Laboratory 14 hoop rate relationship

Laboratory fourteen functions as a laboratory practical for the physical science course, a chance to show that mathematical analyses can be applied to any physical system, and an opportunity to have some fun while doing science. The course is all about science as doing, exploring, engaging. Science as a process and measurement, as discovery. The course hopes to ignite, or reignite a spark of excitement and fun in science. The students are all non-science majors, many of whom have learned negative attitudes towards science. Science was either a lot of memorization or just plain hard. This course seeks to remedy that. There is a "let's go find this out" approach to everything. Not what you know, but what you can show. 

In laboratory fourteen the students were asked to determine the mathematical relationship, if any, between the diameter of a hula hoop and the rate of rotation for the hoop.

Renay hoops while Darla times

The board behind Renay shows the introduction to the laboratory. I am still working to find what the minimal scaffolding required will be. I do not want to overly channel the students.

Renay

At the same time, too little scaffolding could be overly frustrating for the students - the task set will be too vague to lead to data that can be analyzed. 

Renay

This laboratory also hinges on whether the lab partners have one who can hoop. With thanks to my students back in the fall of 2021, I learned how to hoop well enough to demonstrate the basic technique for waist hooping.

Adelina hooping

Adelina hooping. Science lab can be fun! The green hoop, at 97 cm in diameter, is the smallest of the hoops. Unfortunately there are only roughly three sizes at present: 97 cm, 103 cm, and 107 cm. The class could benefit from a few more hoop sizes. 

Richard 

Some of the women have hooped before, but few to none of the men have hooped. 

Renay with a good, flat spin

Adelina measures and Jessie May records the measurements

One group's data. The diameter varies depending on whether the group measures the inside diameter, outside diameter, or a midline diameter.

Adelina

Renay and Adelina measure the blue hoop diameter, Richard watches

Data including the diameter, time duration in seconds, and number of spins. This is what I mean about scaffolding. Once this was written down, one group was looking at graphing diameter versus spins, but spins are just an arbitrary number related to how long the hooper was able to hoop. Here I pointed this out to group and suggested they look for a rate of rotation. In the morning class I went specific and recommended rotations per second, or, effectively, Herz. This does lead to a negative relationship, which was perhaps a tad bit of a curve ball as this introduces a non-zero y-intercept, something most of the labs avoided during the term. The students are not well prepared to think in terms of a non-zero y-intercept, which makes this particular harder to analyze. 

The class included little hoops called doughnuts, plus the child's hoop. The child's hoop, however, is too small for an adult to waist hoop, and that introduces arm hooping. But arm hooping appears to work differently from waist hooping. In the 8:00 section I instructed the students to horizontally arm hoop the little ring. Which is difficult - one has to bend over and try not hit themselves, or use an overhead horizontal arm hoop approach. 

In the 11:00 class I removed the "rotations per second" specification from the board and left that an open choice as to how to measure the rate of rotation. 

I also put away all of the non-waist hoops. This makes the domain very small, but keeps the exercise limited to waist hoop data. 

Bethlyanne clearly had prior experience

Bethlyanne

Leipolanda

Leipolanda was perhaps the most experienced and capable hooper of the day. She could hoop with minimal motion at a consistent rate without any apparent limit.

Leipolanda

Saya timing and graphing, Donnalynn recording

Saya, Donnalynn, Leipolanda, Bethlyanne

Saya and Leipoland measuring

Blossom

Malika had hooped as a child and quickly regained her abilities

Malika

Data in the 11:00 section, this group figured out the rotation rate formula on their own

A closer look at the board at lab end. I remain uncertain what the proper amount of scaffolding is for this laboratory. I want the lab to have an open, exploratory feel. The downside is that the students may, as one group did, fail to realize that they needed to combine spins with time to get a rotation rate. Specifying the rotation variable would also allow specifying use of the rotation period, rather than the rotation rate in Hertz. The period may be a direct linear relationship. Or closer to direct, as the slope will be positive. One could argue zero diameter has a period of zero and an infinite rate of rotation (bigger hoops produce slower rotation rates, smaller hoops rotate naturally faster).