College

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 [tex]37.1 \, \text{m/s}[/tex] (about 83 mph) and the ball is [tex]0.330 \, \text{m}[/tex] from the elbow joint, what is the angular velocity of the forearm?

Answer :

Answer:

112.4 rad/s

Explanation:

[tex]v[/tex] = velocity of the ball in the pitcher's hand = 37.1 m/s

[tex]r[/tex] = distance of ball from the elbow joint = 0.330 m

[tex]w[/tex] = angular velocity of the forearm

Angular velocity of the forearm is given as

Inserting the values

[tex]w = \frac{v}{r}[/tex]

[tex]w = \frac{37.1}{0.330}[/tex]

[tex]w[/tex] = 112.4 rad/s

The angular velocity is the ratio of the velocity to the distance. Hence, the angular velocity of the forearm is 112.42 rad/s

Given the Parameters :

  • Velocity of ball, v = 37.1 m/s

  • Distance from elbow joint ; r = 0.330 m

The angular velocity of the forearm can be defined thus :

  • [tex]Angular \: velocity = \frac{velocity}{distance} = \frac{v}{r} [/tex]

[tex] Angular\: velocity = \frac{37.1}{0.330} = 112.42 rad/s [/tex]

Therefore, the angular velocity of the forearm is 112.42 rad/s

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