Hula hoop physics

Laboratory 14 in physical science is an investigation into the relationship between the diameter of a hula hoop and the rotation period of the hoop. This summer was the first time this laboratory had been done on Kosrae. 

The small hoop is one that is in still in the form in which the hoop was packed. The next larger hoop is one with an overlap introduced, duck tape was used to hold the hoop loop together. The area of overlap can be seen at the bottom of the hoop. The purple hoop is the standard hoop, up around 107 cm in diameter. The largest hoop has a piece of three-quarter inch PCV pipe spliced into the hoop, held again by duck tape. This began to give us, for the first time, hoops of different diameters that could be hooped around the waist. 

Renee-Ann-Seshrue and Sina

Only the smallest hoop was too small to hoop around the waist, the smallest hula hoop was hooped on the arm. Leg hooping this hoop might retain the horizontal orientation with respect to gravity, a factor that is thought to potentially influence rotation rate.

Sina

Although I initially suggested that the students explore diameter versus frequency - in part because I always have the sense that frequency is more intuitively understood - I realized that the negative slope would generate a y-intercept, while diameter versus period might not.

Desmos graph for diameter versus frequency (top) and period (bottom)

Although not all groups wound up with clearly linear data there are suggestions that in the range in which a hoop can be hooped on the waist the relationship between diameter and rate of rotation is linear. Whether a zero diameter hoop would have a zero period is unclear. 

The core point to the laboratory is to expand what the students consider to be the realm of physical science. The laboratory is also intended to show that fun and science labs can go together. This also demonstrates that math governs more systems than one might imagine, which dovetails nicely into the theme this week that the universe is, or is not, mathematical. 

Plans for future runs would be to improve on the material used to splice a hoop to a larger size and to work on maybe cutting and drilling some hoops to a smaller size without an overlap. My theory is that waist hooping and arm hooping are not going to be mathematically equivalent and that the path to a stronger relationship would be to eliminate arm hooping and run only with waist hooping. That means creating five hoops of distinctly different diameters that can still be hooped on the waist. 

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