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Number revolutions with constant angular decelleration

  1. Oct 26, 2009 #1
    # revolutions with constant angular decelleration

    1. A well-lubricated bicycle wheel spins a long time before stopping. Suppose a wheel initially rotating at 120 rpm takes 65 s to stop.

    If the angular acceleration is constant, how many revolutions does the wheel make while stopping?




    2. a = omega^2*r



    3. I already know the solution is theta = 65 revolutions. What is the calculation?
     
  2. jcsd
  3. Oct 26, 2009 #2
    Re: # revolutions with constant angular decelleration

    ok so:

    120rpm = 12.57rad/s << obtained by dimensional analysis 'cause you know 1 rev = 2(pie)rads

    12.57 rad/s is your initial omega

    your final omega = 0 rad/s

    using the kinematics equation : omega final = omega initial + alpha (delta time)
    you get : 0 = 12.57 + (alpha)(65s)

    -0.1934rad/s^2 = alpha << angular deceleration

    so, using another kinematics equation, the one with the angular displacement:
    final position = initial position + 12.57(65) + (0.5)(-0.1934)(65^2)
    then you get 408.4925 rads
    as a result, (use the dimensional analysis again) to get the revolutions! which is 65.01 revolutions.

    i hope that helped. i might be a tad confusing :S
     
  4. Oct 27, 2009 #3
    Re: # revolutions with constant angular decelleration

    I understand the first part, and the reasoning used in the second, but I don't understand this part:

    -0.1934rad/s^2 = alpha << angular deceleration
     
  5. Oct 27, 2009 #4
    Re: # revolutions with constant angular decelleration

    you know the kinematics formula : omega final = omega initial + (alpha)(time) ?

    it's the same as
    final angular velocity = initial angular velocity + (angular acceleration)(time)
    since you have the final angular velocity and the initial, and the time, you can figure out the angular acceleration. :)

    and ... why use : a = omega^2*r?
    that formula is for the centripedal acceleration, and NOT the angular acceleration. centripedal is a linear acceleration! :)
     
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