Interactive LearningWare 8.1 reviews the approach that is necessary for solving problems such as this one. A motorcyclist is traveling along

Question

Interactive LearningWare 8.1 reviews the approach that is necessary for solving problems such as this one. A motorcyclist is traveling along a road and accelerates for 4.36 s to pass another cyclist. The angular acceleration of each wheel is 6.10 rad/s2, and, just after passing, the angular velocity of each is 75.2 rad/s, where the plus signs indicate counterclockwise directions. What is the angular displacement of each wheel during this time?

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Xavia 3 days 2021-07-21T21:07:05+00:00 1 Answers 0 views 0

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    2021-07-21T21:08:54+00:00

    Answer:

    The angular displacement of each wheel is 269.92 rad

    Explanation:

    Given:

    Angular acceleration \alpha = 6.10 \frac{rad}{s^{2} }

    Time to pass cyclist t = 4.36 s

    Angular velocity \omega _{f} = 75.2 \frac{rad}{s}

    According to the equation of kinematics,

      \omega _{f} = \omega _{i} + \alpha   t

       \omega _{i} = \omega _{f} - \alpha   t

       \omega _{i} = 75.2 - 6.10 \times 4.36

      \omega _{f} = 48.60 \frac{rad}{s}

    For finding angular displacement,

        \omega _{f} ^{2}  - \omega _{i} ^{2}  = 2 \alpha  \theta

    Where \theta = angular displacement,

      \theta  = \frac{\omega _{f}^{2} - \omega _{i} ^{2}  }{2\alpha }

      \theta  = \frac{5655.04 - 2361.96  }{2\times 6.10 }

      \theta = 269.92 rad

    Therefore, the angular displacement of each wheel is 269.92 rad

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