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 0.653 m. At one point on this circle, the ball has an angular acceleration of 63.0 rad/s^2 and an angular speed of 11.9 rad/s. Find the magnitude of the total acceleration (centripetal plus tangent-al) of the ball. Determine the angle of the total acceleration relative to the radial direction.

Explanation / Answer

(a) Total acceleration is the vector sum of the tangential and radial acceleration .
Radial acceleration AR  = W2R where W is the angular velocity and R is the radius of the circle.
AR = (11.9)2*(0.653) = 92.47 rad/s2
Tangential or angular acceleration AT = 63.0 rad/s2
Total acceleration magnitude A = (AR2 + AT2)1/2 = 111.89 rad/s2
(b) Angle with the radial
Angle = tan-1(AT /AR) = 34.267 degree

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