NYC Gazette

Hula hooping, a popular and seemingly simple activity, has been the subject of a study by mathematicians seeking to understand its underlying physics. The research explores questions such as "What keeps a hula hoop up against gravity?" and "Are some body types better for hula hooping than others?"

Led by Leif Ristroph, an associate professor at New York University's Courant Institute of Mathematical Sciences, the team conducted experiments in NYU's Applied Mathematics Laboratory. They used 3D-printed models representing human forms to test different shapes and motions on robotic hula hoopers. These models were driven by motors to simulate human gyrations, with high-speed video capturing the results.

The study found that neither the exact form of gyration motion nor the cross-section shape of the body significantly affected hula hooping success. According to Ristroph, "In all cases, good twirling motions of the hoop around the body could be set up without any special effort."

However, maintaining a hoop's elevation against gravity required specific physical attributes. A sloping surface as "hips" provided the angle needed to push up the hoop, while a curvy form as a "waist" helped keep it in place. This finding may explain why some individuals are naturally adept at hula hooping while others struggle.

The researchers also developed mathematical models to derive formulas explaining these dynamics. These calculations have potential applications beyond understanding hula hoops; they could inspire engineering innovations and improvements in energy harvesting from vibrations and robotic positioners used in industrial settings.

Ristroph noted their surprise at discovering that such a widespread activity was not well understood at even a basic physics level: “We were surprised that an activity as popular, fun, and healthy as hula hooping wasn’t understood even at a basic physics level.”

The paper was co-authored by Olivia Pomerenk and Xintong Zhu from NYU. The research received funding support from the National Science Foundation (DMS-1847955).