   Chapter 7, Problem 49AP

Chapter
Section
Textbook Problem

One method of pitching a softball is called the “wind-mill” 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 98.0 mi/h. Assume 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 rev/s at the instant of release, (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, (c) Determine the force exerted on the ball by the pitcher’s hand (both radial and tangential components) just before it is released.

(a)

To determine
The angular speed of the arm in rev/s at the instant of release.

Explanation

Given Info:

The speed of the ball is 98.0mi/h .

The distance between the soft ball and the shoulder is 74.2cm .

Explanation:

Formula to calculate the angular speed of the arm is,

ω=vr

• v is the speed of the soft ball
• r is distance between the soft ball and the shoulder

Substitute 98.0mi/h for v and 74.2cm for r to find the angular speed of the arm at the instant of release,

ω=98.0mi/h74

(b)

To determine
The angular acceleration in rev/s2 , radial and tangential acceleration of the ball just before it is released.

(c)

To determine
Both radial and tangential components of the force exerted on the ball by the pitcher’s hand.

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