Math Magic Land - Spinning Cups

One of the most popular rides at Math Magic Land is the Spinning Cups. During the ride, the large outer disk rotates counter-clockwise and makes a complete revolution every 30 seconds. The medium size disk rotate clockwise every 4 seconds. The passenger can rotate the smallest disk (the cup) counter-clockwise as fast as they want. Janelle (labeled as J) loves making her friends dizzy on the ride. When she rides, she spins the cup one full turn every two seconds. The main disc has a radius of 100 feet. The medium disc has a radius of 40 feet and the cups each have a radius of 4 feet.

Tip

You can view the Desmos graph in a new window by clicking here.

\(t_e\) controls the time elapsed in seconds. You can adjust the slider to see how the cups move.

\(a_{speed}\) controls the animation speed. You can adjust the slider to see the cups move faster or slower.