Final answer:
To find out how many revolutions a ball made given its initial and final angular speeds and the time of travel, calculate the average angular velocity, apply the formula to find angular displacement, and then convert radians to revolutions. In this case, the ball made approximately 3.34 revolutions.
Step-by-step explanation:
The formula for angular motion related to angular displacement (θ), angular velocity (ω), and time (t) is given by the equation θ = ωaverage * t, where ωaverage is the average angular velocity.
In this scenario, the pitcher gives the ball an initial angular speed of 36 rad/s, and when the catcher gloves the ball after 0.6s, the angular speed is 34 rad/s.
To find the average angular speed, we sum the initial and final angular speeds and divide by 2.
ωaverage = (ωinitial + ωfinal) / 2
ωaverage = (36 rad/s + 34 rad/s) / 2 = 35 rad/s
Now, we calculate the angular displacement which is the total angle the ball has rotated through:
θ = ωaverage * t = 35 rad/s * 0.6s = 21 rad
To find the number of revolutions, we convert radians to revolutions knowing that one revolution is 2π radians:
Revolutions = θ / (2π) = 21 rad / (2π) ≈ 3.34 revolutions
Therefore, the ball made approximately 3.34 revolutions before being caught, but since only whole number options are provided, the number of complete revolutions must be 3.