Hula hooping is so commonplace that we might overlook some fascinating questions it raises: “What retains a hula hoop up towards gravity?” and “Are some physique varieties higher for hula hooping than others?” A crew of mathematicians explored and answered these questions with findings that additionally level to new methods to raised harness vitality and enhance robotic positioners.
The outcomes are the primary to elucidate the physics and arithmetic of hula hooping.
“We had been particularly inquisitive about what sorts of physique motions and shapes may efficiently maintain the ring up and what bodily necessities and restrictions are concerned,” explains Leif Ristroph, an affiliate professor at New York College’s Courant Institute of Mathematical Sciences and the senior writer of the paper, which seems within the Proceedings of the Nationwide Academy of Sciences.
To reply these questions, the researchers replicated, in miniature, hula hooping in NYU’s Utilized Arithmetic Laboratory. They examined totally different shapes and motions in a collection of experiments on robotic hula hoopers utilizing 3D-printed our bodies of various shapes (e.g., cylinders, cones, hourglass shapes) to signify human varieties at one-tenth the dimensions. These shapes had been pushed to gyrate by a motor, replicating the motions we take when hula hooping. Hoops roughly 6 inches in diameter had been launched on these our bodies, with high-speed video capturing the actions.
The outcomes confirmed that the precise type of the gyration movement or the cross-section form of the physique (circle versus ellipse) wasn’t a consider hula hooping.
“In all instances, good twirling motions of the ring across the physique might be arrange with none particular effort,” Ristroph explains.
Nevertheless, preserving a hoop elevated towards gravity for a major time period was tougher, requiring a particular “physique sort” — one with a sloping floor as “hips” to supply the right angle for pushing up the ring and a curvy type as a “waist” to carry the ring in place.
“Folks are available in many alternative physique varieties — some who’ve these slope and curvature traits of their hips and waist and a few who do not,” notes Ristroph. “Our outcomes may clarify why some persons are pure hoopers and others appear to have to work further onerous.”
The paper’s authors performed mathematical modeling of those dynamics to derive formulation that defined the outcomes — calculations that might be used for different functions.
“We had been stunned that an exercise as well-liked, enjoyable, and wholesome as hula hooping wasn’t understood even at a primary physics degree,” says Ristroph. “As we made progress on the analysis, we realized that the maths and physics concerned are very refined, and the data gained might be helpful in inspiring engineering improvements, harvesting vitality from vibrations, and bettering in robotic positioners and movers utilized in industrial processing and manufacturing.”
The paper’s different authors had been Olivia Pomerenk, an NYU doctoral pupil, and Xintong Zhu, an NYU undergraduate on the time of the examine.
The work was supported by a grant from the Nationwide Science Basis (DMS-1847955).
