A pitcher throws a curveball that reaches the catcher in 0.51 s. The ball curves because it is spinning at an average angular velocity of 345 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?
angular displacement= w*time
To determine the angular displacement of the baseball as it travels from the pitcher to the catcher, we can use the formula:
Θ = ω * t
Where:
Θ = Angular displacement
ω = Angular velocity
t = Time
First, let's convert the given angular velocity from rev/min to radians/second. We know that 1 revolution is equal to 2π radians.
So,
ω = (345 rev/min) * (2π radians/1 revolution) * (1 min/60 s) =
(345 * 2π) / 60 radians/s ≈ 36.13 radians/s
Now, we'll substitute the values into the formula:
Θ = (36.13 radians/s) * (0.51 s) ≈ 18.42 radians
Therefore, the angular displacement of the baseball as it travels from the pitcher to the catcher is approximately 18.42 radians.