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.

Answer 1

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

`\omega = (\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 ((1min)/(60s))((2\pi rad)/(1rev))`

`\omega = (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`