Physics can be a difficult subject for students to begin to wrap their minds around – with its complex mathematics and back catalogue of theories, formulas and more, it can be hard to know what will capture both student attention and ensure they learn the fundamentals of the subject.

We sat down (virtually) with Physics Senior Lecturer Dr Paul Lasky from Monash University, to learn about his experience teaching first year physics students and how he uses gravitational and nuclear physics to spark their curiosity with the subject.

We hope this guest post provides you with some new ideas to teach the subject and engage your students in their studies.

Dr Paul Lasky

Senior Lecturer and Australian Research Council Future Fellow in the School of Physics and Astronomy at Monash University

When stars exhaust their fuel, they explode spectacularly as supernovae that are observed throughout the electromagnetic spectrum. Depending on the mass of the progenitor star, the remnant may form a neutron star – a star so compact that common atoms are no longer recognisable.

Neutron stars are some of the most exotic objects in the Universe. Not only are they fascinating to study, providing us with insights into the workings of fundamental physics such as gravitation and nuclear physics, but they also provide an opportunity to get first-year undergraduate students to think about a variety of physical problems and mechanisms in ways that will both challenge and excite them.

Neutron stars have approximately the same mass as our Sun, but squeezed into an almost perfect sphere of approximately ten kilometres radius. Their densities throughout most of the star are greater than that of atomic nuclei. They rotate incredibly fast, with the fastest yet observed spinning on its axis more than 700 times every second. To boot, some neutron stars, known as magnetars, have the strongest magnetic fields in the Universe reaching some twelve orders of magnitude stronger than the magnetic field that creates sunspots on the surface of our Sun.

**Neutron Stars and glitches – engaging first year students in gravitation and nuclear physics**

As an example of a first-year undergraduate problem, one can use simple back-of-the-envelope estimates together with the principle of conservation of angular momentum to understand why neutron stars spin so fast. Start with a star of mass and spin period similar to that of the Sun, and imagine it suddenly contracts to have a radius of ten kilometres.

*Assuming conservation of angular momentum, what is this compact star’s new spin period?*

Depending on the level of first-year physics, one can extend the above thought experiment to ask about the magnetic field – assuming conservation of magnetic flux in the star, what is the compact star’s new magnetic field strength? One can emphasise that these questions are really Fermi problems.

We are not interested in understanding an accurate numerical answer, but simply to get an order-of-magnitude estimate and see if this explains our observations of neutron stars. In this case, it turns out that you do not derive magnetic fields strong enough to explain magnetars. For that, one needs to think about much more complicated physics that involve things like dynamos in the core of the star. But that is also the same process that generates the magnetic field inside the Sun, so this provides an excellent opportunity to stretch the students’ understanding and challenge them to think about physics beyond that of the classroom.

I study a variety of phenomena associated with neutron stars physics, including trying to understand their strong magnetic fields. I also study strange phenomena called glitches: sudden increases in the star’s angular velocity caused by complicated, as yet ill-understood dynamics of the various components in the neutron star core. Neutron star glitches typically cause the star to spin faster by fractions of rotations per second.

“Students enjoy thinking about exotic problems… They provide an opportunity for the students to get their heads around complicated and cutting-edge research topics using physical principles that they are learning about at the time”

For example, one of the most-studied neutron stars, known as the Vela Pulsar, has a rotation frequency of 11.186433 Hz (yes, we really do know it to this accuracy!), which increased by 0.00002 Hz on December 12, 2016. This may sound like a tiny amount, but first-year physics undergraduates are capable of calculating what this implies for the change in rotational kinetic energy of the star, and also for the torques required inside the star to exert sufficient forces. It turns out these numbers are huge! Unfathomably big!!

In a first-year assignment this year, I asked the students to calculate the change in rotational kinetic energy during the Vela glitch, and then asked them to compare this number to things that they know about. In an attempt to get them to think about the scale of energy we were talking about, this was left open to the students to decide what they would use as a comparison. As an example, the answer is akin to the release of energy from approximately 10^{26} atomic bombs. But even that number doesn’t help drive intuition. A more sensible answer is that the change in energy is equivalent to the amount of energy the Sun releases through nuclear burning in approximately 30 years!

**Paul’s learnings from this teaching this topic**

My personal teaching experiences indicate that students enjoy thinking about exotic problems like the ones described above. They provide an opportunity for the students to get their heads wrapped around complicated and cutting-edge research topics using physical principles that they are learning about at the time. It allows the educator to discuss the varying levels of approximations one should make when tackling physical problems; starting from the broadest strokes, back-of-the-envelope calculations to get a feel for the most salient physics associated with the problem, before deep diving into more in-depth calculations. It gives students a feeling for research, and research problems, without burdening them upfront with overly complicated and cumbersome physical principles.

We hope you’ve learned something new or found inspiration in this post. What are some examples you’ve found useful when teaching undergraduates? Reach out if you would like to share your own story!

**About the writer:**

Dr Paul Lasky is a Senior Lecturer and Australian Research Council Future Fellow in the School of Physics and Astronomy at Monash University. He is part of the international LIGO Scientific Collaboration that in 2015 made the first discovery of gravitational waves from colliding black holes. He also contributed significantly to the 2017 discovery of gravitational waves from colliding neutron stars. Paul’s research encompasses many different aspects of astrophysics with a focus on the most extreme regions of the universe, including black holes and ultra-dense stellar corpses, known as neutron stars.

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