A pitcher throws a baseball that reaches the catcher in 0.75 s. The ball curves because it is spinning at an average angular velocity of 230

Question

A pitcher throws a baseball that reaches the catcher in 0.75 s. The ball curves because it is spinning at an average angular velocity of 230 rev/min (assumed constant) on its way to the catcher. a) Determine the angular velocity in rad/sec. b) Determine the angular displacement spend by the ball from the pitcher to the catcher.

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Mộc Miên 1 week 2021-07-22T08:20:33+00:00 1 Answers 2 views 0

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    2021-07-22T08:21:33+00:00

    The change in angular displacement as a function of time is the definition given for angular velocity, this is mathematically described as

    \omega = \frac{\theta}{t}

    Here,

    \theta = Angular displacement

    t = time

    The angular velocity is given as

    \omega = 230rev/min

    PART A) The angular velocity in SI Units will be,

    \omega = 230rev/min (\frac{1min}{60s})(\frac{2\pi rad}{1rev})

    \omega = \frac{23}{3}\pi rad/s \approx 24.08rad/s

    PART B) From our first equation we can rearrange to find the angular displacement then

    \theta = \omega t

    Replacing,

    \theta = (24.08)(0.75)

    \theta = 18.06 rad

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