Things that orbit: planets and hula hoops

May 02, 2025

Hula hoop period versus diameter data

Monday began with a planetary playlist updated with recent Perseverance and Curiosity rovers. Uranus landed at 12:44 on an 11:58 start. So the list could use some trimming if Pluto is to be reached by class end. Neptune start would have been 12:48 but in the process of skipping the extra Uranus videos the playlist wound up at Pluto at 12:50. Class was dismissed at this point. After class the playlist was pruned. Any additions need to be accompanied by deletions.

Wednesday's solar system scale model across campus was done on a cold open. The book 13 planets was found in the next curriculum shelf unit over filed under QH instead of CRC QB501.3.A9 2014. Marbles, the measuring wheel, and the sun were prepped at 8:00, which proved prescient. The sun was introduced using the blurb in the book and then without other introduction Mercury was located at 18 feet away. In the past the class has started on a "Where do you think Mercury should be located and how big should Mercury be?" This term this was dropped for a faster exit, allowing time to show each planet's page in the 13 planets book.

Vanette wound up in charge of the book, Silane carried the sun.

Hula hoops also orbit. Is there an underlying mathematical relationship underneath hooping?

Galileo said:

Philosophy [science] is written in that great book which ever lies before our eyes—I mean the universe…This book is written in mathematical language and its characters are triangles, circles and other geometrical figures, without whose help one wanders in vain through a dark labyrinth.

Freeman Dyson echoed this when he wrote:

For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created... ...equations are quite miraculous in a certain way. I mean, the fact that nature talks mathematics, I find it miraculous. I mean, I spent my early days calculating very, very precisely how electrons ought to behave. Well, then somebody went into the laboratory and the electron knew the answer. The electron somehow knew it had to resonate at that frequency which I calculated. So that, to me, is something at the basic level we don't understand. Why is nature mathematical? But there's no doubt it's true. And, of course, that was the basis of Einstein's faith. I mean, Einstein talked that mathematical language and found out that nature obeyed his equations, too.

Max Tegmark took this to the next level in his mathematical universe hypothesis:

The physical world doesn't just have mathematical properties, it has only mathematical properties. It is mathematics.

Do orbiting hoops obey a mathematical relationship?

The Thursday laboratory began with the quotes from Galileo and Max Tegmark. Then an introduction to the hula hoop exploration.

In the morning class the first demonstration timing was 21 rotations in 10.97 seconds. Thereafter 50 rotations were used to calculate periods. Two sets of 50 were averaged to obtain the period for a hoop. While the recommendation was 50 rotations, an alternative of taking the median time of five sets of ten rotations was also suggested. The goal was an accurate measurement of a single rotation.

Right board after class

For the morning class jeans were worn and everything that could interfere with hooping was set aside.

Some groups obtained more linear data than others. Anecdotally groups that generally used the same hooper for all data gathering appear to have stronger correlations. That said, one underlying intent of the laboratory is for the students to have fun while engaging in science. Hula hoops are a physical system. There also provide an example of a system that generates mathematical relationships. For this laboratory the equation is not given - the students are asked to come up with an equation on their own.

Although the students have engaged in multiple laboratories involving mathematical models, somewhat surprisingly the students struggle to obtain an equation. One of the more common approaches was d₁~T₁ which does not yield a line. Although the students have taken college algebra and have performed six laboratories modeled by linear equations and another four modeled by non-linear equations, the students still struggle when not told the specific equation.