Review Multiple-Concept Example 7 in this chapter as an aid in solving this prob

Question

Review Multiple-Concept Example 7 in this chapter as an aid in solving this problem. In a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so that the ball in her hand moves in a circle. In one instance, the radius of the circle is 0.682 m. At one point on this circle, the ball has an angular acceleration of 62.5 rad/s2 and an angular speed of 19.7 rad/s. (a) Find the magnitude of the total acceleration (centripetal plus tangential) of the ball. (b) Determine the angle of the total acceleration relative to the radial direction. (a) Number Units (b) Number Units

Explanation / Answer

Here ,

angular speed , w = 19.7 rad/s

angular acceleration = 62.5 rad/s^2

radius , r = 0.682 m

Now , as centripetal acceleration , ac = w^2 * r

ac = 19.7^2 * 0.682

ac = 264.7 m/s^2

tangential acceleration , at = 62.5 * 0.632

at = 39.5 m/s^2

magnitude of acceleartion = sqrt(at^2 + ac^2)

magnitude of acceleartion = sqrt(39.5^2 + 264.7^2)

magnitude of acceleartion = 267.6 m/s^2

the magnitude of the total acceleration is 267.6 m/s^2

b)

angle = arctan(at/ac)

angle = arctan(39.5/264.7)

angle = 8.5 degree

the angle of the total acceleration relative to the radial direction is 8.5 degree

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