September 2019 AJPSeptember 2019 Issue,

Volume 87, No. 9


Rattlebacks for the rest of us

Rattlebacks are semi-ellipsoidal tops that have a preferred direction of spin (i.e., a spin-bias). If spun in one direction, the rattleback will exhibit seemingly stable rotary motion. If spun in the other direction, the rattleback will being to wobble and subsequently reverse its spin direction. This behavior is often counter-intuitive for physics and engineering students when they first encounter a rattleback, because it appears to oppose the laws of conservation of momenta, thus this simple toy can be a motivator for further study. This paper develops an accurate dynamic model of a rattleback, in a manner accessible to undergraduate physics and engineering students, using concepts from introductory dynamics, calculus, and numerical methods classes. Starting with a simpler, 2D planar rocking semi-ellipse example, we discuss all necessary steps in detail, including computing the mass moment of inertia tensor, choice of reference frame, conservation of momenta equations, application of kinematic constraints, and accounting for slip via a Coulomb friction model. Basic numerical techniques like numerical derivatives and time-stepping algorithms are employed to predict the temporal response of the system. We also present a simple and intuitive explanation for the mechanism causing the spin-bias of the rattleback. It requires no equations and only a basic understanding of particle dynamics, and thus can be used to explain the intriguing rattleback behavior to students at any level of expertise.



Ocean wave energy, solar radiation, and characteristic times on the back of a Purcell envelope by Yoav Green, Emil J. Millet, and James P. Butler. DOI: 10.1119/1.5119684


Calling all physicists.  DOI: 10.1119/1.5117828


2019 AAPT Award Citations at the Summer Meeting, Provo, Utah by Gordon P. Ramsey.  DOI: /10.1119/1.5123356


Rattlebacks for the rest of us by  Simon Jones, and Hugh E. M. Hunt.  DOI: 10.1119/1.5115498

Determination of aerodynamic drag coefficients using a drop test with a wireless accelerometer and its application to model rockets by  Simon Pettersson Fors, and Carl Nord.  DOI: /10.1119/1.5121281

A computer model of classical rolling friction by  Robert Knop.  DOI: 10.1119/1.5111940

Illustrations of Maxwell's term and the four conservation laws of electromagnetism by  Timothy H. Boyer.  DOI: 10.1119/1.5115339

Calculating fissility without Legendre polynomials: A walk in the woods by  J. M. Pearson.  DOI: /

Magnetic Aharonov-Bohm effects and the quantum phase shift: A heuristic interpretation by  Keith J. Kasunic.  DOI: /10.1119/1.5115499

Analysis of thermodynamic problems with the Lambert W function by  J. Wang, and N. J. Moniz.  DOI: 10.1119/1.5115334

Reciprocity principle and relative accelerations in the theory of relativity by  Reza Rashidi, and Fatemeh Ahmadi.  DOI: /10.1119/1.5115338

Low-entropy expressions by Sanjoy Mahajan. DOI:  10.1119/1.5111838

Notes and Discussions

Erratum: “Free falling inside flattened spheroids: Gravity tunnels with no exit” [Am. J. Phys. 86, 924–933 (2018)] by  Richard Taillet.  DOI: 10.1119/1.5119508

Book Reviews

Anxiety and the Equation: Understanding Boltzmann's Entropy by  Kannan Jagannathan.  DOI: 10.1119/1.5116583

Student's Guide to Analytical Mechanics by Craig F. Bohren.  DOI: /10.1119/1.5119509


American Journal of Physics 87, 768 (2019); .  DOI: /10.1119/1.5120016

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