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Angular Acceleration Problem

  1. Dec 15, 2013 #1
    Problem(physics class 201/Portland Community College)
    During the time a compact disc (CD) accelerates from rest to a constant rotational speed of 477 rev/min, it rotates through an angular displacement of 0.250 rev. What is the angular acceleration of the CD?
    (a) 358 rad/s2 (c) 901 rad/s2 (e) 794 rad/s2
    (b) 126 rad/s2 (d) 866 rad/s2


    This is my formula from my Kinetics formula in my book where ∂ = angular acceleration

    (1)Kinetics formula
    V^2 = V(initial)^2 + 2ax

    (2)so I converted to:
    ω^2 = ω(initial)^2 + 2∂θ
    (477 rev/mins)^2 = (0 rad/s)^2 + 2(∂)(0.250 rev)
    [(477 rev/mins)^2 - (0 rad/s)^2)]/ (2 (0.250 rev))= ∂
    [(477 rev/mins)^2 - 0] / (.50 rev) = ∂
    (477 rev/mins)^2 / .50 rev = ∂
    (227529 rev^2/mins^2) / .50 rev = ∂
    455,058 rev/mins^2 = ∂

    **** I can not get the answer! the Answer is "e" ****
     
  2. jcsd
  3. Dec 15, 2013 #2

    TSny

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    Hi, gcombina.

    Watch the units.

    Note the units in your answer compared to the units in the choices of answer.
     
    Last edited: Dec 15, 2013
  4. Dec 15, 2013 #3
    so 477 rev/min = 477 rad/60 s??? meaning 7.095 rad/s??
     
  5. Dec 15, 2013 #4

    TSny

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    How many radians in a revolution?

    Note: I believe your original answer is correct in rev/min2. So, you could just convert it to rad/s2. However, I think it would be worthwhile for you to also work the problem by first converting the given data to SI units.
     
  6. Dec 15, 2013 #5
    I got it!
    thanks!
    ω^2 = ω(initial)^2 + 2∂θ

    converted
    477 rev/min into rad/s ===> converted to 477 (2pi)rad/60s) because 1 revolution equals a 2pi radian
    0.25 rev ====> converted to 1.57 because 1rev = 2pi therefore, 0.25 (2pi) = 0.25 (2(3.1415)) = 1.57a

    after converting the revolutions to radians, I just plug in the numbers
    (49.95 rad/s )^2 = (0 rad/s)^2 + 2(α)(1.57)
    [(2495 rad/s) - (0 rad/s)^2] = 2 (α) (1.57)
    2495 rad/s = 3.14 (α)
    (2495 rad/s) / (3.14) = α
    α = 795

    :))))) thanks!
     
  7. Dec 15, 2013 #6

    TSny

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    Good work!
     
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