The \"pitch speed\" of a baseball is how fast it\'s moving when it crosses the p

Question

The "pitch speed" of a baseball is how fast it's moving when it crosses the plate. But baseball pitchers also put "spin" on the ball to make it do all kinds of wonky things. The ball's rotational axis and spin direction are shown in the figure for three different pitches. Baseball pitches 1. The Astro's pitcher threw two strikes in a row, both crossing the plate at a speed of 39 m/s. The first pitch, a fastball, was spinning at 496 rpm while the second, a slider, was spinning at 649 rpm. Assume that the baseball acts like a uniform solid sphere of mass 0.15 kg and radius 35 cm. (a) What was the translational kinetic energy of each ball? Kcm = 114.075 Correct: Your answer is correct. J What did you use for the rotational inertia? Check your unit conversions maybe? (b) Determine the rotational kinetic energy of each pitch. Fastball: Krot = Incorrect: Your answer is incorrect. J Slider: Krot = J (c) What was the total kinetic energy of each pitch? Fastball: Kfastball = J Slider: Kslider = J

Explanation / Answer

a) translational KE =   m v^2 /2

       = 0.15 x 39^2 /2 = 114.075 J for both ball

b) rotational KE = I w^2 /2

I = moment of inertia = 2 m r^2 / 5

For !st ball :

angular speed w = 496 rpm = 496 x 2pi rad / 60 sec = 51.94 rad/s

I = (2 x 0.15 x 0.35^2 / 5) = 7.35 x 10^-3 kg m^2

Krot = 7.35 x 10^-3 x 51.94^2 / 2 = 9.91 J

For second Ball :

w = 649 x 2pi rad / 60 sec = 67.96 rad/s

Krot = 7.35 x 10^-3 x 67.96^2 / 2 = 16.97 J

c) !st ball :

totak KE = 114.075 + 9.91= 123.98 J

For 2ns Ball :

total KE = 114.07 + 16.97 = 131.045 J

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