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

[tex]\omega = \frac{\theta}{t}[/tex]

Here,

[tex]\theta[/tex] = Angular displacement

t = time

The angular velocity is given as

[tex]\omega = 230rev/min[/tex]

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

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

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

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

[tex]\theta = \omega t[/tex]

Replacing,

[tex]\theta = (24.08)(0.75)[/tex]

[tex]\theta = 18.06 rad[/tex]

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