L). Should I use Pythagoras here? Or am I using mL^2 twice for each sphere to account for the x and z components?
     
  9. Apr 30, 2013 #8

    SammyS

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    Use Pythagoras.

    I would write the coordinates as ordered triples, i.e. (L, 0, L) and (-L, 0, -L) .
     
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