The Physics of Hula Hooping: Insights into Motion, Energy, and Engineering

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The Physics of Hula Hooping: Insights into Motion, Energy, and Engineering

Asked by terryaster at 9:16am on Jan 8 2025

Hula hooping may seem like a simple pastime, but it raises intriguing questions: What keeps the hoop spinning against gravity? Are certain body types better suited for hula hooping? A team of mathematicians has explored these questions, uncovering insights that extend beyond the playground, with potential applications in energy harnessing and robotic positioning systems.

These findings, published in the Proceedings of the National Academy of Sciences, provide the first mathematical explanation of the physics behind hula hooping.

"Our study focused on understanding the body motions and shapes required to keep a hoop aloft and the physical constraints involved," said Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and the senior author of the study.

To investigate, the researchers recreated hula hooping on a miniature scale in NYU’s Applied Mathematics Laboratory. Using 3D-printed shapes like cylinders, cones, and hourglasses to mimic human forms at one-tenth scale, they conducted experiments with robotic hula hoopers. The robotic models, driven by a motor to replicate human gyrations, spun hoops approximately six inches in diameter, while high-speed cameras captured their movements.

The experiments revealed that the specific gyration motion or body cross-section shape (e.g., circular or elliptical) did not significantly affect the ability to initiate spinning. "In all cases, good twirling motions of the hoop around the body could be set up without any special effort," Ristroph explained.

However, keeping the hoop spinning against gravity required a unique "body type" with key physical traits: sloping surfaces at the "hips" to push the hoop upward and a curvy "waist" to hold it in place.

"Some people naturally have these traits, while others may need to work harder to achieve the same result," Ristroph noted.

The team developed mathematical models to describe the observed dynamics, deriving formulas that not only explained the results but also hinted at broader applications.

"We were surprised to find that such a popular, healthy, and fun activity wasn’t fully understood at a basic physics level," Ristroph said. "The math and physics we uncovered are surprisingly intricate and could inspire engineering innovations, from energy harvesting systems that use vibrations to improved robotic movers for industrial processes."

Co-authors of the study included NYU doctoral student Olivia Pomerenk and Xintong Zhu, an undergraduate researcher at the time. Their work underscores how everyday phenomena can provide profound insights into both fundamental science and practical technology.

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