The Robots That Solved the Hula Hoop
Nobody had explained how a hula hoop stays up. It took a mathematician watching street performers and a set of 3D-printed wiggling robots to crack it. The answer involves geometry, gravity, and a toy everyone knows doing something nobody had understood.
The hula hoop has been around since 1958. In all that time, nobody had properly explained why it stays up.
Physicists had written about angular momentum and torque. But the basic mechanics, what actually prevents a spinning ring from sliding to the floor, remained an open question. It took Leif Ristroph, an applied mathematician at New York University, watching street performers near his home in Greenwich Village to notice the gap. He has a habit of noticing gaps like this. His lab has previously worked out how many licks it takes to reach the centre of a lollipop (about 1,000, using fluid dynamics and homemade candy balls), solved a sprinkler puzzle that had baffled physicists since the 1880s, and discovered that paper aeroplanes stay level by a mechanism completely different from actual aircraft. Ristroph describes his approach simply: "I like to think of the whole world as a laboratory."
For the hula hoop problem, his team 3D-printed a series of small robot bodies at roughly one-tenth human scale, each a different shape. They attached a motor to make each one gyrate in tight circles, launched a hoop about six inches across, and filmed the results with high-speed cameras.
The cylinder failed immediately. The hoop slid straight down, nothing to push back against gravity. A cone-shaped robot did slightly better: its slope gave the hoop an upward push. But with no curve to hold the hoop in place, it drifted. Start too high, it climbed off the top. Start too low, it fell. Only one shape worked: the hourglass. The inward curve, what the researchers call a "waist," kept the hoop from migrating up or down. The outward slope at the bottom, the "hips," provided the upward force. Together, they created a stable zone where the hoop could spin indefinitely.
The paper, published in the Proceedings of the National Academy of Sciences in January 2025, describes hula hooping as a form of mechanical levitation. The hoop is not just spinning. It is being held aloft by the geometry of the surface it rolls against, a rolling contact problem that turned out to involve subtler physics than anyone expected.
Ristroph's team also found something that matters for anyone who has ever failed at hula hooping: body shape is not destiny. They got the cone-shaped robot, the one that kept losing its hoop, to succeed by adjusting the speed of its gyrations depending on where the hoop sat. People do this instinctively, compensating with faster hip movements when the hoop starts to slip. A few practical findings fell out of the research too. A slow launch will fail. The hoop and the body need to be moving in the same direction from the start. And bigger hoops are easier for beginners because they require slower gyrations to stay up.
Why this is worth sharing with kids
Most children have tried a hula hoop. Many have failed at it, watched someone else keep it going effortlessly, and wondered what they were doing wrong. This gives that experience a frame: it is not about talent. It is about shape, speed, and the forces that show up when a ring rolls around a curved surface.
But the bigger story here might be Ristroph's lab itself. A mathematician who investigates lollipops, sprinklers, paper aeroplanes, insect flight, and hula hoops is a useful corrective to the idea that science only happens in serious-looking labs with serious-looking equipment. His research is driven by the same impulse most children already have: noticing something ordinary, asking how it actually works, and discovering that the answer is stranger than expected.
Ask your child what they think would happen if you changed the shape of the hoop, or spun it faster, or tried it on a different part of the body. The physics is accessible enough to reason about and odd enough to be worth the effort.
Seventy years of hula hooping, and it took a set of 3D-printed robots, wiggling under high-speed cameras in a maths lab in Manhattan, to explain what was happening all along.
Source: Zhu, X., Pomerenk, O. & Ristroph, L. "Geometrically modulated contact forces enable hula hoop levitation." Proceedings of the National Academy of Sciences, Vol. 122, January 2025. Reported by Science News Explores.
