A pitcher throws a curveball that reaches the catcher in 0.67 s. The ball curves because it is spinning at an average angular velocity of 340 rev/min (assumed constant) on its way to the catcher's mitt. What is the angular displacement of the baseball (in radians) as it travels from the pitcher to the catcher?
340rev/min * 2π rad/rev * 1 min/60sec * 0.67 sec = 23.9 rad
To find the angular displacement of the baseball, we can use the formula:
θ = ω * t
Where θ is the angular displacement, ω is the angular velocity, and t is the time.
First, we need to convert the angular velocity from rev/min to radians/second. Since there are 2π radians in one revolution and 60 seconds in one minute:
ω = (340 rev/min) * (2π radians/1 rev) * (1 min/60 s)
= (340 * 2π / 60) radians/s
≈ 35.7 radians/s
Now, we can calculate the angular displacement:
θ = (35.7 radians/s) * (0.67 s)
≈ 23.95 radians
Therefore, the angular displacement of the baseball as it travels from the pitcher to the catcher is approximately 23.95 radians.
To find the angular displacement of the baseball, we need to first convert the given angular velocity from rev/min to radians/second.
1 revolution (rev) is equal to 2π radians.
So, 340 rev/min is equal to (340 rev/min) * (2π radians/rev) = 680π radians/min.
To convert this to radians/second, we divide by 60 (since 1 min = 60 s):
(680π radians/min) / 60 = 34π radians/second.
Now, we can find the angular displacement using the formula:
Angular Displacement = Angular Velocity * Time.
Given that the angular velocity is 34π radians/second and the time is 0.67 seconds, we can calculate the angular displacement:
Angular Displacement = (34π radians/second) * (0.67 seconds)
Angular Displacement ≈ 22.78 radians.
Therefore, the angular displacement of the baseball as it travels from the pitcher to the catcher is approximately 22.78 radians.