How does a hula hoop master gravity? Mathematicians prove that shape matters
The hula hoop is so common that we might overlook some of the interesting questions it raises: “What makes a hula hoop defy gravity?” and “Are some body types better suited to hula hoops than others?” A team of mathematicians These questions were explored and answered, and their findings also point to new ways to better harness energy and improve robot positioners.
This result explains for the first time the physics and mathematics of the hula hoop.
“We are particularly interested in what body movements and shapes can successfully lift the rim, and what physical requirements and constraints are involved,” said Dr. Liu, an associate professor at NYU’s Courant Institute for Mathematical Sciences. The paper appears in Proceedings of the National Academy of Sciences.
To answer these questions, researchers at NYU’s Applied Mathematics Laboratory replicated a hula hoop in miniature. They conducted a series of experiments on a robotic hula hoop, testing different shapes and movements, using 3D printed bodies of different shapes (e.g. cylinder, cone, hourglass shape) to represent a tenth of the size of the human form. . The shapes are rotated by motors, replicating the movements we make when spinning a hula hoop. Iron hoops about 6 inches in diameter were fired at the bodies, and the action was captured on high-speed video.
The results showed that the exact form of the rotational motion or the cross-sectional shape of the body (circular vs. oval) were not factors in the hula hoop.
“In all cases, it is possible to develop a good rotational movement around the body without any special effort,” Ristrov explains.
However, keeping the rim elevated against gravity for a significant period of time is more difficult and requires a special “body type” – one with a sloping surface as “hips” to provide the proper angle to lift the rim and The curved shape acts as a “waist” to hold the hoop in place.
“People come in many different body types—some have these slopes and curves in their hips and waists, and some don’t,” Ristroff points out. “Our results may explain why some people are natural shooters, while others seem to have to work extra hard.”
The paper’s authors mathematically modeled these dynamics and came up with formulas to explain the results – calculations that can be used for other purposes.
“We were surprised that an activity as popular, fun and healthy as the hula hoop was not understood even at a basic physical level,” Listrov said. “As the research progressed, we realized that the The mathematics and physics are very subtle, and the knowledge gained can be used to inspire innovations in engineering, harvesting energy from vibrations, and improving robotic positioners and movers used in industrial processing and transportation manufacturing.
Other authors of the paper include Olivia Pomerenk, a doctoral student at NYU, and Xintong Zhu, an undergraduate student at NYU at the time.
This work was supported by a grant from the National Science Foundation (DMS-1847955).
2025-01-02 21:26:39