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Calculating moment of inertia and torsion constant

  1. Jul 29, 2016 #1
    1. The problem statement, all variables and given/known data
    A clock balance wheel has a period of oscillation of 0.250 s. The wheel is constructed so that its mass of 10.0 g is concentrated around a rim of radius 0.600 cm.
    a) What is the wheels moment of inertia? kg m^2
    b) What is the torsion constant of the attached spring? N m / rad


    2. Relevant equations
    I=mr^2



    3. The attempt at a solution
    starting with part a)
    I have gone mr^2 and gotten 3.6x10^-7 so i assumed that answer didnt make sense, I thought it could be because it says the mass is concentrated around the rim so do i treat that as if it was a ring?
    If so I know that dI = dm r^2
    so ∫dI = r^2 ⋅ ∫dm
    so I = r^2 M
    where M is the mass of the whole ring system.
    Am I correct in this working or was my first calculation correct ?
     
  2. jcsd
  3. Jul 29, 2016 #2

    haruspex

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    Assuming that's in kg m2, that is correct. What bothers you about it?
     
  4. Jul 29, 2016 #3
    yeah I put the values into kg and m when I calculated, I just thought that because it was such a low number it was wrong.
    say for example sake it was a ring, would my calculations I put down be correct to determine the moment of inertia??
     
  5. Jul 29, 2016 #4

    haruspex

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    mr2 works for a point particle, a ring (about an axis through the centre of the ring and normal to its plane) and a hollow cylinder (about the axis of the cylinder). In each case, each part of the object is at the same distance from the axis.
     
  6. Jul 30, 2016 #5

    David Lewis

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    The radius at which all the mass is assumed to be concentrated (for calculation purposes) is also called the radius of gyration.
     
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