Classical Mechanics I

I have quickly come to the realization that if I do one post about each year (with a "Cool Aside" here and there), then I'm going to run out of material very quickly. To combat this, I will give some of my classes their own post. I will probably choose classes that are interesting or hard, and I will definitely choose classes that are both. Up first, both interesting and hard: Classical Mechanics. Now, I have only taken second year "Class. Mech." and will be beginning my last course in Class Mech this coming semester. So a "Classical Mechanics II" will probably be due some time next year.

Onto PHYS 2010!!
The Professor was very intimidating the first day. Professor Kumarakrishnan (Kumar for short) turned out to be one of our favorite lecturers. Although it was very clear to us that he was no normal human being. We're pretty sure the man didn't need sleep. In fact, after one very typical lecture he asked us how we thought the quality of the lecture had been. We told him it was on par with his usual delivery and he was relieved. He told us that he had not slept for over 72 hours and was worried that it might affect his teaching!
I have Professor Kumar again this semester (or I did. I finished exams 4 hours ago) and his class is one of my favorites. Don't worry. I will definitely do a post about his laser lab course.

Another name for "classical mechanics" is "analytical mechanics" and that is the name of the course textbook.

The beginning of the course focused on some simple motion and forces. These topics are covered in first year, but now we've been equipped with some better math and can approach them differently. For example, in first year we were taught that the famous equation of Newton's 2nd Law of Motion is

F = ma

Force = Mass x Acceleration

While this is true, it is only part of the picture. We learned that this is something called a "differential equation" and that there are general and particular solutions to it, and that we need to figure out what they are. 

The main focus of this course was something called The Harmonic Oscillator. Now, I was not aware at the time how fundamental this is to upper-level physics. Kumar told us that almost anything can be modeled by the Harmonic Oscillator. While we of course believed him, we did not know just how true his claim was. 

The model we use is simply a mass on a spring in different configurations. Sometimes there is an outside force periodically driving the motion of the mass like a kid being pushed on a swing (The Driven Harmonic Oscillator). Sometimes there is some type of drag or friction slowing its motion like a guitar string (The Damped Harmonic Oscillator). And of course we did both (actually the kid on the swing is both since the friction of the chain at the top and air drag on his body both slow him down) (The Damped Driven Harmonic Oscillator). Now, damping can take on three classes. One is underdamped: it reduces the system's energy very slowly. Another is overdamped, which reduces the system's energy very quickly. Then there's critically damped, which is tuned to damp a particular system in just the right way to kill the oscillations as fast as possible. The shocks in your vehicle are critically damped. Otherwise you would bounce for several seconds after every bump. The ugliest equation (by far) of each of these is that of the underdamped H.O. I found it online at www.hyperphysics.com. While the one we used was a little different, it encompasses all the same things, and gives a very good idea as to how nasty this thing is.

click here to go to source website

Some of the shock and awe of the equation comes from all of the unfamiliar symbols. They're just Greek letters that after some practice you get used to. It's like using an extended alphabet to have more to work with (in fact, that's exactly what it is). I see a phi, an omega, a gamma, and variations (such as phi-sub-d in the top right corner). Other than that, you're familiar with the different things in there. Cosines and Sines, "t" is for time, "A" is just an undetermined coefficient (a number whose value we don't know yet), some square-roots. Before you become all impressed, understand that the blue highlighted equation is the one you work with. The other boxes help us know what the different parts mean, but we don't have to manipulate this whole nasty beast all at the same time. We work with it in small parts. I don't think I could have managed everything at once.

Well, about two thirds into the course Kumar got a big fat grant for some of his research and was pulled out of our class. We got another professor, named Terekidi. It quickly became clear that he was another brilliant mind, but this switch really messed with us. It was around the time that we were starting to run out of steam. It was when we had become accustomed to Kumar's style of marking and teaching. And it was right when we were transitioning into the topic of the "Motion of Rigid Bodies in Three Dimensions" (even harder than the H.O.) The combination of these things made finishing the class on a high note ten times more difficult, and I didn't. I landed right on the class average and came out disappointed.

One of my favorite moments of this class was when Kumar had set up a very long and tedious derivation and was taking us through it. He went through four to five chalk boards of equation after equation building up to something when suddenly things started to fall into place and out popped a very familiar form of Newton's 2nd Law. We were all so pleased and impressed we actually applauded when he finished his lecture and we all walked out talking about how awesome that was. One student said "it was like wandering in the woods and finding a road and suddenly recognizing the neighbourhood and knowing how to get home" which I thought was a very good analogy.

Thanks for reading! My next post will be about another class. Maybe a third year class. Cheers!

Cool Aside #1: Einstein's Theory of Special Relativity

So I decided to take a post to go into a little more detail about Relativity.

A few things that are good to know:

There are two branches of Relativity. One is Special Relativity, the other is General Relativity (often called "GR"). Special Relativity deals mostly with the effect of travelling at really high speeds (like close to that of light), while GR deals with the warping of space-time by massive objects ("massive" does not necessarily mean big. It just means "having mass").

I should make something very clear: GR is beyond my current level. While I understand some of the really cool basics, and some of the implications that it has; I do not pretend to understand it well enough to write about it.

Alright, so onto Special Relativity.

First, let's imagine you're in a car and you're travelling in some North-North-West direction and you're going at 100 km/h. In fact, let's say that your car can only travel at 100 km/h, no more and no less. Now, I only want to know how quickly you're moving West; I don't care how quickly you're moving North. I'm going to do a little bit of trig to figure out how much of your NNW speed is carrying you purely West.

Now, if we look at these arrows and say that the Green arrow shows how fast you're moving and in what direction. The Blue arrow, then, shows how fast you're moving West and the Red arrow North. We call the Blue and Red arrows "components" of the Green arrow. The West component, and the North component. If we turn the Green arrow to point more upwards then the Red arrow will become longer and the Blue arrow shorter. Whereas if you turn your car more westwards, then the Blue will become longer and the Red shorter.

"Okay okay! Where are you going with this?!"

Well, have you ever heard that if you travel at the speed of light time stops? Well it's kind of true. Imagine that North represents the speed of our passage through time and West represents the speed of our movement through space (i.e. when you walk in one direction or another). One of Einstein's theories was that our total speed (over space and time) is ALWAYS the speed of light. The idea is that the Green arrow (which for us is going the speed of light) is pointing almost entirely in the Time direction. But if we move fast enough in a spaceship then we will pull the Green arrow down towards the space direction. This causes the Red arrow to get shorter. Remember the Red arrow represents how quickly we pass through time! So if the Red arrow gets shorter then we move through time more slowly!! And if we move through space at a speed close to the speed of light, then the Green arrow points almost completely in the "Space" direction. So the faster you fly, the slower time goes by for you. This is absolutely true, but you cannot experience the effects of it unless you travel at incredibly high speeds (much much faster than planes or bullet trains).

Isn't that cool?!?! As a result of this there is something called The Twin Paradox.

The idea behind the twin paradox is that if two twins, Bob and Deb, walked together to NASA and Deb got into a rocket and took off into space. Depending on how fast the spacecraft moved, when she got back, say, 15 years later, her twin brother Bob would be much older than her!! Because she is moving so quickly in the space dimension that there's not as much total speed left over for the time dimension, so she would age more slowly than Bob!

This isn't a cool thing potheads talk about while playing hackie-sack. This is a legitimate postulate of Einstein's, one of the greatest minds of the past several hundred years (some say the greatest).

This effect is known as Time Dilation. There is also something called Length Contraction, which I referred briefly to in my last post. The explanation for Length Contraction is quite a bit lengthier (heh heh) and more of a brain buster. If you want a "Cool Aside #2" about Length Contraction, let me know.

Well, this has been fun!

Thanks for reading!

Year Four: It's All Fun and Games Until Classical Mechanics

Remember when I said that each year my program becomes exponentially harder? Well, for those who don't use math terms in their everyday speech, let's see what "exponential" looks like.

You see how when you move to the right, the line gets higher and higher, faster and faster? This is Physics: it gets harder, faster and faster.

2nd year is a lot harder than 1st. And, spoiler alert, 3rd year makes 2nd look easy.

But the great thing about Physics is that Harder = Awesome-er.

One of my favorite classes of that year (no, definitely my favorite) was Relativity and Modern Physics. Man, what a cool class!!

Relativity:

I learned about how when THING A moves really fast (like a decent fraction of the speed of light) that it get shorter! What?! No, I'm dead serious. GUY B sees THING A moving really really fast and THING A is shorter.

Here's the really crazy part: To THING A, it's GUY B that's shorter! You read right! They both see the other as being shorter. This next bit is the part where Professor Menary blew our minds and we're still reeling from it.

GUY B and THING A are both right! It's not that one of them is right, and the other sees something that isn't true. And it's not that they are both mistaken and their perspectives distorted. They. Are. Both. Right.

Now, this sounds like a bunch of garbage, right? Something that stoned teenagers talk about? 

"Hey man, have you ever thought about, like, maybe when they're both looking at each other they, like, see the same thing?"

Lemme tell you: this is mathematically and physically sound. Relativity is definitely one of the coolest studies in physics, by far. Physical experiments have been performed to prove something called "time dilation", in order to show that the math in Special Relativity is physically true (I know that statement is extremely vague and not at all convincing to the skeptic, but to go into the details would require a post all on its own...    hm....).

Anyways, that's just me getting all hopped up on Physics!

Lemme tell you what it was like to go through this year.

First semester was very challenging. A heavy math course, a mind-blowing relativity course (and hard too), a course all about electric and magnetic forces, and a very tedious course in error analysis. This was the year that I finally began to learn how to be a good student. I was very blessed. On the first day of a lab course I had, everyone had a partner. Everyone except myself and a random guy on the other side of the room. Rob Noehammer. we partnered up and thank goodness we did. We ended up sitting together in classes and studying together. This man taught me work ethic. And we had all the same classes. There were a few of us, and we spent nearly everyday studying or doing homework.

I was still new at this whole "being a good student" thing, and I needed to check on my Clash of Clans base every twenty or so minutes. But I did more work in that one semester than in the past three years of my education combined. 

It was stressful.

It was exhausting.

It felt really good.

I didn't always do as well as I wanted to, and looking back I wish I had worked even harder. But my average that year was about 15-20% better than my previous years. I snagged myself a few A's, and I felt pretty proud of myself.

Then the winter semester started.

Optics and Spectra

Differential Equations

Computational Methods

and

Classical Mechanics

Ho man was "Class Mech" ever hard! We had to use differential equations (which looking at the above list you can see we were learning at the same time) to solve equations of motion. The class was super interesting! And it was probably (definitely) the most difficult class of 2nd year. Ten times harder than anything in 1st year. I should add that the proper title of the course is "Introduction to Classical Mechanics".

I also had a very hard time with Differential Equations. Like I said: I'm not that strong mathematically.

Optics was a pretty cool course. There were some more difficult concepts, but overall it was manageable and enjoyable. 

Don't even get me started on the waste of time that the computational methods class was. That teacher had no idea what she was doing, and we didn't learn a damn thing.

If there's one thing I would tell you about being in the community of physics students it's this:

Everyone has to work hard. No one is smart enough to just coast by. There are some pretty smart kids in my program. But the brilliant kids in high school that got good grades without trying? They don't exist here. We all have to work hard. The purpose of this clarification is to say that physics is easy for NO ONE. We're not all geniuses waiting to be let loose on the world. We're not riding the bus thinking about how smart we are. We are all working with our heads down. We're sweating, scared that we'll fail. 

Cheers!

Next Post: A special surprise! (hint: it's about something awesome!)

Year Three(-ish):Hope

William A. Van Wijngaarden.

Sounds pretty intense, right? He was the Dutch Physics Professor that taught PHYS 1410. Taking this class over the Summer of 2013 finally wrapped up all the things I needed to be able to go into 2nd-year physics.

Wait. 

Hold on.

You just said that you were ready to start taking Physics. How did you leap to second year?

Heh heh. If I didn't pull this off I think the extra year I saved would have stopped me from continuing.

See, first year physics is really just one class: PHYS 1010. Everything else is chemistry, math, computer science, etc. So I just made sure I had 1410 (a replacement for 1010 with a high enough grade) to go straight into 2nd year (in my fourth year, mind). This meant that over the following summers I would need to scrape up those 1st-year classes like comp. sci. and chem. 

In fact, this past summer I just took one of the two 1st-year chem classes, and this coming summer I'll be taking the other one.

Let's talk about PHYS 1410!

You learn about:

1d and 2d motion

gravity

friction

electricity and charges

heat
pressure
fluid flow

and a few other things.

Let me give you a taste of some of these:

Motion:

A ball is kicked off of a roof that is THIS high at THIS angle (up and away) and THIS velocity. How long until the ball hits the ground? How high up is the ball at THIS many seconds? How far will the ball go before falling back down to the same height as the building?

Friction:

A man is standing on a wet roof. The roof is at THIS angle to the ground, and the "coefficient of friction" between rubber and wet shingles is SUCH. Can the man stand on the roof, or will he fall off?

Electricity and Charges:

An object with THIS MUCH positive charge is THIS FAR from another object with THIS MUCH negative charge. How much force is required to keep them in the positions they are in?

So, anyone who has done grade 12 physics right now is going: "this doesn't look so bad"

The answer is: it isn't, really.

This class was fascinating to me, as I learned how some things worked that I didn't understand. It was challenging for me. The professor required a lot of us. Overall, I really en(hated)joyed it.

One snag.

I still wasn't a good student. I only did well enough because the professor pushed us so hard.

Next post: 2nd-Year Classes (This is where physics starts to become really interesting!!)

Year Two(-and-a-half): The Labyrinth

So now I know that I want to switch over to physics.
My grades aren't good enough.
I don't have the prerequisite courses.
I don't even know how to make the change or who to talk to.

So after some searching on the York website (which was horrendous at the time) I figured out what courses I needed in order to even take real physics classes.

So my second year was a split between Physics and English. (This was to get full-time status for my student loans).

My favorite class this year was an Intro to Calculus course, taught by Prof. Stephen Watson. Anybody that has taken High School calculus knows about rates of change and optimization.  For some reason, this stuff captured my imagination! It turns out it was all just physics hiding under the guise of math!
Well, I had a hard time with my other math class (functions), as well as a chemistry class that I had to take.

"Wait, you're doing physics and you had a hard time with functions?!" says the reader that is good at math.

Yes, I struggled in my bridging and first year math classes. At this point in the story I'm still a really bad student. In fact, I dropped and retook the high school level physics course PHYS 1510!! Can you believe I flunked out of high school physics and I still thought it was a good idea to go into physics?!

It was that A+ in Light and Sound from my first year. I knew I was capable, I just wasn't working hard enough.
So it took me a year and a half to transition into even being able to take physics!
Don't worry. It gets better. I do learn my lesson, eventually.

Next post: first-year physics.