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Rotational kinetic energy(flywheel) problem

  1. Jan 17, 2015 #1
    1. The problem statement, all variables and given/known data
    You have been assigned the task of designing a flywheel capable of storing
    the translational kinetic energy of a 600 kg car traveling at 100 km/hr. The
    flywheel is to be manufactured out of steel and the maximum rotational
    speed is 12,000 rpm.
    a. Assuming that the flywheel is a uniform cylindrical disk 50 mm in
    thickness, calculate the mass and diameter of the flywheel.

    2. Relevant equations
    ω=2π/60
    TKE=1/2mv^2
    Ig=1/2mr^2
    RKE=1/2Ig*ω^2
    3. The attempt at a solution
    Solving for ω

    12000rpm*2pi/60=1256.6 rad/s

    Solving for energy TKE
    100*1000/3600=27.8m/s
    1/2*600*27.8m/s=231481J
    Solving for Ig(moment of inertia flywheel)
    RKE=1/2Ig*ω^2

    231481=1/2Ig*1256.6^2
    Ig=0.293KG

    At this point I'm not sure how to go further.
     
  2. jcsd
  3. Jan 17, 2015 #2

    TSny

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    Can you think of a way to relate the diameter and mass of the wheel using the fact that the wheel is made of steel?
     
  4. Jan 18, 2015 #3

    SteamKing

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    You've made a small mistake in the units for Ig, which should be ...
     
  5. Jan 18, 2015 #4
    Density and volume?
    So I googled the density of steel is 7830 kg/m^3

    So would it be m=d*(h*π*r^2)?

    I'm confused on what to do with the Ig value mostly, I know it's not the mass but I don't know how to put it into an equation to solve for mass.
    I=mr^2?
    I=1/2mr^2?

    So if I say 0.293=1/2m*r^2
    m=7830*(.05m*π*r^2)

    0.293=1/2*7830*(.05m*π*r^2)*r^2

    r=0.1476m?
     
  6. Jan 18, 2015 #5

    TSny

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    That looks good. You used the correct expression for I for a cylinder. (As SteamKing pointed out, the unit for I is not kg.)

    The density of steel varies, so I'm not sure what value you should use. If you are using a textbook, then you can see if there is a table of densities there that you can use.

    Anyway, your answer looks correct to me.
     
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