Final answer:
The linear velocity of the wrist can be found using the equation v = rω, where v is the linear velocity, r is the distance from the rotation point, and ω is the angular velocity. For the arm's individual segments, you need to know the distance from the rotation point and the angular velocity to calculate the wrist's linear velocity. To include the elbow's movement, add its linear velocity to the forearm's contribution.
Step-by-step explanation:
To find the linear velocity of the wrist in terms of the angular velocities of each arm segment, we use the relationship between linear velocity (v) and angular velocity (ω) given by the equation v = rω, where r is the radius or distance from the rotation point. For example, for a forearm rotating about the elbow, if the velocity of the ball in the pitcher's hand is 35.0 m/s and the distance from the elbow joint is 0.300 m, the angular velocity of the forearm is ω = v / r = 35.0 m/s / 0.300 m = 116.7 rad/s. For the linear velocity of the elbow and the angular velocity of just the forearm, if we know the linear velocity of the elbow, we can add it to the linear velocity of the wrist due to the forearm's rotation to get the total wrist velocity.
To compare with recorded values, you would substitute the recorded angular velocities and distances into the same v = rω equation. For example, if you have an angular velocity of 30.0 rad/s and a radius of 1.30 m (as in the lacrosse example), the velocity of the ball would be v = 1.30 m × 30.0 rad/s = 39.0 m/s.