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Moment of inertia (formula problem)

  1. Jul 16, 2015 #1
    1. Material
    DMkRCvV.jpg
    2. Questions:

    a) (pink) Why does the author use two different values of inertia for the same slender rod ?


    3. The attempt at a solution

    a) I could assume that 1/3 is holding it at the end and 1/12 is holding it in the center.
    But it's not interchangeable because if I chose 1/3 instead of 1/12 in the example (17.10) I would get totally different final result.
     
  2. jcsd
  3. Jul 16, 2015 #2

    Doc Al

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    Staff: Mentor

    They are the rotational inertias about the end and about the center, respectively. It is up to you to figure out which is the most useful point for calculating moments in any particular problem. (Sometimes it doesn't matter.)

    Realize that 17.10 uses both values of rotational inertia. :)
     
  4. Jul 16, 2015 #3
    Ok, thank you :)
     
  5. Jul 16, 2015 #4
    Ok I have realized that I don't understand it fully (I miss something basic probably)
    GwP1NjA.png

    According to this example we should calculate the moment of inertia using formula I=1/12ml2+md2

    So why did the author in 17.10 use simply [1/12ml2]*α

    Instead of [1/12ml2+md2]*α
     
  6. Jul 16, 2015 #5

    Doc Al

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    Staff: Mentor

    Only because you want the moment of inertia about point O.

    Because the author was calculating the moment of inertia about the center of mass, not the end of the rod.
     
  7. Jul 16, 2015 #6
    Ok, finally I understand it (hope so)

    I can choose I=1/12ml2 = in that case (17.10) 1/12*20*32=15
    or I=1/3ml2 = (center at 1.5) 1/3*20*1,52=15

    It works :biggrin:


    EDIT: but if that what I have just written is true, I have got the following question:

    Why did the author write in 17.12 (1/3ml2) instead of 1/3m * (l/2)2 ?
     
    Last edited: Jul 16, 2015
  8. Jul 16, 2015 #7

    Doc Al

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    Staff: Mentor

    Don't do that!

    In both formulas, the "l" stands for the length of the rod. It's the same value in both formulas. The moment of inertia about one end (the 1/3 formula) is different from the moment of inertia about the center (the 1/12 formula).
     
  9. Jul 16, 2015 #8
    That was very concise and clear.
    Thank you :-)
     
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