Abaseball pitcher, loosening up his arm before a game, tosses a 0.15-kg ball using only the rotation of his forearm, 0.32 m in length, to accelerate the ball. if the ball starts at rest and is released with a speed of 12 m/s in a time of 0.40 s, what is the average angular acceleration of the arm and ball?

To solve this problem we will apply the concepts given about acceleration in rectilinear motion and angular movement. Tangential acceleration can be described as the change of the final and initial velocity in an instant of time, that is,

Our velocities are given as,

And the time taken to increase the speed of the ball is t = 40s

The length of the forearm is

The angular acceleration is defined as the change of the tangential acceleration in proportion to the turning radius, therefore

Therefore the angular acceleration of the arm and ball is

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