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I Finding Moment of Inertia of a wheel experimentally

  1. Oct 2, 2016 #1
    Hello all, and forgive me if I'm making newbie mistakes as I haven't posted here much.

    I realize this appears to be a homework assignment, but it is not. I am trying to develop an easy method for determining the actual moment of inertia for real wheels, for bicycles and other vehicles. I googled the topic and many related results came up, but not explicitly for finding the MOI with a simple formula.

    I believe I have the correct formula, but I need confirmation from more knowledgeable people. I made a pdf file summarizing the problem including a drawing. I hope the link works.


    All of the quantities are constant, as in not varying with time.
    I neglect friction, but realize it can be a significant factor on a real wheel if not dealt with properly.

    In case the link doesn't work, here is what I have:
    A wheel of radius R is mounted with its axle horizontal.
    A string is attached, and wrapped around the perimeter of the wheel (at radius R distance from the center).
    The free end of the string is attached to a free-weight of mass M.
    The free weight is allowed to fall a distance H, vertically, which accelerates the wheel.
    The time it takes the weight to travel H is time t1.
    g is the acceleration of gravity.

    The MOI = ( (g t12 / 2 H) - 1 ) M R2

    Can someone please confirm that for me? Thank you very much for your time.
  2. jcsd
  3. Oct 2, 2016 #2
    I forgot this can probably also be done using energy equations, so I forgive me, as that would have been a way I could check my results. If someone has that solution handy, that would be great as well. I will attempt that, but it will likely take me some time to brush up on those equations/concepts.
  4. Oct 5, 2016 #3


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    Perhaps see ...
  5. Oct 6, 2016 #4
    Thanks. That does at least confirm the relationship of I to a.
  6. Oct 8, 2016 #5


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    You might be able to devise a way to take into account friction in your calculation of MOI.
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