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Rotational motion of a spinning disk

  1. Apr 15, 2012 #1
    1. The problem statement, all variables and given/known data
    A spinning disk is rotating at a rate of 30 rad/s in the counterclockwise direction. The disk is slowing down at a rate of 6 rad/s2. Find the angle through which the disk has turned after 3 s in radians, degrees, and revolutions.


    2. Relevant equations

    θ=θi + ωi*t + αt^2



    3. The attempt at a solution

    So when i plugged the variables into the equation I got 36.

    θ = 0 + 90 - 54 = 36

    I thought the units were in radians so that's what I entered for the radians part and I also got 2062 degrees, and 5.71 revolutions. But I got the question wrong.

    The answer was:

    Angle through which wheel has turned (in radians) = 63 radians
    (in degrees) = 3610.0000 degrees
    (in revolutions) = 10.0300 revolutions

    I don't understand what I did wrong.
     
  2. jcsd
  3. Apr 15, 2012 #2

    PeterO

    User Avatar
    Homework Helper

    I see the question as:

    Initial ω = 30,
    Final ω = 12 [loses 6 each second for 3 seconds]
    Average ω = (30 + 12)/2 = 21

    21 for 3 seconds gives 63 radians.

    I think there should have been a 1/2 factor in the "αt^2" term of your formula !


    [Note: I left the rad/s unit out throughout for clarity]
     
  4. Apr 15, 2012 #3
    aw man. I can't believe i missed that :/
    thanks for the help.
     
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