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Time to Rotate Metal Sphere 1 Time

  1. Aug 4, 2014 #1
    1. The problem statement, all variables and given/known data

    A girl pushes on a large stone sphere. The sphere has a mass of 8200 kg and a radius of 90 cm and floats with nearly zero friction on a thin layer of pressurized water.

    Suppose that she pushes on the sphere tangent to its surface with a steady force of F = 45N and that the pressured water provides a frictionless support. How long will it take her to rotate the sphere one time, starting from rest?

    m = 8200kg
    r = 90cm = 0.90m
    Fapplied = 45N

    2. Relevant equations

    τ = RF_perpendicular
    α = τ/I
    I = 2/5MR2
    θ = ω0t + 1/2αt2
    θ = 2∏r

    3. The attempt at a solution

    Solve for τ = (45N)(0.90m) = 40.5 N*m
    Solve for α = 40.5N*m/[2/5(8200kg)(0.90m)2] = 0.01524 rad/s2
    Solve for θ = 2∏(0.90m) = 5.65486 rad

    Solve for t: 5.65486 rad = 0 + 1/2(0.01524 rad/s2)(t2)
    t = 27.24 s

    The answer isn't right when I submitted it; I thought my process was correct. Where did I go wrong here?

    Thanks!
     
    Last edited: Aug 4, 2014
  2. jcsd
  3. Aug 4, 2014 #2

    Orodruin

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    The angle θ does not depend on the radius. A full turn is always 2pi radians.
     
  4. Aug 4, 2014 #3
    You're absolutely right; for some reason, I was thinking circumference. Thanks for catching that!
     
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