Close X

# George Ferris's Valentine's Day gift to science teachers

## George Ferris, whose 154th birthday is celebrated with a Valentine's Day-themed Google Doodle, didn't just come up with a new amusement park ride; he provided an opportunity for physics teachers to come up with truly terrifying scenarios.

View video

A Ferris wheel is displayed for Christmas 2012 on the Place Masséna in Nice, southern France. Google celebrated Valentine's Day with a tribute to 19th century engineer George Ferris.

Lionel Cironneau/AP

View photo

George Ferris, whom Google praises on its home page Thursday, did more than just invent a beloved theme park ride. His eponymous wheel serves as a perfect opportunity for physics teachers to engage in two of their favorite activities: 1) revealing the simple mathematical equations that govern the motions of everything around us, and 2) coming up with horrifying thought experiments.

Moving its occupants in a circle at a constant rate, the Ferris wheel offers a straightforward lesson in centripetal force, the force that pulls a body moving in a curved path toward the center of the curvature of that path. We often experience centripetal forces as "centrifugal" forces, that is, we feel pushed away from the center. This feeling is the effect of inertia. Like everything else with mass, you tend to travel in a straight line; when you are pulled in a circular motion, say, by a gondola bolted to a giant wheel, from your perspective you will feel as though you are being tugged outward.

Thanks to gravity, this feeling is most acute at the highest and lowest points of the wheel. The centripetal forces are always pulling the gondola toward the center, sometimes working in the exact same direction as gravity and sometimes working in the opposite direction. At the bottom, centripetal forces accelerate the seat upward into your backside, and you weigh more; at the top, the seat is pulled straight down, and you weigh less.

In 1659, the Dutch scientist Christiaan Huygens came up with the formula for centripetal acceleration:

ac =  v2 / r

The "v" stands for velocity. The "r" stands for the radius of the circle.

This equation gives you everything you need to terrorize your imaginary amusement park visitors with one simple question: How fast does a gondola need to be moving so that its passengers briefly experience weightlessness as they crest the top of the wheel?

For that to happen, the centripetal acceleration needs to equal that of gravity, or g, as physicists like to call it, which at sea level is about 9.8 meters per second per second.

So, based on Huygens formula, we present you with the formula for Ferris wheel weightlessness. It works on a wheel of any size, on any planet: