A success hula hooping calls for a frame sort with the suitable slope and curvature. Credit score: NYU’s Implemented Arithmetic Lab
Hula hooping is so not unusual that we might forget some fascinating questions it raises: “What helps to keep a hula hoop up towards gravity?” and “Are some frame sorts higher for hula hooping than others?” A crew of mathematicians explored and replied those questions with findings that still level to new techniques to higher harness power and support robot positioners.
The effects are the primary to provide an explanation for the physics and arithmetic of hula hooping.
“We have been particularly inquisitive about what varieties of frame motions and shapes may just effectively hang 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 Lawsuits of the Nationwide Academy of Sciences.
To respond to those questions, the researchers replicated, in miniature, hula hooping in NYU’s Implemented Arithmetic Laboratory. They examined other shapes and motions in a chain of experiments on robot hula hoopers the usage of 3-d-printed our bodies of various shapes (e.g., cylinders, cones, hourglass shapes) to constitute human bureaucracy at one-tenth the scale.
This film is taken from high-speed video of the experiments on a robot hula hooper, whose hourglass shape holds the ring up and in position. Credit score: NYU’s Implemented Arithmetic Lab
Those shapes have been pushed to gyrate by way of a motor, replicating the motions we take when hula hooping. Hoops roughly 6 inches in diameter have been introduced on those our bodies, with high-speed video taking pictures the actions.
The effects confirmed that the precise type of the gyration movement or the cross-section form of the frame (circle as opposed to ellipse) wasn’t a consider hula hooping.
“In all circumstances, just right twirling motions of the ring across the frame might be arrange with none particular effort,” Ristroph explains.
Overlaid frames from movies display {that a} cone-shaped frame fails to hula hoop however a curvy frame succeeds. Credit score: NYU’s Implemented Arithmetic Lab
Then again, retaining a ring increased towards gravity for a vital time period used to be tougher, requiring a distinct “frame sort”—one with a sloping floor as “hips” to give you the correct perspective for pushing up the ring and a curvy shape as a “waist” to carry the ring in position.
“Folks are available in many alternative frame sorts—some who’ve those slope and curvature characteristics of their hips and waist and a few who do not,” notes Ristroph. “Our effects may provide an explanation for why some persons are herbal hoopers and others appear to have to paintings additional onerous.”
This animation presentations the top-down view of the ring twirling motions from a pc simulation. Credit score: NYU’s Implemented Arithmetic Lab
The paper’s authors performed mathematical modeling of those dynamics to derive formulation that defined the consequences—calculations that may be used for different functions.
“We have been stunned that an job as well-liked, amusing, and wholesome as hula hooping wasn’t understood even at a fundamental physics stage,” says Ristroph.
“As we made development at the analysis, we discovered that the mathematics and physics concerned are very delicate, and the information won might be helpful in inspiring engineering inventions, harvesting power from vibrations, and bettering robot positioners and movers utilized in business processing and production.”
The paper’s different authors have been Olivia Pomerenk, an NYU doctoral scholar, and Xintong Zhu, an NYU undergraduate on the time of the find out about.
Additional information:
Xintong Zhu et al, Geometrically modulated touch forces permit hula hoop levitation, Lawsuits of the Nationwide Academy of Sciences (2024). DOI: 10.1073/pnas.2411588121
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How does a hula hoop grasp gravity? Mathematicians turn out that frame form issues (2025, January 2)
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