In a fast-pitch softball game the pitcher is impressive to watch, as she deliver

Question

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 0.648 m. At one point on this circle, the ball has an angular acceleration of 63.1 rad/s2 and an angular speed of 13.3 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.

Explanation / Answer

Centripetal accl = 2R = 13.3 * 13.3 * 0.648

= 114.624 m/s2

tangential accl = R ( = angular accl)

= 63.1 x 0.648 = 40.888 m/s2

(A) Total accl = sqrt[Centripetal2 + tangential2]

= sqrt[114.6242 + 40.8882]

= 121.698 m/s2

(B) direction with radial = arctan(tangential / Centripetal)

= arctan(40.888/114.624)

= 19.63 degrees

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