One method of pitching a softball is called the \"windmill\" delivery method, in

Question

One method of pitching a softball is called the "windmill" delivery method, in which the pitcher's arm rotates through approximately 360° in a vertical plane before the 198 gram ball is released at the lowest point of the circular motion. An experienced pitcher can throw a ball with a speed of 90.0 mi/h. Assume that the angular acceleration is uniform throughout the pitching motion, and take the distance between the softball and the shoulder joint to be 80.0 cm.

(a) Determine the angular speed of the arm in rev/s at the instant of release. rev/s

(b) Find the value of the angular acceleration in rev/s2 and the radial and tangential acceleration of the ball just before it is released. rev/s2, ac m/s2, at m/s2

(c) Determine the force exerted on the ball by the pitcher's hand (both radial and tangential components) just before it is released. Fr N, Ft N

Explanation / Answer

Using SI units:
90.0 mph / 2.25 = 40m/s

a) Tangential speed at release v = 40 m/s
so angular speed is = v / r = 40m/s / 0.8m = 50 rad/s
= 50rad/s / 2pi = 7.96 rev/s

b) = 1 rev
a = ^2 / 2 = 7.96^2 / (2*1) = 31.7 rev/s^2

ac = v^2 / r = 40^2 / 0.8 = 2000 m/s^2

at = r * a = 0.8m * 31.7 rev/s^2 * 2pi rad/rev = 159.34m/s^2

c)
fr = m*ac = 0.198kg * 2000 m/s^2 = 396 N

ft = m*at = 0.198kg * 159.34 m/s^2 = 31.55 N

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