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Moment of Inertia

  1. Nov 21, 2015 #1
    1. The problem statement, all variables and given/known data
    An object rolls down a ramp starting from rest, demonstrate symbolically the calculation needed to go from time given to a measured κ value here. Pick your favourite object and perform the calculation.
    d, m, R, t, h are known
    http://puu.sh/luare/10352d0479.png [Broken]

    Soccer Ball:
    m = 331.2 kg
    R = 10.54 cm
    t = 2.25 s
    d = 0.2805 m
    h = 0.0445 m


    2. Relevant equations
    Derived from an earlier problem:
    a = (g*h)/(d*(1+k))
    d = 1/2*a*Δt2

    KEtotal = 1/2*m*v2 + 1/2*I*ω2
    I = κ*m*R2
    U = m*g*h
    v = v0 + a*t

    3. The attempt at a solution

    Ui = KEf
    m*g*h = 1/2*m*v2 + 1/2*I*ω2
    m*g*h = 1/2*m*v2 + 1/2*κ*m*R2*(v/R)2
    g*h = 1/2*v2 + 1/2*κ*v2
    κ = (g*h)/v2 - 1
    v = (g*h)/(d*(1+k))*t

    Solving a system of equations gives me:
    v = (2*d)/t
    κ = (g*h*t2 - 2*d2)/(2*d2)

    Plugging in values gives me v = 1.65 m/s and k = 30.8. Compared to a chart which gives a value of κ = 2/3 for a thin spherical shell, my κ value is extremely large.
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Nov 21, 2015 #2

    haruspex

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    You lost a factor of 2 there, but it reappeared later.
    That seems like a very long time, given the set-up. It should be more like 0.6 s.
    How do you get that from these numbers? (2*0.2805)/2.25=0.25
     
  4. Nov 21, 2015 #3
    Thanks for your help, I've been told the units for this problem were all messed up and have successfully solved the corrected version.
     
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