Answer to Question #280091 in Physics for Faith

Question #280091

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?


1
Expert's answer
2021-12-20T10:28:59-0500

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."

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