On Oct 14, 2013, at 1:24 PM, Celil Ekici <firstname.lastname@example.org> wrote:
> I. Rides: Think of a smaller circle whose center fixed on a point on the larger circle. Now think about rotating both circles about their centers and study the relationship between height and time for a point on the large circle and then for a point on smaller circle. You can build such constructions using Geometers' Sketchpad or GeoGebra. If you want, you can introduce this problem in the context of fair rides. A vertically ride example would be Ferris Wheels. Lateral thrill rides such as tea cups ride can be fun to model as well instead. For the vertical ride, you can then ask students trace the changes in height with time, which is generated by combination of sinusoids. It would be great if you keep them adding smaller and smaller circular rides, and observe the changes in combined sinusoids. The rate of change in height can be associated with the amount of thrill. You can ask students predict most thrilling moments of those rides, in larger, and smaller circles.
All three of your examples are great examples, but they are probably of intermediate complexity and would be placed towards the end of a chapter on uniform circular motion. How do you prepare your students for the technical challenges of translating the complex motion in these examples into mathematical terms? How do you introduce them to the significance of choosing coordinate systems and frames of reference? How do you show them that much of this involves cleverly parameterizing aspects into relatable terms like frequency, amplitude and angular velocity, makes it more manageable and applicable?
Can you elaborate more on the preparation of your students prior to taking on these examples?