Question

A Ferris wheels with a diameter of 50.0 meters rotated 2 times in 60.0 seconds ( calculate the velocity of the Ferris wheel)

Answer 1

Given data:

* The diameter of the wheel is d = 50 m.

* The number of rotations of the wheel in 60 seconds is 2.

Solution:

The linear frequency of rotation is,

`\begin{gathered} f=\frac{2}{60\text{ seconds}} \\ f=0.033\text{ Hz} \end{gathered}`

The angular frequency of the wheel is,

`\begin{gathered} \omega=2\pi f \\ \omega=2\pi*0.033 \\ \omega=0.21\text{ rad/s} \end{gathered}`

The radius of the wheel is,

`\begin{gathered} r=(d)/(2) \\ r=(50)/(2) \\ r=25\text{ m} \end{gathered}`

The linear velocity of the wheel is,

`\begin{gathered} v=r\omega \\ v=25*0.21 \\ v=5.25\text{ m/s} \end{gathered}`

Thus, the velocity of the wheel is 5.25 meters per second.