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

Answer:

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:

$\displaystyle \omega=\frac{v}{r}$

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:

$\displaystyle f=\frac{n}{t}$

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

$\displaystyle f=\frac{1}{60}\ Hz$

The angular speed is:

$\displaystyle \omega=2\pi \frac{1}{60} =\frac{\pi}{30} \ rad/s$

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

$\displaystyle \omega=\frac{v}{r}$

$v=\omega . r$

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

$\displaystyle v=\frac{\pi}{30} . 50$

Calculating:

v = 5.24 m/s

The speed of the passengers is 5.24 m/s