calculate the angular velocity in radians per minute of ferriswheel 250ft. in diameter that takes 45second to rotate once. express the answer in term of pie
the diameter of the wheel makes no difference.
The angular velocity is
2π rad / 45sec = 2π/45 rad/s
And that's pi, not pie !
To calculate the angular velocity of the Ferris wheel, we need to determine the circumference of the wheel and divide it by the time it takes to complete one rotation.
Step 1: Calculate the circumference of the Ferris wheel.
The diameter is given as 250 feet, so we can calculate the radius as half of the diameter:
Radius (r) = Diameter / 2 = 250 ft / 2 = 125 ft
The circumference of a circle is given by the formula: Circumference = 2 * π * r
Circumference = 2 * π * 125 ft
Step 2: Calculate the time taken to complete one rotation.
The given information states that the Ferris wheel takes 45 seconds to complete one rotation.
Step 3: Calculate the angular velocity.
Angular velocity (ω) is defined as the angle traversed per unit time.
We know that the angle traversed in one rotation is 360 degrees (or 2π radians).
Angular velocity (ω) = Angle traversed / Time taken
Angle traversed = 2π radians (from one complete rotation)
Time taken = 45 seconds
Angular velocity (ω) = 2π radians / 45 seconds
Finally, we can simplify the fraction by dividing both the numerator and denominator by 5:
Angular velocity (ω) = (2π / 45) radians/second
To express the answer in terms of pi, we can leave it as:
Angular velocity (ω) = (2/45)π radians/second
To convert this into radians per minute, we multiply by 60 (as there are 60 seconds in a minute):
Angular velocity (ω) = (2/45)π * 60 radians/minute
Thus, the angular velocity of the Ferris wheel is (2/45)π radians/minute.
To calculate the angular velocity in radians per minute of a Ferris wheel, we need to use the formula:
Angular Velocity = 2π * (Number of rotations) / Time
Given that the Ferris wheel has a diameter of 250 feet, we can calculate the radius by dividing the diameter by 2:
Radius = Diameter / 2
Radius = 250 ft / 2
Radius = 125 ft
We need to convert the time from seconds to minutes, so:
Time = 45 seconds / 60
Time = 0.75 minutes
Since the Ferris wheel completes one rotation in 0.75 minutes, the number of rotations is 1.
Angular Velocity = 2π * (1) / 0.75
Angular Velocity = 2π * (4 / 3)
Angular Velocity = 8π / 3 radians per minute
Therefore, the angular velocity of the Ferris wheel is 8π / 3 radians per minute.