A pitcher throws a curveball that reaches the catcher in 0.65 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?
theta=wi*time= 350*2PI/60sec *.65s
To calculate the angular displacement of the baseball, we need to first convert the given angular velocity from rev/min to radians/s.
1 revolution (rev) is equal to 2π radians. Hence, we can use the following conversion factor:
1 rev/min = (2π radians / 1 min) * (1 min / 60 s) = (2π / 60) radians/s
Now we can calculate the angular velocity in radians per second (rad/s) by multiplying the given angular velocity in rev/min by the conversion factor:
Angular velocity = 350 rev/min * (2π / 60) radians/s = 11π/3 radians/s
Next, we need to find the time it takes for the baseball to reach the catcher. We are given that it takes 0.65 seconds.
Finally, we can calculate the angular displacement (θ) using the formula:
θ = Angular velocity * Time
θ = (11π/3 radians/s) * 0.65 s
Now let's calculate the angular displacement:
θ = (11π/3) * 0.65
θ ≈ 7.80 radians
Therefore, the angular displacement of the baseball as it travels from the pitcher to the catcher is approximately 7.80 radians.