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Angular Acceleration (Grindstone Problem)

  1. Dec 9, 2014 #1
    1. The problem statement, all variables and given/known data
    A grindstone, initially at rest, is given a constant angular acceleration so that it makes 20.0 rev in the first 8.00 s. What is its angular acceleration?

    (a) 0.313 rad/s2 (c) 2.50 rad/s2 (e) 3.93 rad/s2

    (b) 0.625 rad/s2 (d) 1.97 rad/s2


    2. Relevant equations
    Rotational Kinematic equations

    3. The attempt at a solution

    Ok so I am using the equation ω = ω (initial) + ∝ T
    BUT my answer is the wrong one. It seems that I have to use this equation ω^2 = ω (initial) ^2 + 2∝Θ
    but what do I put in liew of "Θ"??????

    I just don't understand why is that I have to use that equation?
     
  2. jcsd
  3. Dec 9, 2014 #2

    haruspex

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    I don't see how you can use that equation directly since you don't know the final angular speed.
    These equations for uniform angular acceleration are completely analogous to the SUVAT equations for uniform linear acceleration.
    linear.......angular
    distance......angle
    speed..........angular speed
    acceleration..angular acceleration
    Given a distance, an initial speed and a time, what equation would you use to find the acceleration?
     
  4. Dec 9, 2014 #3
    angular acceleration = change in angular velocity/time

    =(final ang vel-initial ang vel)/time

    here, initial ang vel =0
    final ang vel = 20 rev/s = 125.6 rad/s (there are 2 pi radians/rev)

    so, ang accel = (125.6rad/s)/8s=15.7rad/s/s or

    I still don't have the answer!!!!
     
  5. Dec 9, 2014 #4

    haruspex

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    Yes, but that's not what I asked. Forget this question and angular motion for the moment. In linear uniform acceleration,
    I.e., what SUVAT equation relates distance, time, initial velocity, and acceleration?
     
  6. Dec 9, 2014 #5
    θ = ω t + 1/2 t^2

    that one
     
  7. Dec 9, 2014 #6

    haruspex

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    Yes (except that you missed out one symbol).
     
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