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Moment of inertia vs friction

  1. Feb 11, 2009 #1
    1. The problem statement, all variables and given/known data
    If a fan is disengaged from the motor, how long does it take for it to slow down to 1/2 of its original speed. Assuming the only work done during coasting is to accelerate the air the fan pulls in to its exit velocity. Friction loss due to bearings, etc will be ignored.

    2. Relevant equations
    Energy of Rotor = E_k=1/2 Iω^2 where I=Inertia of rotor, ω=angular velocity
    Work done by fan = E_d= 1/2 mv^2 where m = mass of air being blown out, v = air exit velocity.
    Each revolution of the fan rotor moves a fixed volume of air, so v is a fuction of ω.
    m is a fuction of ω and time. ∆m = kω∆t, k is a constant

    3. The attempt at a solution
    Rate change of energy of rotor = ∆(Work done by fan) =1/2 ∆mv^2
    How do I proceed?
     
  2. jcsd
  3. Feb 11, 2009 #2

    LowlyPion

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    Homework Helper

    Welcome to PF.

    Figure that the force is proportional to the volume of air moved and hence the f is proportional to velocity. I would look to construct an integral that takes into account the variable force.
     
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