A pitcher throws a curveball that reaches the catcher in 0.64 s. The ball curves because it is spinning at an average angular velocity of 350 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?
D = 350rev/60s * 0.64s * 6.28rad/rev =
To find the angular displacement of the baseball, we need to use the formula:
θ = ω * t
Where:
θ is the angular displacement,
ω is the angular velocity, and
t is the time.
First, let's convert the angular velocity from revolutions per minute (rev/min) to radians per second (rad/s):
ϖ = (2π/1 rev) * (1 min/60 s) * (350 rev/min)
Simplifying this expression, we get:
ϖ = (2π * 350) / 60 rad/s
Now, let's substitute the values into the formula to find the angular displacement:
θ = (2π * 350 / 60) * 0.64 s
Calculating this expression, we get:
θ = (2π * 350 * 0.64) / 60 rad
Simplifying this expression, we find:
θ ≈ 11.49 rad
Therefore, the angular displacement of the baseball as it travels from the pitcher to the catcher is approximately 11.49 radians.