A baseball pitcher brings his arm forward during a pitch, rotating the forearm about the elbow. If the velocity of the ball in the pitcher's hand is 33.5 m/s (about 75 mph) and the ball is 0.290 m from the elbow joint, what is the angular velocity of the forearm

Angular velocity of the forearm = 115.52 rad/s

Explanation:

This problem can be modelled as a circular motion problem.

With the elbow joint being the centre of the circle.

The linear velocity (v), angular velocity (w) and radius of circular motion (r) are related through

v = rw

v = Velocity of the pitcher's arm = Velocity of the ball in the pitcher's arm = 33.5 m/s

r = radius of the circular motion = distance from the ball to the elbow joint = 0.290 m

w = ?

33.5 = 0.29w

w = (33.5/0.29) = 115.52 rad/s

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