The Hills Are Alive (With the Sound of Music)

Happy Monday! I must say, it is wonderfully pleasant to have a busy Monday doing things that I actually care about to look forward to. Also apparently, when left to my natural rhythm, I need about 9 hours of sleep. Zzzz. Perhaps this will decrease as I become fully rested, but perhaps not.

Today I set for myself three chapters to study: Oscillations, Traveling Waves, and Superposition and Standing Waves. This was pretty ambitious, honestly. It’s the entire Part II of this book! But I got through it all, and it makes sense. I hit this pretty hard when studying for the pGRE, so I feel relatively comfortable with the material presented. There are a lot of interesting practical examples regarding music and musical instruments that are very interesting. Amazing how people came up with this stuff intuitively/through trial and error long before we could show the principles behind what is happening in even a relatively simple instrument!

I returned to Mathematical Methods today, and luckily this chapter went more smoothly than the last one. This was a re-introduction to calculus, covering derivatives and integrals. Weird that I find this easier to follow than the algebra chapter, but this is (as stated in the book) the kind of math most frequently found in physical sciences, so perhaps that is not surprising.

And I even had time to take a long midday break to go see Wonder Woman and buy exorbitant amounts of junk food at Sam’s Club with my boyfriend! What a nice Monday. =)

Today’s fun “new” fact: Okay, so this has mostly been about physics so far, but today I’m giving the honors to math. While I’ve always known in the back of my mind what a derivative is and how to derive one (hehe), if yesterday you’d asked me to do it, I might have flailed a little. But it’s really actually simple to show, for example, the derivative of a simple power function. For f(x)=x2, take the limit as ∆x approaches zero of [f(x+∆x)-f(x)]/∆x.

((x+∆x)2-x2)/∆x

(x2+2x∆x+∆2-x2)/∆x

(2x∆x+∆x2)/∆x

2x+∆x

And as ∆x goes to zero: f'(x)=2x.

Fun!

Your Fingertips, Well They Know the Code*

Oops, a bit tardy getting this post up! Been having a little trouble self-motivating the past couple days, in fact, because I didn’t get my Friday chapters done until Saturday night. I have properly chastised myself, but I’m not too worried. I’ve given myself weekends off, so there is some flexibility in my schedule, and I did get it done eventually!

So Friday AM I scheduled myself to work on coding. I learned to code in Basic a long time ago, and I loved making little text games and mazes and such. While my skills are a little (a lot) outdated, it gives me a decent grounding in the mindset of coding. I also started doing a Codecademy course in Python about 2 years ago, although I only made it about halfway through. However, the general consensus on the best language to know for physics seems to be Python, so I’m revisiting the course. I spent Friday going back through the lessons I had already done to remind myself of the syntax and such. It was pretty simple, but it felt good to go through some basic lines of code.

Once I finish the Python course (I anticipate that being in the next week or so), I plan to check out a resource I found specifically for physics called Computational Physics by Dr. Mark Newman. Some of it is available for free on his site, so I will start with that. If it is a useful resource, I’ll purchase the full book and try to work through it. I think this will place me in excellent footing for the fall.

For my slightly delayed Tipler and Mosca studying, I had 2 chapters: Static Equilibrium and Elasticity and Fluids. I’m not going to lie, the fluids stuff was tedious. I am not sure why. Perhaps it reminds me too much of my Navy science experiences, or maybe it is just a weak spot for me. In any case, these two chapters brought me to the end of Part I! That was an exciting little milestone for me.

It was the first time that I found something I had written in my textbook. In general, I am not a big fan of writing in my books, but here I had made a small pencil note rewriting the equation for buoyancy to show the relation between apparent weight and weight. It was a small thing, but I was really struck by it. For one thing, it shows that this must have been something I kept getting mixed up for no good reason (hello, weak spot…), but for another it was a blast out of my past. I used this textbook for my first semester of physics, which was way back in the fall of 2006 (!). Could my past self have imagined that, over 10 years later, I would be poring over this book again, preparing myself to go back into physics? It’s a strange thought. It reminded me that I once wrote a vision statement–later, after graduating from college, after deciding I wouldn’t stay in the Navy–that placed me at MIT studying planetary science. And then I ended up turning that chance down! But for another awesome opportunity!

Anyway, it’s been an intro/retrospective couple days. I look forward to knuckling back down tomorrow and tackling some more math, physics, and blasts from my past.

Today’s fun “new” fact: The hydrostatic paradox. I understand why the pressure in a fluid is the same at any horizontal point, and water level is independent of container shape, but it’s still weird to see it play out.

*Today’s lyric title is a bit more obscure, but it comes from a song by one of my favorite bands (Jack’s Mannequin), so you should check it out!

Welcome to the Jungle

Well, I am back from Peru and ready to dive back in to some physics! Trekking the Andes was definitely not a rest for my body, but it was a nice mental break. Plus I got to do some practical application of the angle of repose while trying to decide if I could stand on a particular muddy slope! If you are interested in my Peru adventures, I will have a more detailed post over on my writing/lifestyle blog, The Write Side of Life. But for now, back to business!

The fall and school feel a lot closer now that the calendar has ticked over to June. I promised myself I would kick into high gear in June, and I got off to a good start today. I wrote myself a study schedule through next week, continuing with my Tipler and Mosca adventures while adding in some Python courses and Mathematical Methods for Physics and Engineering, 2nd Edition, by Riley, Hobson, and Bence. Ah, yes. This brick of a book. I thought that I would be able to sail blithely through the first couple chapters, which deal with introductory mathematics.

Silly me.

I forgot that this book is dense and difficult to read. This is not Tipler and Mosca, with bright colorful pages and fun facts and pictures. This is math. There are words, equations, proofs, diagrams, and so much knowledge in every paragraph. I don’t mean to slam on the authors, but this is not an easy book to follow. And I like math! I took an unnecessary semester of summer school just so I could take a Differential Equations class in college! But my brain wants to scream when getting hit with sentences like this in the very first section:

To take the most obvious example, comparison of the constant terms (formally the coefficient of x0) in the first and third expression shows that , or, using the product notation, .

It’s not even that it’s terribly difficult, it’s just hard to focus on and lots of panic begins to set in that I am hopelessly behind and will never be able to hack it in graduate school. I am a smart person, but eight years is a long time to have been out of school. No one has been asking me to factor polynomials in a very long time!

But math panic aside, it feels good to be getting right back into it with my studying. And on the physics side, today I did chapters on Relativity and Gravity, which are both interesting and mind-blowing topics. I love reading about things like time dilation. They seem so crazy and out there, but they follow implacably from a base set of tenets.

Today’s fun “new” fact: Clocks that are moving in parallel don’t show the same time! The clock that is in the lead lags by xc/v2. Synchronization goes out the window. For some reason, this boggles my mind way more than time dilation or length contraction on their own, although of course this is merely an extension of the same principles.

You Spin My Head Right Round

I’m a little late in posting about it, but I am happy to say I was not late in actually doing my studying on Friday. I was 4/4 for meeting my study schedule last week! That makes me feel like a powerful Productive Goddess. Hopefully this momentum can continue when I am back from Peru.

Speaking of momentum, that was what I studied! Well, one chapter on Rotation and one chapter on Conservation of Angular Momentum. These are mind-bending topics if you’re not familiar with them. Or maybe just for me. In any case, it all makes sense, but I find that I have to think it through very carefully. The vectors are starting to get more complicated, and the conclusions aren’t always intuitively obvious. One example that I remember vividly from my high school AP Physics class (I couldn’t help but do the math and realize that was thirteen years ago holyshit) is someone holding a spinning bicycle wheel horizontally and then tilting it upwards, resulting in an opposite rotation of the person, assuming they are on something that is free to spin.

Amazing that something so simple as a bicycle wheel operates under the same concepts that help aim the Hubble Space Telescope via massive reaction wheels.

Today’s fun “new” fact: Angular momentum is a quantized quantity. Of course, this fact is immaterial at macroscopic levels, but it is important to keep in mind! Understanding the layers of what is “actually” happening versus our useful approximations is, I think, an important part of understanding physics.

Work, Work, Work, Work, Work

(I’m not sure why all my posts titles have ended up being from songs. Not planned! I’m not even that much of a music person.)

I got a bit of a late start today, after falling down a rabbit hole of nostalgia while going through some boxes containing stuff from my college years. I read my journal from that time and had some panic when I saw past-self complaining about the difficulty of the Heat, Sound, and Light course. How am I ever going to manage graduate level classes?! But then I remembered that I’m a physics boss and decided not to worry. I did eventually get around to my studying, and I reviewed three chapters today: Work and Energy, Conservation of Energy, and Systems of Particles and Conservation of Momentum.

Most of the concepts here are pretty straightforward, and the “shortcuts” from using scalar quantities make for some fun problem sets. I also appreciate the refresher on elastic vs. inelastic collisions because I always mix that up for some reason. Basic introduction to Einstein concepts (energy quantization and rest energy/Newtonian mechanics applicability), although without any of the fun space-time bendiness yet.

Last night I remembered that I had also planned to learn some Python coding this summer. So that’s another thing to add to the list–but it’s going on the post-Peru list, so I have some time. I’ve done some Python before, but I never stuck with it because I had no use for it. Hopefully having a more concrete motivation will help.

Today’s fun “new” fact: Because the center of mass will always lie on the line straight down from a pivot, if you hang an object from a pivot at two different points, you can find the center of mass!

And I’m Freeeee, Free Bodying!

Today I had scheduled myself for a study session in the AM. I slept in a bit (I must say this no-alarm-clock business is divine), went for a walk, brewed up a mug of decaf coffee in my French press, and go to work. I only had two chapters today: Newton’s Laws and Applications of Newton’s Laws. Which means–heck yeah, free body diagrams!

Free body diagrams are probably loathed by most introductory physics students. In fact, I don’t recall being fond of them myself, way back when in my AP Physics course in high school. But seriously, they are SUPER cool. I love the way they simplify down problems that sound crazy complicated into something solvable. Plus they are the quintessential “spherical cow” object! Throw in a couple massless, frictionless pulleys and you’ve got yourself a party.

I have to admit that I had to read the sections on rolling friction a couple times. I know this is basic stuff, but for some reason my brain does a little fritz when I first try to picture the forces involved and I really have to break it down for myself.

Today’s fun “new” fact: The angle of repose! This is the maximum angle that something will stay stationary due to the force of static friction. I always like nifty little things like this that are way simpler than you might think at first glance. Also it’s kind of funny that this is something I forgot given that this equation was one I learned for the pGRE like six months ago.

It’s a New Day, It’s a New Life, It’s a New Blog!

Last night I had a dream that it was my first day of graduate school, and I had to do some sort of physics audition for the professors. One guy even wanted us to go in this closet, read a problem, write the answer on a whiteboard, and then leave, so that it was a totally blind audition. And of course I didn’t know anything! So–needless to say, I clearly have some anxiety about this upcoming phase in my life.

Given that I am also a writer, and that writing helps me to order my thoughts, I decided to cope with this anxiety by starting a blog to chronicle my time as a PhD student (to be). I anticipate that this will be a combination of written posts, like this one, as well as vlogs.

A little background: I have accepted an offer to enroll as a PhD student in the Department of Astronomy and Astrophysics at the University of Chicago, where I plan to study exoplanets. I have my Bachelors degree in Astrophysics from the United States Naval Academy–but that was a long time ago! I’m transitioning back to astrophysics from an entirely unrelated field, and I’ll be in my 30s for grad school. Eek!

Friday was my last day at my job. I now have a glorious stretch of months ahead of me before classes start in September. I intend to study, to travel, to write, to spend time with my boyfriend, to house-hunt, and to just generally enjoy myself as much as possible. My boyfriend encouraged me to take some time to relax first, but I cannot escape that pressing feeling that I will never be able to re-learn all of physics in four months, so I best get started now. In pursuit of that object, I put together a study schedule for this week. Next week, we’re going to Peru (yay!). In June, then, I plan to really start getting into it in earnest. This week is just sort of a warm-up.

Today I reviewed three chapters from my introductory physics text (I am using my old undergrad books–in this case, Tipler and Mosca Physics for Scientists and Engineers: Standard Version, 5th Edition), which is basically barely dipping my toes in. The chapters were: Systems of Measurement, Motion in One Dimension, Motion in Two and Three Dimensions. This is the sort of basic kinematic stuff that I really love. I had to stop myself from working through simple problems that I didn’t actually need to practice just because I think they’re kind of fun. Equations here that I know by heart, concepts that I didn’t really need refreshed, but it’s a solid starting point. Good to boost my confidence a little–hey, looky here, this gal still knows what a vector is! She’ll have a PhD in no time! Ha.

It feels good to be started, though. I am already excited about tomorrow!

Today’s fun “new” fact:* The candela (cd) is one of the base SI units (there are seven), for luminous intensity.

*I plan to choose one of these from the material I am studying, an interesting thing that I knew at one point but have since forgotten and it has therefore become new again!