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Moment of inertia of a stiff wire bent into a wheel with spokes

  1. Nov 1, 2011 #1
    1. The problem statement, all variables and given/known data

    A stiff uniform wire of mass M0 and length L0 is cut, bent, and the parts soldered together so that it forms a circular wheel having four identical spokes coming out from the center. None of the wire is wasted, and you can neglect the mass of the solder.

    What is the moment of inertia of this wheel about an axle through its center perpendicular to the plane of the wheel? Express your answer in terms of the given quantities.

    2. Relevant equations

    Irim = MR2
    Ispoke = 1/3ML2
    Itotal = Irim + 4*Ispoke

    3. The attempt at a solution

    The length of one spoke, which should also be the radius of the rim, should be L0/(2[itex]\pi[/itex]+4)

    I am unsure of the mass of one spoke, as well as the mass of the rim. Would the mass of one spoke be the same ratio? (Mspoke = M0/(2[itex]\pi[/itex]+4)) ?
    If so, then what would be the mass of the rim? I thought Mrim = M0 - 4*Mspoke
    therefore Mrim = (M0*(1-4/(2[itex]\pi[/itex]+4))
    but I am not getting it right when I submit it.
     
  2. jcsd
  3. Nov 1, 2011 #2

    lewando

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    Gold Member

    What, exactly, are you submitting?
     
  4. Nov 1, 2011 #3
    This is what I have: I = (1-4/(2[itex]\pi[/itex]+4))*M0*(L0/(2[itex]\pi[/itex]+4))2+4*M0/(2[itex]\pi[/itex]+4)*(L0/(2[itex]\pi[/itex]+4))2

    It seems very messy/cumbersome. Am I going about this wrong?
     
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