Question

A Ferris wheel with 60 spokes has a diameter of 100 m. It makes one rotation every 60 seconds. Find the speed of the passengers when the Ferris wheel is rotating at this rate.

Answer 1

The speed of the passengers is 5.24 m/s

Step-by-step explanation:

Uniform Circular Motion

It occurs when an object in a circular path travels equal angles in equal times.

The angular speed can be calculated in two different ways:

`\displaystyle \omega=(v)/(r)`

Where:

v = tangential speed

r = radius of the circle described by the rotating object

Also:

`\omega=2\pi f`

Where:

f = frequency

Since the frequency is calculated when the number of revolutions n and the time t are known:

`\displaystyle f=(n)/(t)`

The Ferris wheel has a diameter of 100 m and makes n=1 rotation in t=60 seconds, thus the frequency is:

`\displaystyle f=(1)/(60)\ Hz`

The angular speed is:

`\displaystyle \omega=2\pi (1)/(60) =(\pi)/(30) \ rad/s`

Now we calculate the tangential speed, solving this formula for v:

`\displaystyle \omega=(v)/(r)`

`v=\omega . r`

The radius is half the diameter, r=100/2=50 m:

`\displaystyle v=(\pi)/(30) . 50`

Calculating:

v = 5.24 m/s

The speed of the passengers is 5.24 m/s