Episode 025: The Signs of Sine and Cosine & Understanding Quadrants!

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As a goodbye to sines and cosines, we can add one more piece to the puzzle. Understanding how to calculate sin and cos with the simple 0,1,2,3,4 trick (as described in episode 24), and how this relates to the unit circle, i.e. the x-coordinate being the cosine value and the y-coordinate being the sine value of the angle w/r/t (with respect to) the positive axis, is the bulk of the material.

If one can understand cartesian coordinate quadrants, it adds another dimension to your arsenal. Our Cartesian Coordinate Axes can be divided into four quadrants. Starting with upper right quadrant, called the first quadrant, we will begin to move counter-clockwise around the coordinate axes. These quadrants also correspond to 90 degree increments of the unit circle.

The upper right quadrant is an area which has only positive values for both the x and y values. This means that FROM 0-90 DEGREES BOTH SINE AND COSINE ARE POSITIVE.

The upper left quadrant is referred to as the SECOND quadrant. In the second quadrant y-values remain positive and x-values are negative. This means that FROM 90-180 DEGREES SINE IS POSITIVE AND COSINE IS NEGATIVE.

The lower left area is known as the THIRD quadrant. In this area both x- and y-values are negative. This means that FROM 180-270 DEGREES SINE AND COSINE ARE BOTH NEGATIVE.

The lower right area is known as the FOURTH quadrant. In this area the x-values are positive while the y-values are negative. This means that from 270-360 DEGREES SINE IS NEGATIVE AND COSINE IS POSITIVE.

This is illustrated in some detail in the picture below. Combine these tools together and you will have be at a great advantage when calculating vector components, and understanding where those confusing sines and cosines come from in later courses!

BONUS001: Simulation Theory!

An audio version of Physics Phrydays 002, for your listening pleasure.

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Physics Phrydays 003: Tied Up in String- Elegant Universe 01

SO. I managed to read Part I/Chapter 1 of The Elegant Universe, it's called Tied Up In String. In this chapter he basically gives us an overview of the standard model of physics, what we know, and then starts to ask philosophical questions about the "Why" of physics. We find out that we continuously think that our current level of knowledge, from cells to molecules to atoms to quarks is always the "basic" parts of the universe, and there is nothing beyond that, only to find out some fraction of a century later that there is always more below.

We also find out that there are three "families" that the standard model of physics can be broken into. And each family has 4 parts. We also find out that there are four fundamental forces, which range from the very small, to the very large, as well as from the very week to the very strong. The question to all this is why are the families set up this way and why are the forces set up this way? The answer, apparently, will all be clear and solved by string theory. We're about to find out.

If you haven't read this book, I invite you to join in on the fun! Click the links below to get your copy, or just go to your library and grab it!

Episode 024: Sines and Cosines by Counting to 4!

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Physics Phrydays 002: Simulation Theory, aka you MAY be living in the matrix!

Okay, so this is something that has fascinated me for a long time. Simulation theory is this wild notion that we are currently living in a simulation. And to boot, is some really compelling evidence to this wild notion.

Piece of evidence #1: Processing power is getting better and better as the years carry on, and with it, our ability to create better and better simulations. If you have played a video game in the last 10 years, you are aware of this. Eventually, the processing power will reach a point where humans will be able to simulate at least a small part of an entire universe. This could be use for research of earlier cultures, or initial conditions to study possible outcomes. It starts raising a lot of questions indeed about what sort of moral code of conduct there is, if any, regarding shutting off a simulation which may or may not contain lives.

Piece of evidence #2: If a simulation is indeed being run, there would be some limit to the computing power involved in the simulation, and thus there would be some sort of upper limit on the size of the universe in question. Sound familiar?

Piece of evidence #3: If a simulation is indeed being run, there would be some limit to the computing power involved in the simulation, and thus there would be some resolution limit on the size of all the pieces which made the universe in question. Sound familiar? If not, let me direct your attention to the Heisenberg Uncertainty Principle, and also this excellent comic: here.

Piece of evidence #4: There would be an incompatibility of the behavior of large scale and small scale objects. This would probably be due to the fact that things would need to behave a certain way in the large scale, and the inner mechanics of how those things worked on the small scale wouldn't be all that important, unless small creatures inside the simulation started to examine what was going on at a small scale and developing theories for why that might be. You could also characterize this as the current incompatibility of classical and quantum mechanics. As of right now the do not jibe.

Anyone considering the ledge of the nearest window at this point, read on, stay your hand. There may be some good news after all. Unfortunately that news is string theory. String theory in its current state is our hope to unite classical and quantum mechanics, and gives us some glimmer of hope that we are indeed dealing with a universe that at least pretends to have continuous laws.

Wouldn't that simplify so many questions in life, though? It would explain why there are physical laws, why you need to go to sleep all the time, why reality gets "fuzzy" sometimes, why the uncertainty principle exists, why there's an edge to the universe, and on and on. Plenty of unsubstantiatable questions and answers. Cold comfort indeed.

Episode 023: Sines & Cosines and The Unit Circle, Triangles, Components and More!

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Understanding how sine and cosine really work is something that eludes most first year physics students. In my estimation it is in some sense the entire point of first year and certainly the most important thing to grasp, an yet at the same time one of the most difficult. That is why we will do a deep dive on this over the course of several episodes. Included below are several screenshots from the Exploring Mathematics: Sine and Cosines app, available for free above by clicking the link.

To start to tell the story of sin and cosine, one must first visualize a circle, centered at the origin of a cartesian coordinate system. We must also consider the circle to have a radius of one unit, any unit you like, thus leading to the name the unit circle.

Starting with respect to the horizontal, or positive x-axis, we can begin to sweep our radius around the circle. This angle will be referred to as theta.

We also know, since this is a cartesian coordinate system, that we can refer to any point by its coordinates [x,y].

Using the radius as a hypotenuse, we can create a right triangle using our point to create legs parallel to each coordinate axis.

We will now define our x-coordinate to be cos(theta), and our y-coordinate to be sin(theta). Replacing the x and y values on the triangle legs with this definition may start to look familiar from classes past.

One can't help ones self but try out the pythagorean theorem with this new definition...

Which leads to a rather familiar identity.

It is then possible to expand this relation out to any circle or triangle we like, simply by multiplying by the radius, r.

This explains how your physics professors can "magically" break vectors into components and why the x-component is multiplied by cos(theta) and y-component by sin(theta).

More next week.

Physics Phrydays 001: Dumber Than Dinosaurs!

I don't know why the idea of the dinosaurs is so fascinating. Is it because we're so much smaller than them? Is it because they lived so long ago on the same blue ball? I think the big reason is that they have such larger physical prowess and yet somehow didn't make the cut to live until today.

I like to think that I'm at least a little bit smarter than our dino bretheren. However, even with our current technological advancement being leaps and bounds beyond what the Cretacous reptiles had available, we're in roughly the same position in terms of being able to avoid the same fate. In fact, having the tools, we're almost actively avoiding working on a solution. So who, pray tell, is the smarter species?

Episode 022: 8 Hot Tips to Prepare for the Next Semester and Start Off With a Bang!

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Alright, alright...you've had a few days to catch your breath, now get back to work! Your upcoming spring semester or second half of the year is fast approaching, and the best way to keep yourself from burning out during the semester is to do as much as you can to prepare now!

And, Christmas came late or early this year for you, depending on which one you're thinking of. I have made you a list of 8 tips that you would be wise to implement in lieu of sitting on the couch eating chips and binge watching the last 2 seasons of House of Cards to get ready for Season 3. Do 1 ep a night and take some time to save yourself from impending doom this semester. At the end of these tips, I've also included an image version for you to print out and put above your desk, to keep you motivated as the resuming of work fast approaches.

1) Brush up on Prereqs- If you have notes from any of the prerequisite courses, this is a great place to start. Make some cheat sheets covering the highlights of all these courses to pin above your desk. Chances are you'll be using these quite a bit!

2) Grab The Textbook Early- Usually the textbook doesn't change from semester to semester (or year to year). Having this early will give you the chance to get ahead while your classmates who are your competition are off doing other things. If you don't have the exact text grab a similar one as it will give you an added perspective and probably cover very similar topics.

3) Skim the Text- Since you aren't in the hot seat yet, don't kill yourself, but casually start to look over some of the topics, especially the first few chapters. These intro chapters usually provide the foundation for the entire course. Start getting this information into your subconscious.

4) Get Lost in The Topics You Like- If you find a topic or subtopic that particularly interests you, this is the time to really take a deep dive into that topic. When the course is in full gear, you're not going to have the time to take many deep dives, so try and savor some of the topics in your down time. This keeps you passionate about physics while at the same time is keeping you in the zone!

5) Try Some Problems- Now is the best time to muck around with some practice problems. There is absolutely no pressure, and there is no penalty for making mistakes! This is such a great tool because if you can only work a problem to a certain point, you will be able to ask about it when the semester starts. If it's a sample problem, it might even be covered in class so you will know exactly where to pay close attention.

6) Check Your Professor's Website for Resources- Chances are there is a website for older versions of this course that may still be available.

7) Make Friends- See what other classmates are doing to prepare for the upcoming semester! Start networking and see what anyone else has heard about past classes to stay on the cutting edge of what's coming up.

8) Start Building Momentum- A body in motion tends to stay in motion. If you hit the ground running you won't start out behind!

If you want a copy of the pdf, listen to the podcast for my e-mail given at the end of the episode! Alternatively, tweet me and we'll figure something out.

Physics Phrydays 000: Welcome and Your Teeth Are Made From Stars!

So as an added supplement to the podcast I have started a Youtube Video series entitled Physics Phrydays. I consistently find myself tempted to go into strange territories with the podcast which steer it away from being an educational series and more of an inspiration.

Physics Phrydays will serve to support the podcast as extra content to keep its watchers inspired with cool and interesting physics factoids and science-related concepts but be much more centered around coolness and less about education.

As you'll see in the first episode, I have a monster commute each morning, and so I thought I would break it up and keep my mind off the traffic with a little bit of spontaneous one-sided conversation. I hope you enjoy it!

So, one of the coolest things I know about our universe is that the calcium that is in your bones and teeth can only have been formed inside of a star. Stars are these phenomenal furnaces which generate extreme temperatures, pressures and energies which can stuff enough protons and neutrons together to form something as heavy as Calcium.

To think that all those particles were in a star far far away, and then floated over to our planet and made its way into my bones is quite phenomenal!