#  The Surprising Physics of Irregular Rolling Objects 

 





March 20, 2025

 

 

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   ![Image of rolling balls_L.Mahadevan_PNAS_2025](/sites/g/files/omnuum6811/files/styles/hwp_1_1__360x360_scale/public/2025-04/L.Mahadevan%20Rolling%20Ball_PNAS_2025.png?itok=aNIbiqhx) 

 

Gravity might make a perfect ball roll down a ramp in a textbook, but real-world objects rarely follow such neat rules. A new [study](https://www.pnas.org/doi/10.1073/pnas.2417161122) from Professor L. Mahadevan's lab takes a deep dive into the messy reality of how irregular spheres and cylinders roll—revealing a world of unexpected order in chaotic motion.

The team used theory, computer simulations, and hands-on experiments to study how imperfectly shaped objects behave on inclined planes. The research, published in *Proceedings of the National Academy of Sciences*, shows that irregular objects don’t always roll predictably. Instead, their behavior hinges on a “critical angle” where a transition occurs—from standing still to rolling—mirroring the kind of sharp shift seen in phase transitions.

The study found that irregular spheres and cylinders reach a stable rolling motion once they pass this critical point, and their behavior depends heavily on shape, size, and inertia. Unlike perfect spheres, irregular ones roll jerkily—but fascinatingly, their motion always becomes periodic. That is, the path repeats in a consistent cycle. Remarkably, the object rotates over itself twice before returning to its original orientation—an echo of the mathematical Dirac’s Plate Trick and the quirky “Hairy Ball Theorem.”

The findings could have implications for fields as diverse as cellular transport, robotics, and materials science—anywhere irregular objects need to roll.



 

 

 



 

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