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Pure rolling motion and the cycloid

This applet has been created for didattic purposes for high school students. The student is able to find the condition of pure rolling motion using this app interactively and guessing which are the right interplay between the physical quantities. The app should make the student think about the ratio between the velocity of the center of mass of the wheel and the one of a point on the edge, when the wheel is nor creeping nor slipping, but appear as a real moving wheel that rolls without friction. The app is also intended to introduce the parametric equation of the cycloid. Other physical questions tha could be posed are: How many conditions of creeping are there? How many conditions of slipping are there? What is the pure rolling motion condition? What are the simple equations that relates the physical quantities in the game and describe these dynamic constraints? I would like to thank Prof. C. Falcolini (Università di Roma Tre) for the pleasing discussions that gave birth to this app.