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Rotational Dynamics / Moment of Inertia Question

  1. Jul 2, 2013 #1
    1. The problem statement, all variables and given/known data
    An oxygen molecule consists of two oxygen atoms whose total mass is 5.3x10^-26 kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is 1.9 x 10^-46 kg*m^2. From this data, estimate the effective distance between the atoms.


    2. Relevant equations
    ## I = M1R^2 + M2R^2 ##


    3. The attempt at a solution
    I = (M1+M2)R^2
    1.9 x 10^-46 kg*m^2 = (5.3 x 10^-26kg)R^2
    R = 5.99 x 10^-11 m

    Although I got that this is the radius, this is not the answer to the problem. I'm not exactly sure what I did wrong, as it seems right to me. Could anyone check my work? Thanks!
     
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  3. Jul 2, 2013 #2

    TSny

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    Geometrically, what do you mean by "radius" here? How does this radius relate to the distance between the atoms?
     
  4. Jul 2, 2013 #3
    OH. Ugh, stupid mistake on my part! I used trig and got D to be 1.20 x 10^-10 m.
    Thanks!
     
  5. Jul 2, 2013 #4

    TSny

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    trig? How?
     
  6. Jul 2, 2013 #5
    a209f0bb1bd1fb3d67d28f80a53a8df9.png
    This is the diagram I drew, and you get that D/2 = sqrt(R^2 - I^2).
    I then just solved for D, and it actually turned out to be approximately 2R.
     
  7. Jul 2, 2013 #6

    TSny

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    Hmm. I imagine an oxygen molecule as being a little "dumbbell". What is "I" in your drawing?
     

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  8. Jul 2, 2013 #7
    I had I as the Moment of Inertia.
     
  9. Jul 2, 2013 #8

    TSny

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    When you wrote the equation D/2 = sqrt(R^2 - I^2), does "I" represent moment of inertia? If so, do you see a problem with that? Note that I is not a distance, and therefore cannot be used as one side of a right triangle.
     
  10. Jul 2, 2013 #9
    Hmm, I see what you mean. I seem to have confused the moment of Inertia with the Moment Arm. In that case, I'm not sure how to use the information I have to get an answer :/
     
  11. Jul 2, 2013 #10

    TSny

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    What is the meaning of the ##\small R\:##'s in the formula ##\small I = m_1R_1^2 + m_2R^2## for the moment of inertia? Would you be able to label ##\small R_1## and ##\small R_2## in the figure of the oxygen molecule that I posted earlier?
     
  12. Jul 2, 2013 #11
    Ohhh I see. So it is 2R, I was just lucky that the numbers worked out when I did it my way.
     
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