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Centripetal Acceleration of two masses when one mass is half a radius away

  1. Oct 31, 2012 #1
    1. The problem statement, all variables and given/known data

    Two objects, m1 and m2, both of mass m, are place on a horizontal platform which is rotating at a constant angular velocity. m1 is located at a distance R from the axis of rotation and m2 is located at a R. The centripetal acceleration of mass m1 ____ to the centripetal acceleration of m2.


    2. Relevant equations

    aci=rω2

    3. The attempt at a solution
    Okay,the correct answer (according to my homework) should be "less than," but I do not understand why. Here's what I did:

    Mass 1: aci=(1/2)Rω2
    so (2aci)=Rω2
    Mass 2: aci=Rω2

    So shouldn't mass 1 have more centripetal acceleration? Or should I not have brought the (1/2) to the other side of the equation. My professor gives a lot of questions like this, and I seem to always get them wrong because I make them more complicated than they should be. But it makes sense that an object farther away from the center of rotation should have more acceleration since it would be traveling a greater distance in a larger circle.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 31, 2012 #2

    tiny-tim

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    hi anomalocaris! :smile:
    (i take it you mean m2 is located at 2 R ?)

    yes, your common-sense is correct :smile:

    i honestly don't see how you got the opposite result, even from those equations

    but anyway i strongly recommend that you don't use the same letter for two different things …

    in this case, call the accelerations a1 and a2 (and not both aci), and then you can put them both into the same equation, and compare them! :wink:
     
  4. Oct 31, 2012 #3
    Okay! Thanks tiny-tim! So Should I live a1=(1/2)ω^2? Not 2a1=a1=(1/2)ω^2 ? Because that would make a2 the smaller one?

    Thank you!
     
  5. Oct 31, 2012 #4
     
  6. Oct 31, 2012 #5

    tiny-tim

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    hi anomalocaris! :smile:
    it really doesn't matter, so long as you end up with an equation with a1 on the LHS and a2 on the RHS :wink:
     
  7. Oct 31, 2012 #6
    Wow embarrassing typographical error! Sometimes I type faster than I think!

    Why should they be on opposite sides? How would this look? Sorry for all these questions, I'm probably making a simple concept more complicated, but I just want to understand this since this kind of problem is helpful for solving all kinds of other problems.
     
  8. Oct 31, 2012 #7

    tiny-tim

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    you're aiming for an equation 2a1 = a2

    it doesn't matter how you get there (there's more than one way)

    anyway, try it and see :smile:
     
  9. Oct 31, 2012 #8
    Okay so then a1=(a2/2)? But either way, a1 is greater than a2. The "correct" answer states that a1<a2. Sometimes the HW keys are wrong though.
     
  10. Oct 31, 2012 #9

    tiny-tim

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    no, a1=(a2/2) means a1 is less than a2 :confused:
     
  11. Oct 31, 2012 #10
    OH!!! :redface: Epiphany moment! Okay I finally get it! a2 is greater because half of it would be equal to one whole a1. Thanks for sticking with me, tiny-tim! I really really appreciate it! :smile:
     
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