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Angular Displacement and Velocity

  1. Feb 5, 2009 #1
    1. The problem statement, all variables and given/known data
    A person is riding a bicycle, and its wheels have an angular velocity of +22.0 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is +11.0 revolutions.

    (a) How much time does it take for the bike to come to rest?

    (b) What is the angular acceleration of each wheel?

    2. Relevant equations
    theta = (angular velocity)(time)

    3. The attempt at a solution
    11/22 = t=1/2

    thats wrong i guess.
    can you help me out?
  2. jcsd
  3. Feb 5, 2009 #2


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    Here's an interesting thing: The kinematic equations for rotational motion (be sure to use radians) have the same form as those for straight line motion:

    [tex] X = X_o + V_o t + \frac{1}{2} a t^2 [/tex]


    [tex] \theta = \theta_o + \omega_o t + \frac{1}{2} \alpha t^2 [/tex]

    and so on. Therefore you can use many of the same ideas that you would use for straight line motion problems with simple rotational kinematics. For example, you could use

    [tex] \omega^2 = \omega_o^2 + 2 \alpha(\theta - \theta_o) [/tex]

    to find the angular acceleration in your problem above. I'll leave it to you to figure out the other parts.

    [tex] \omega [/tex] is the angular velocity; [tex] \alpha [/tex] is the angular acceleration in the above equations.
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