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A team of mathematicians from New York University’s Courant Institute of Mathematical Sciences recently conducted a study to explore the physics and mathematics behind hula hooping. Their research aimed to answer questions such as “What keeps a hula hoop up against gravity?” and “Are some body types better for hula hooping than others?” Their findings not only shed light on the mechanics of hula hooping but also have implications for energy harnessing and improving robotic positioners.

In order to address these questions, the researchers conducted experiments in NYU’s Applied Mathematics Laboratory using robotic hula hoopers and 3D-printed bodies of different shapes. They studied the effects of various body shapes and motions on hula hooping, replicating the movements involved in the activity. High-speed video recordings were taken to capture the movements of hoops approximately 6 inches in diameter on these bodies, which were driven by a motor to gyrate.

The results of the study showed that the form of the gyration motion and the cross-section shape of the body were not significant factors in hula hooping. However, keeping a hoop elevated against gravity for an extended period of time required a specific “body type” with sloping hips to provide the proper angle for pushing up the hoop and a curvy waist to hold the hoop in place. This may explain why some people are natural hoopers while others find it more challenging.

The researchers also conducted mathematical modeling to derive formulas that explained the dynamics of hula hooping. They were surprised to find that such a common activity as hula hooping had not been fully understood at a basic physics level. The knowledge gained from this study could have potential applications in inspiring engineering innovations, energy harvesting from vibrations, and improving robotic positioners and movers used in industrial processing and manufacturing.

The study was conducted by senior author Leif Ristroph, an associate professor at NYU, along with doctoral student Olivia Pomerenk and undergraduate student Xintong Zhu. The research was supported by a grant from the National Science Foundation. The findings of the study provide new insights into the physics of hula hooping and offer a deeper understanding of the mechanics involved in the activity.

In conclusion, the research conducted by the team of mathematicians at NYU has provided valuable insights into the physics and mathematics of hula hooping. Their findings have implications for energy harnessing, robotic technology, and engineering innovations. By studying the dynamics of hula hooping, the researchers have uncovered new information that could be used to improve a variety of practical applications. This study highlights the importance of understanding the subtle math and physics behind seemingly simple activities like hula hooping and demonstrates the potential for valuable discoveries in unexpected places.

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