Question

A pitcher throws a curveball that reaches the catcher in 0.64 s. The ball curves because it is spinning at an average angular velocity of 290 rev/min (assumed constant) on its way to the catcher's mitt. What is the angular displacement of the baseball (in radians) as it travels from the pitcher to the catcher?

Answer 1

Answer:

$\Delta \theta=19.44\ rad$

Explanation:

We just have to calculate what angular displacement a ball with an average angular velocity of 290 rev/min experiments in 0.64s. By definition, angular velocity $\omega$ is the angular displacement $\Delta \theta$ divided by the time elapsed:

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

Since $1\ rev=2\pi \ rad$ and $1\ min=60\ s$, we can covert:

$\omega=290\ rev/min=\frac{290\ rev}{min}(\frac{1\ min}{60s})(\frac{2\pi \ rad}{1\ rev})=30.37\ rad/s$

Where the terms between parenthesis are equal to 1, so they just change the units. Then for our values we have:

$\Delta \theta=\omega \Delta t=(30.37\ rad/s)(0.64s)=19.44\ rad$