Photo credit: celesteh

Ferris wheel physics is directly related to centripetal acceleration, which results in the riders feeling "heavier" or "lighter" depending on their position on the Ferris wheel.

The Ferris wheel consists of an upright wheel with passenger gondolas (seats) attached to the rim. These gondolas can freely pivot at the support where they are connected to the Ferris wheel. As a result, the gondolas always hang downwards at all times as the Ferris wheel spins.

To analyze the Ferris wheel physics, we must first simplify the problem. The figure below shows a schematic of the Ferris wheel, illustrating the essentials of the problem.

Where:

(1) is the top-most position and (2) is the bottom-most position

Point

Point

The forces acting on the passengers are due to the combined effect of gravity and centripetal acceleration, caused by the rotation of the Ferris wheel with angular velocity

We wish to analyze the forces acting on the passengers at locations (1) and (2). The figure below shows a free-body diagram for the passengers at these locations.

Where:

The centripetal acceleration is given by

The centripetal acceleration always points towards the center of the circle. So at the bottom of the circle,

By Newton's second law

where Σ

To solve for

The acceleration of the passengers at point

First, solve for

Next, solve for

We can see that

So basically, Ferris wheel physics affects your bodies "apparent" weight, which varies depending on where you are on the ride. The riders only feel their "true weight", when the centripetal acceleration is pointing horizontally and has no vector component parallel with gravity, and as a result it has no contribution in the vertical direction. This occurs when the riders are exactly halfway between the top and bottom (i.e. they are at the same height as the center of the Ferris wheel).

It's informative to look at an example to get an idea of how much force acts on the passengers.

Let's say we have a Ferris wheel with a radius of 50 meters, which makes two full revolutions per minute.

Two full revolutions per minute translates into

Substituting this into the above equations we find that

Therefore,

With

At the top of the Ferris wheel the passengers experience 0.78

At the bottom of the Ferris wheel the passengers experience 1.2

Now that we understand Ferris wheel physics, one can imagine how important it is for a large radius Ferris wheel to turn slowly, given how much influence the rotation rate

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