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 0.629 m. At one point on this circle, the ball has an angular acceleration of 66.5 rad/s2 and an angular speed of 17.0 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

a) Tangential acc. a_t = alpha * r

a_t = 66.5 x 0.629 = 41.83 m/s^2

Centripetal acc. aC = w^2 r = 17^2 x 0.629 = 181.78 m/s^2

Total acc. = sqrt ( a_t^2 + aC^2 ) = 186.53 m/s^2

b) @ = tan^-1 [ a_t / aC ] = 12.96 deg

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