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

Question

1. One method of pitching a softball is called the "windmill" delivery method, in which the pitcher's arm rotates through approximately 1 revolution 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 98.0 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 74.2 cm. (a) Determine the angular speed of the arm in rad/s at the instant of release. (b) Find the magnitude of the value of the angular acceleration. Determine the magnitude of the force exerted on the ball by the pitcher's hand (both radial and tangential components) just before it is released. SHOW ALL WORK

Explanation / Answer

A)

1 mi/h = 0.44704 m/s

then v = 98*0.44704 = 43.809 m/s

then angular speed is w = v/r = 43.809/0.742 = 59.04 rad/s

B) a = v^2/r = 43.809*43.809/0.742 = 2586.56 m/s^2

angular accelaration alpha = a/r = 2586.56/0.742 = 3485.92 rad/s^2

C) net accelaration anet = Sqrt(a^2+alpha^2) = Sqrt(2586.56^2+3485.92^2) = 4340.73 m/s^2

net force is Fnet= m*anet = 0.198*4340.73 = 859.5 N

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