A Ferris Wheel
Mathematical Modeling
It's a classic example but you can put your own twist on it.
Introduction
A Ferris wheel is the perfect real-world example of circular motion and periodic functions. As you ride, your height above the ground changes in a predictable sinusoidal pattern. While this is a classic mathematics exploration, you can make it unique by investigating unusual designs like the London Eye (which moves at constant speed) or exploring what happens mathematically when a Ferris wheel malfunctions and has to slow down or speed up.
Guiding Questions
- How can you model the height as a function of time using trigonometry?
- What parameters affect the period and amplitude of your model?
- How does angular velocity relate to the time for one complete rotation?
- Can you use calculus to find when the height is changing most rapidly?
- How would your model change for non-circular motion?
Key Mathematical Concepts
Circular Motion
Trigonometric Functions
Engineering Applications
Periodic Functions