Question

A pitcher throws a curveball that reaches the catcher in 0.14 s. The ball curves because it is spinning at an average angular velocity of 400 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

Let's first convert rev/min to rad/s:

$$\omega=400\ \dfrac{rev}{min}\times\dfrac{1\ min}{60\ s}\times\dfrac{2\pi\ rad}{1\ rev}=41.9\ \dfrac{rad}{s}.$$

Then, we can find the angular displacement of the baseball from the definition of angular velocity:

$$\omega=\dfrac{\Delta\theta}{\Delta t},$$ $$\Delta\theta=\omega\Delta t=41.9\ \dfrac{rad}{s}\times0.14\ s=5.87\ rad.$$