A clothoid is a section of a spiral in which the radius is constantly changing. Roller coaster loops assume a tear-dropped shape that is geometrically referred to as a clothoid. The most obvious section on a roller coaster where centripetal acceleration occurs is within the so-called clothoid loops. These sections include the clothoid loops (that we will approximate as a circle), the sharp 180-degree banked turns, and the small dips and hills found along otherwise straight sections of the track. And in this part of Lesson 2, we will focus on the centripetal acceleration experienced by riders within the circular-shaped sections of a roller coaster track. Roller coasters are about acceleration that's what makes them thrilling. Roller coasters thrill us because of their ability to accelerate us downward one moment and upwards the next leftwards one moment and rightwards the next. The thrill of roller coasters is not due to their speed, but rather due to their accelerations and to the feelings of weightlessness and weightiness that they produce. It is more than likely that most of us sustain higher speeds on our ride along the interstate highway on the way to the amusement park than we do once we enter the park. The thought prompts one to consider what is it about a roller coaster ride that provides such widespread excitement among so many of us and such dreadful fear in the rest? Is our excitement about coasters due to their high speeds? Absolutely not! In fact, it would be foolish to spend so much time and money to ride a selection of roller coasters if it were for reasons of speed. Each day, we flock by the millions to the nearest park, paying a sizable hunk of money to wait in long lines for a short 60-second ride on our favorite roller coaster.
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