Amusement Park Engineers is one of Camp Galileo‘s most exciting themes, teaching campers – depending upon age – about kinetic energy, Newton’s Laws of Motion, electric circuitry and how each of those things are used to build and move a roller coaster. It’s fun to reinforce what is learned during camp with a field trip to an amusement park and regardless of whether you visit to Disneyland, Great America, Six Flags or the county fair, the rides are typically preceded by waiting in line, allowing plenty of time to talk physics.

Centrifugal force is a good place to start. It’s the reason riders get whipped from one side of a car to another on twists and turns, and it also explains how roller coasters stay pushed down on the tracks during cork screw flips (although safety equipment is in place to help too). It’s centrifugal force that also helps push the riders down into the car on the loops, not the safety bar. The safety bar hugging the rider mostly becomes crucial during the lifts and dips when riders get slightly airborne.

The Mad Hatter’s Tea Cups at Disneyland is a fun ride for kids, especially if they try turning the steering wheel in the center, to spin the tea cups faster. The conundrum is that despite turning the wheel as quickly and consistently as possible, sometimes the tea cups whip around faster than at other moments. That’s because there is a big circle that spins (encompassing the entire ride), containing three smaller, independently spinning circles, each holding six independently spinning tea cups. According to Jennifer Ouellette, author of the forthcoming book The Calculus Diaries, the reason for the differing speeds is thus:

Technically, we’re talking here about velocity, not merely speed. Velocity is speed with a direction, traveling along a vector. In the case of the teacup ride, each “circle” moves along its own vector. (That vector is constantly changing its direction, of course, since the “circle” is in rotational motion.) A standard textbook calculus problem would ask students to add together all those vectors at a given point to determine the total velocity. Sometimes the vectors work against each other, pulling in different directions and canceling each other out. That’s when the teacup spun more slowly. Other times, the vectors line up in the same direction and add together, and you get those moments of faster rotation. (And you thought there couldn’t possibly be calculus in a teacup. Hah!)

Suddenly a trip to the amusement park is more complex than a high school math course, but it’s a great opportunity to introduce physics and calculus concepts in a fun way that feels more like solving a mystery than learning math.