Mathematical models and hula hoops

In the morning session the PBS Nova special The Great Math Mystery, alternatively titled Mathematics Explains the Universe, opened the unit on mathematical models. This sets the stage to explore a system that involves physics but is not in any physical science textbook.

At the start of the laboratory this term I put course student learning outcome number three on the board to help frame the intent of the laboratory, "Students will be able to generate mathematical models for physical science systems and use appropriate mathematical techniques and concepts to obtain quantitative solutions to problems in physical science."

Berny measured diameters with the assistance of Etwet. Guidance and directions were intentionally minimal. Although I put the focus on period versus diameter, the order in which data was recorded was up to the students. 

Berny hooped while Sru, off screen, recorded data. 

After six weeks of using the metric system, one group measured diameters in inches. Old habits die hard.

The real point of the laboratory is to see whether students can pull together an analysis of this system based on the past six weeks of laboratory experience. Can they find an appropriate equation? Can they write this lab up in a meaningful way? The upside is that this is a very unusual laboratory, so there is likely to be little to nothing online to guide the students. 

Data suggested a common slope for two laboratory teams once the y-intercept was permitted to float.

Perhaps for any given given hooper change in the diameter produces a constant ratio, with each hooper able to keep a given diameter up at a different rotation speed. I am starting to wonder whether there are body geometries that impact hoop loft and thus the y-intercept for the data. 

The other intent of this laboratory is to have some fun. There is a hidden message that science can be fun, goofy even. Physical science and mathematical models are all around us. 

Loyeesha hooping while Sidney times, Berny hooping.