2) The baseball player throws a curve ball that reaches the catcher in 0.60 seconds. The ball curves because it is spinning at an average angular velocity of 330 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)
ang displacement= w*time
330* 2Pi/60sec* .6 sec=
thank you , but where did you get the .6 sec from ?
"The baseball player throws a curve ball that reaches the catcher in 0.60 seconds."
What is being calculated is the number of degrees that the ball rotates on its way to home plate. That does not tell you how much the direction of the curve ball changes. That is what I would call the angular displacement. That angle is calculable from aerodynamics (Magnus effect) and mechanics formulas, but if that isn't what they want, let it be.
http://library.thinkquest.org/11902/physics/curve2.html
To find the angular displacement of the baseball as it travels from the pitcher to the catcher, we first need to convert the given angular velocity from rev/min to rad/s.
1 revolution (rev) is equal to 2π radians, and 1 minute is equal to 60 seconds. Therefore, to convert rev/min to rad/s, we can use the following conversion factor:
1 rev/min = (2π radians / 1 rev) * (1 min / 60 sec) = π/30 radians/sec.
Now, we can calculate the angular displacement by multiplying the angular velocity by the time:
Angular displacement = angular velocity * time = (330 rev/min) * (π/30 radians/sec) * (0.60 sec).
To simplify the calculation, we can convert 330 rev/min to radians/sec first:
Angular velocity = 330 rev/min * (π/30 radians/sec) = 33π/30 radians/sec.
Now we can substitute this value into the formula:
Angular displacement = (33π/30 radians/sec) * (0.60 sec) = 11π/5 radians.
Therefore, the angular displacement of the baseball as it travels from the pitcher to the catcher is 11π/5 radians.