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.

The speed of the passengers is 5.24 m/s

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:

Where:

v = tangential speed

r = radius of the circle described by the rotating object

Also:

Where:

f = frequency

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

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

The angular speed is:

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

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

Calculating:

v = 5.24 m/s

The speed of the passengers is 5.24 m/s

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