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 94.0 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 74.0 cm. Determine the angular speed of the arm in rev/s at the instant of release.Find the magnitude of the value of the angular acceleration in rev/s2 and the radial and tangential acceleration of the ball just before it is released. 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.

Explanation / Answer

angular speed w = V/R

V = 94mi/hr= 42m/s

R = 74cm = 0.74m

w = 42/0.74

w = 56.75rad/s 56.75/2*pi = 56.75/2*3.14

w = 9 rev/s

Part B

angular acceleration

alpha = w^2/2*theta

theta = 360degrees = 2pi

alpha = 9*9/2*2*3.14

alpha = 6.44rev/s^2

part C

tangential acceleration

at = alpha(rad/s^2)*R = 6.44/2pi*0.74

at = 0.75m/s^2

radial acceleration

a = v^2/R

a = 42*42/0.74 = 2383m/s^2

Part D

radial component Fr = mass * radial acceleration

Fr = 0.198*2383.7

Fr = 472 N

tangential component Ft = mass * tangential acceleration

Ft = 0.15 N

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