Gary White

The shape of “the Spandex” and orbits upon its surface

What is the shape that results when a flat rubber sheet is warped by placing a heavy ball upon it? We show that, at distance R far from the center of a ball of mass M, the height h of the surface above the ball’s center is given by h(R)=AM1/3R2/3, where A is a constant determined by the stretchiness of the rubber and the earth’s gravitational constant. This happy result allows one to analyze the orbits of marbles and coins as they roll across the surface in some detail, providing very nice analogues for a wealth of topics in celestial mechanics, from Kepler’s laws to tides and the Roche limit.

On trajectories of rolling marbles in cones and other funnels

We report on theoretical and experimental results for a ball that rolls without slipping on a surface of revolution, whose symmetry axis is aligned with a uniform gravitational field, particularly investigating both near-circular orbits and scattering-type orbits in cones. The experimental data give support for the theoretical treatment, a non-trivial application of Newtons second law that expands on our previous work and related work of others. Our findings refine those from a recent article in this journal, and largely replicate those obtained from an earlier Lagrangian approach, adding some new details and commentary. While the orbits of marbles rolling in cones do not match inverse-square-law orbits quantitatively (e.g., instead of Keplers 3rd law, we have T2∝R), we argue that students should experience these qualitative phenomena—precession of orbits, escape velocity behavior, spin-orbit coupling, conservation laws for angular momentum, energy, and spin projection—as much for the fun and kinestheti...

Alternative theoretical method for motion of a sand-filled funnel experiment

In “Motion of a Sand-Filled Funnel,” Peter Sullivan and Anna McLoon described how to use numerical methods and a Microsoft Excel spreadsheet to predict the motion of a variant of Atwood’s machine with variable mass. They wrote for noncalculus-based physics classes, but we solve the same problem using the methods of calculus. Our method highlights the less-familiar but more accurate version of Newton’s second law, ∑F =dpdt. This can help introductory physics students understand a broader definition of Newton’s second law and enhance their calculus skills. It also teaches students how to solve a variable-mass problem.

Integration of Physics and Biology: Synergistic Undergraduate Education for the 21st Century

Three aspects of the interactions of physics and biology are covered as seen from the viewpoint of four members of the Division of Undergraduate Education of the National Science Foundation.

Modelling tidal effects

Two models for demonstrating tides and experimenting with various tidal effects are presented. The first takes advantage of the approximately inverse‐square nature of the force law for magnetic poles and exhibits symmetric tidal bulges on opposite sides of the planet, analogous to the tides of the earth. The second demonstration apparatus is a realization of the ‘‘rubber sheet’’ geometry analogy that is often used to model potential wells of massive bodies in space. By rolling various objects on the surface of a stretched elastic cloth one can effectively demonstrate tidal bulges, the Roche limit, and other well‐known astrophysical phenomena.

Unique voices in harmony: Call-and-response to address race and physics teaching

In the February 2016 issue of The Physics Teacher, we announced a call for papers on race and physics teaching. The response was muted at first, but has now grown to a respectable chorale-sized volume. As the manuscripts began to come in and the review process progressed, Geraldine Cochran graciously agreed to come on board as co-editor for this remarkable collection of papers, to be published throughout the fall of 2017 in TPT. Upon reviewing the original call and the responses from the physics community, the parallels between generating this collection and the grand call-and-response tradition became compelling. What follows is a conversation constructed by the co-editors that is intended to introduce the reader to the swell of voices that responded to the original call. The authors would like to thank Pam Aycock for providing many useful contributions to this editorial.

Teaching: Art, craft, science? Yes!

One of my favorite teachers crafted his lectures like a potter molding clay—not likely into a vase, but rather something more solid and utilitarian, yet still elegant, say, a fruit bowl. Vincent Genusa (Dr. G, we called him) was the only person I have ever known to use the word “prodigious” routinely, referring admiringly to a scientist, or perhaps to the applicability of a particular theoretical method, and he would say it with such relish that sometimes a bit of spittle would be evident, to put it delicately. It was impossible not to be swept up in his enthusiasm as he waxed eloquently about this twisty path to discovery or that sinewy bit of logic, and the fact that I have such vivid memories of his lectures decades later speaks to his artistry.