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Moment of Inertia problem

  1. Mar 30, 2013 #1
    1. The problem statement, all variables and given/known data

    You guys might recognize me from a post earlier. Yep, I'm still plugging away at rotation of rigid bodies and have another question.

    The flywheel of a gasoline engine is required to give up 500 J of kinetic energy while its angular velocity decreases from 650 rpm to 520 rpm. What moment of inertia is required?

    2. Relevant equations

    I = moment of inertia

    E = (1/2)I(ω^2)

    I = 2E/(ω^2)

    3. The attempt at a solution

    I converted the rpm's into rad/s. They are 1.13 and 0.91 respectively. Other than that, I sat and thought for a while and couldn't come up with a start. The 500 J obviously needs to be worked in somehow, but this is a change in E not a constant E. Any help would be greatly appreciated.

    -Lee
     
  2. jcsd
  3. Mar 30, 2013 #2

    ehild

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    How did you get these values for the angular speeds? Remember, rpm means revolutions per minute.

    ehild
     
  4. Mar 30, 2013 #3
    650 rpm (2pi/1 rev)(1 min/60 sec) = whoops that should be 68.07 rad/sec and

    520 rpm (2pi/1 rev)(1 min/60 sec) = 54.45 rad/s

    Anyone know how to find the moment of inertia?
     
    Last edited: Mar 30, 2013
  5. Mar 31, 2013 #4

    ehild

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    You know the difference between initial and final rotational energy.

    ehild
     
  6. Mar 31, 2013 #5
    I got it. I did Energy final - Energy initial = -500 J, factored the I out of the 2 terms on the left and got 0.600 kg m^2 for the moment of inertia. Thanks for the hint. I hope I recognize that trick next time I need it!

    Thanks,
    Lee
     
  7. Mar 31, 2013 #6

    ehild

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    Good job!

    ehild
     
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