Aldrin would join Neil Armstrong and Michael Collins on the historic flight of **Apollo 11** in 1969 — and later formally change his first name from “Edwin” to his **other** nickname “Buzz”.

Sunday & dimanche

Monday & lundi

Tuesday & mardi

Wednesday & mercredi

Thursday & jeudi

Friday & vendredi

Saturday & samedi

Hwan Bae, Norah Ali, and I just published a featured article in the journal **Chaos** on another famous anholonomy, **Hannay’s hoop,** which involves a bead sliding frictionlessly on a horizontal **noncircular** hoop: A slow cyclic rotation restores the hoop to its original state but unavoidably shifts the moving bead by an angle that depends on the hoop’s geometry. Rotating a noncircular hoop indelibly imprints its geometry on the bead’s motion.

In the limit of slow rotation and fast beads, the shift is called **Hannay’s angle** (and is analogous to **Berry’s phase** in quantum mechanics). We mathematically generalized the shift to any speed, fast or slow, and were able to observe it in a simple experiment involving wet ice cylinders sliding in 3D printed channels.

Norton’s dome has a cubed square root profile: if the **downward** height is z at dome **arc length** s, then

If max height z_m = 2/3 when max arc length s_m = 1, then

z = \frac{2}{3}s^{3/2}.By the **Pythagorean theorem**, ds^2 = dx^2 + dz^2, and so

Integrate to find the horizontal coordinate in terms of the arc length

x = \frac{2}{3}\left(1 - \left(1-s\right)^{3/2}\right),and inversely

s = 1 - \left(1 -\frac{3}{2}x\right)^{2/3}.Eliminate the arc length to find the profile

x =\frac{2}{3}\left(1 - \left(1-\left(\frac{3}{2}z\right)^{2/3}\right)^{3/2}\right),and inversely

z =\frac{2}{3}\left(1 - \left(1-\frac{3}{2}x\right)^{2/3}\right)^{3/2}.If the arc length 0\le s \le 1, then the rectangular coordinates -2/3 \le x,y \le 2/3 and 0\le z \le 2/3.

For sliding frictionlessly on the dome, form the total **energy** as the **sum** of the kinetic and potential energies

for unit mass and gravity. Differentiate with respect to time to get

0 = \dot{s} \ddot{s} - s^{1/2}\dot{s}and divide by \dot s to get the equation of motion

\ddot{s} = \sqrt{s}.Alternately, form the **Lagrangian** as the **difference** in the kinetic and potential energies

and insert into the **Euler-Lagrange** equation

to again get

\ddot{s} = \sqrt{s}.The acceleration along the dome increases as the square root of the arc length. Combine the equation of motion with the initial conditions s[0]=0 and \dot{s}[0]=0, corresponding to a mass at rest on top of the dome, to form an **initial value problem (IVP)**.

Surprisingly, **two** solutions exist:** infinite rest**

and **spontaneous sliding**

To check the latter, differentiate to get

\dot s = \frac{1}{36} t^3, \ddot s = \frac{1}{12} t^2 = \sqrt{s}.How can a physical system have **two** evolutions?

If an IVP’s equations are continuous, solutions **exist**; if the first derivatives are also continuous, the solution is **unique**. In this case, the square root \sqrt{s} in the equation of motion means that the first derivative is **not** continuous at the origin, so solutions exist but are not unique.

The peak of Norton’s Dome is continuous, and its slope is continuous, but the slope of its slope is discontinuous. The **apex of a cone** is more extreme, as its slope is discontinuous.

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All I can think of to describe my experience in the Standard model’s 50th anniversary conference is to repeatedly yell the word wow, until I have lost the will to do so. I am at a loss of words, but I will attempt to put my flustered speech in perspective.

Imagine Albert Einstein dedicating some of his time to share his findings with you. One of the greatest minds explaining the greatest discoveries to you. Not to get greedy but imagine all the great minds of a generation dedicating a couple of days to do just that. I am of course referring to 1927 fifth Solvay International Conference featuring the most prominent names in physics; names including Albert Einstein, Niels Bohr, Paul Dirac, Erwin Schrodinger, and Wooster’s very own Arthur Compton. Attending a conference of such magnitude is a dream for any aspiring physicist, and this is how it felt to be a part of the Standard Model Conference.

In this conference, I listened to my idols talk about the successes of this field I aspire to be a part of. I also listened to my idols talk of the short comings of this theory. No where is the Greek quote “the more I know, the more I know I know nothing” more true than when the most knowledgeable scientists in a field tell of how little we know. In fact, the Standard Model, often dubbed the Theory of Almost Everything, accounts for a mere 4% of the universe’s constituents and even that we don’t fully understand. I sat in the back when speakers took turns calling upon the back rows of undergraduates for help in advancing this theory in the future. Imagine Einstein passing the torch to you. Imagine Einstein asserting the back rows will certainly produce the next Nobel Laureate. Wow!!”

We also have two big events on campus. The Physics Club runs Science Day, an event for all science clubs on campus to do demos and fun activities for the whole community. And we participate in Expanding Your Horizons, a huge event specifically for middle school girls that incorporates not just women science students and professors from the campus but also professional women from around the community whose job includes an aspect of science.

At Science Day, it’s fun to see what the other sciences on campus are doing. The neuroscience club gets a lot of interest with the brains that they bring.

New this year was a giant size demo from the Astronomy Club to demonstrate how massive objects warp the spacetime around them so that other smaller objects orbit the massive one. This was lots of fun to play with!

Air pressure is always a favorite, of course, with the liquid nitrogen parts. This year the demo even attracted President Bolton! I think she had a fun morning with lots of physics — it’s probably a good change from administration.

For Expanding Your Horizons, I do the same workshop three times for different groups of girls. We do the “Humpty Dumpty” experiment, where the girls have about 20 minutes with limited materials to create a container to try to protect an egg from breaking during a fall. We drop the eggs from the 3rd floor, so it’s pretty challenging! This year, Dr. DeGroot joined me and we had lots of fun. I love seeing the creativity of the girls — not only in making their containers, but also in decorating and naming their eggs.

And the moment of truth — dropping the eggs from a great height! If the eggs survive, we add them to the Egg Hall of Fame!

Most of the eggs this year made it! Lesson learned = parachutes really work!

]]>This Saturday was our last day to work with our dancers before Justine left for LA to present her senior thesis at the March American Physical Society meeting. (From literally thousands of presentations, the APS’s PHYSICS web site would rank Justine’s **Moon Dance **talk as one of the meeting’s top ten highlights.)

We massed Rachel, and Justine helped her into the harness as I fine-tuned the sandbag mass to simulate lunar gravity. With Rachel sitting expectantly on the floor, Justine and I struggled to raise the sandbag and connect the steel wire to the harness with the carabiners. We moved away, and with an almost **surreal** lack of effort, Rachel gracefully stood, the sandbag descending as she ascended. I made a mental note to thank Mike for recommending the low-friction pulleys.

Kim and Justine had choreographed treadmill translation sequences for both Kathlyn and Rachel, but the free-dance improvisation proved most successful. Once we got the physics right, I had hoped we would produce something of artistic value, and we had. Our dancers had the grace, and we gave them the power – a **superpower**.

By approximating lunar and martian gravity for her senior thesis, Justine changed the **physics of dance**. But her central achievement was the unprecedented and dazzling reduced-gravity performances she elicited from her dancers. Later this century, dancers will dance on Luna and Mars, and Justine has glimpsed that future, and it will be spectacular.

Download a high-resolution 659 MB MP4 of our “Back to Black” video. The download may take several minutes, but it’s worth it.

]]>As my first year as department chair winds up, I am preparing to move to the University of Oregon in Eugene for a one-semester research leave. I’m looking forward to reconnecting with five Wooster physics alumni who are now in the Physics Ph.D. program there!

As I look back on the year, I have a few more random highlights to post that I somehow never found the time to blog about during the busy year!

I enjoyed attending the Senior awards banquet earlier this spring, where Justine Walker, Avi Vajpeyi, and Zane Thorburg (left to right below) were honored for their academic accomplishments. Congrats to all three of you!

The department’s new 3-D printer, housed in Dr. Manz’s Wave Lab, experienced heavy use in multiple research projects, including Collin Hendershot ’18’s project studying the aerodynamics of race car wings of various curvatures. We also used it to 3-D print a plaque honoring Maggie Lankford 16 whose selection as an Apker Award finalist for her I.S. research helped fund the purchase of the printer. Thanks for Jack Mershon ’18 for his help with the plaque!

Last summer, students and professors who participated in our NSF-sponsored summer research program paused their work for an afternoon to go on a hike at Wooster Memorial park, a lovely 300 acre wooded area including many miles of trails around a large ravine. I hope this becomes an annual tradition!

The department is looking forward to another exciting summer of research as our 2018 program begins in less than one week! I’ll be sure to blog from Oregon during my leave, so stay tuned.

]]>For long times, Mercury’s orbit precesses due to the gravity of Jupiter, the oblateness of Sol, and **spacetime curvature**, first described by Albert Einstein’s theory of **General Relativity**. For short times, as the animation shows, one solar day lasts two years!

In particular, spin a conducting disk in a perpendicular magnetic field, and connect its axle to its circumference using a **wire** and two sliding contacts, as in the animation. The magnetic field deflects free changes in the disk radially, and they push other charges through the wire. This rotary electric** generator** converts mechanical motion into electrical current, which can heat the wire and toast bread.

Is the **external** magnetic field necessary? No! Bend the wire into circles just above and below disk, as in the animation. If the disk spins fast enough, the **internal** magnetic field of the charges moving in the wire deflects the charges in the disk, which then push the charges through the wire! This **dynamo** is the closest thing to perpetual motion in classical physics. It generates the magnetic fields of stars and planets, including Earth’s.