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Rotational Kinematics - Angular Acceleration

  1. Nov 23, 2013 #1
    1. The problem statement, all variables and given/known data

    A phonograph turntable with an initial angular velocity of 78 rpm continues turning for 40 rotations after being switched off. What is the angular deceleration of the turntable? Assume constant angular deceleration.

    2. Relevant equations

    [itex]\alpha[/itex]=([itex]\omega[/itex]-[itex]\omega[/itex]0)/t

    θ-θ0=1/2([itex]\omega[/itex]0+[itex]\omega[/itex])t

    3. The attempt at a solution

    t = (40 rot - 0 rot) / 1/2(78 rpm + 0 rpm) = 40/39 min

    [itex]\alpha[/itex] = (0 rpm - 78 rpm) / (40/39 min) = -76.05 rpm2

    The answer needs to be in rad/s2

    (-76.05 rpm2)(2∏ rad/rot)(min2/s2)=-7.96 rad/s2


    The back of the book tells me this answer is incorrect. I would appreciate any insight into the error(s) I am making.

    Thank you!
     
  2. jcsd
  3. Nov 23, 2013 #2
    sure you made the right unit convertion? I get 0.84 rad/s^2 is that what you needed? Else I think the mistake lies elsewhere.
     
  4. Nov 23, 2013 #3
    Hi hjelmgart,

    Thanks for your reply. I'm pretty sure that my error lies in the unit conversion - did you do what I did in the conversion in the original post, or something else?
     
  5. Nov 23, 2013 #4
    Not entirely. I don't understand how you reached that result also. rpm = rev/min

    (1/min)^2 = 1/(60min/s)^2

    rev^2 = (2*Pi)^2
     
  6. Nov 23, 2013 #5
    Ah, I wasn't squaring the seconds unit when converting. Thanks!
     
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