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Angular Velocity Problem

  1. May 1, 2008 #1
    1. The problem statement, all variables and given/known data

    A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means of storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 300 mile trip in a typical mid-sized car produces about 1.2x10^9 J of energy. How fast would a 13kg flywheel with a radius of 0.3m have to rotate to store this much energy? Give your answer in rev/min


    2. Relevant equations
    Rotational Kinetic Energy (KEr) = (1/2)Iw^2
    where I = mr^2


    3. The attempt at a solution
    So doing some basic algebra, and solving for w, I came up with:

    w = sqrt(KEr/.5mr^2)

    w = sqrt(1.2x10^9J / .5(13kg)(.3m^2)

    w = 45291 rad/s

    (45291 rad/s) / 2pi = 7208 rev/s * 60s = 432497 rev/min

    The answer that the book is providing is: 6.1x10^5 rev/min

    I'm not sure what I'm doing wrong, or If this is even the correct approach I should be taking to solve this problem.

    Any help would be greatly appreciated.
     
  2. jcsd
  3. May 1, 2008 #2

    Hootenanny

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    Welcome to PF cchase88,
    Are you sure that's the moment of inertia of a disk about an axis passing through it's centre?
     
  4. May 1, 2008 #3

    tiny-tim

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    Welcome to PF!

    Hi cchase88! Welcome to PF! :smile:

    Have you noticed you're out by a factor of √2? :rolleyes:

    When in doubt, wkikpedia is often helpful: see http://en.wikipedia.org/wiki/Flywheel#Physics :smile:
     
  5. May 1, 2008 #4
    Thank you both for your help. I forgot about that 1/2. I guess that's what I get for doing a problem at 4 in the morning :rolleyes:
     
  6. May 1, 2008 #5

    tiny-tim

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    :zzz: cchase 88 z's ! :zzz:​
     
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