Final answer:
To find the angular velocity in degrees given a linear velocity and the distance from the point of rotation, we use the formula ω = v/r. For example, with a pitcher's arm where the linear velocity is 35.0 m/s and the ball is 0.300 m from the elbow joint, the angular velocity in radians per second is calculated as 116.67 rad/s, which converts to approximately 6682.81 degrees/s.
Step-by-step explanation:
If the initial velocity of a baseball hit is 28 m/s, we need additional information such as the distance from the point of rotation (shoulder joint) to the baseball to compute the angular velocity. However, using the provided reference scenario where a baseball pitcher rotates the forearm about the elbow and the velocity of the ball in the pitcher's hand is 35.0 m/s at a distance of 0.300 m from the elbow joint, we can calculate the angular velocity of the forearm with the formula:
v = rω
Where:
- v is the linear velocity of the ball (35.0 m/s)
- r is the radius from the elbow joint to the ball (0.300 m)
- ω is the angular velocity we want to find
By rearranging the formula to solve for ω, we get:
ω = v/r
Substituting the known values:
ω = 35.0 m/s / 0.300 m
ω = 116.67 rad/s
To convert rad/s to degrees/s, we use the conversion factor of 180/π:
ω in degrees/s = 116.67 rad/s × (180/π)
ω in degrees/s = 6682.81 degrees/s
Hence, the angular velocity of the pitcher's forearm in degrees per second is approximately 6682.81 degrees/s.