Angular speed can be used when an object has rotational motion
The angular speed of the Ferris wheel is approximately 25.13 rad/min
The linear speed of the person seating in a seat on the Ferris wheel is approximately 753.9 ft./min
The reasons why the above values are correct are given as follows:
The given parameter are;
Time it takes the Ferris wheel to make a complete revolution = 15 seconds
The distance of the person from the axle of the wheel = 30 ft.
Required:
The angular speed in radians per minute
Solution:
Angular speed, ω = (Angle rotated)/(Time taken)
[tex]\omega = \dfrac{\Delta \theta}{\Delta t}[/tex]
The angle of one revolution, θ = 2·π radians
The time it takes the Ferris wheel to make a complete revolution = 15 seconds = (1/4) minute
Therefore;
Angular speed of the Ferris wheel = (Angle of one revolution )/((1/4) minute)
Angular speed of the Ferris wheel = (2×π)/((1/4) minute) ≈ 25.13 rad/min
The angular speed in radians per minute, ω ≈ 25.13 rad/min
Required: The linear speed
Solution:
The linear speed, v, is given by the angular speed, multiplied by the radius of the Ferris wheel, r
∴ v = ω × r
The radius of the Ferris wheel is given by the distance of the person's seat from the axle of the wheel = 30 ft.
∴ r = 30 ft.
The linear speed, v ≈ 25.13 rad/min × 30 ft. = 753.9 ft./min
Learn more about linear angular speed here:
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