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Conservation of Angular Momentum Experiment: Moment of Inertia

  1. Jul 29, 2012 #1
    1. The problem statement, all variables and given/known data
    I did a lab where there was a rotating solid disk with mass= 0.915kg and diameter=0.253m.
    This was rotating horizontally with an initial angular velocity of 3 different values ω radians/second. After recording the initial angular velocity, I dropped a thin-walled hollow cylinder with mass=0.708kg and diameter=0.125m in the center and measured the final angular velocity, testing the conservation of angular momentum.

    Issue: If I placed the ring off center of the disk by say, 1cm (0.01m), how will that affect my moment of inertia?


    2. Relevant equations
    Idisk=(1/2)(Mass)(radius)2
    Ihoop/hollow cylinder=(Mass)(radius)2
    Li=Idiskωdisk initial
    Lf=(Idisk+Ihoop/hollow cylindercombined final

    3. The attempt at a solution
    First, I calculated the moments of inertia-
    Idisk=(1/2)(Mass)(radius)2=(1/2)(0.915kg)(0.253m/2)2=0.00732kgm2

    Ihoop/hollow cylinder=(Mass)(radius)2=(0.708kg)(0.125m/2)2=0.00277kgm2

    Icombined=(0.00732kgm2)+(0.00277kgm2)=0.01009kgm2

    The Icombined is for the ideal situation of the ring being completely centered, but I have no idea what I would do to get the experimentally flawed moment of inertia. Would I just change the radius of the hoop/cylinder by 1cm? If so, would I add or subtract? I'm really not sure how I'd calculate it. I understand this all generally pretty well, but executing this has me a little stumped. I need a way to get the new final moment of inertia instead of the ideal (Idisk+Ihoop/hollow cylinder) to calculate a percent error.
     
  2. jcsd
  3. Jul 29, 2012 #2

    TSny

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    Gold Member

    Hi, chrismoon. Have you studied the "parallel axis theorem"? You can use it to calculate the moment of inertia of the hollow cylinder when it is placed off-center on the disk.
     
  4. Jul 29, 2012 #3
    have you used the parallel axis theorem?

    ok then...

    late again, sorry. Its getting strange how I am right behind Tnsy.

    I will now bow out again.
     
    Last edited: Jul 29, 2012
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