So I have decided to slightly postpone what was to be my next published diary (on creating a headless computer and sharing from within a network) and write about something else. Namely what I hold a degree in, physics.
I apologize to those waiting for the other diary, it should be published soon (tomorrow afternoon if I can but no holding me to it). That said, I wanted to start what I hope to become something regular here and that is a discussion on physics.
Now to make these easier to understand, I will not be invoking calculus here and I do not plan on doing so later. While it is true that to fully understand physics and work in the field you need to understand calculus I am going to avoid it as much as I can.
Because I understand that not everyone is weird like me and finds the math beautiful. So please follow me over the jump and let's start with the most basic building block of physics, the difference between scalars and vectors.
Now I suppose many here might expect me to start with Newton's Laws or Kepler's Laws or momentum or any number of things besides vectors and scalars. The truth is that how vectors and scalars relate and differentiate form the basis for modern physics.
So what are they? Well I am going to start with scalars which I know everyone is familiar with.
A scalar is formally defined thus: a variable compromising only magnitude multiplied by a physical unit.
Now I know what people are thinking, great drache but what the hell does that mean? Well let's use some examples, for example when you get pulled over by an officer and say "I was only going 65 mph officer" you are using a scalar.
Time is another example of a scalar, as to is temperature. There are a handful of other examples but I would rather stick to what I think are the three most well known examples.
Basically a scalar is just a number, the unit part gives the number more meaning but all you are dealing with is a number. This means that scalars are treated just like any other number (though you have to pay attention as time for example is effectively a different base then we are used to) and so the normal rules for subtraction, addition, multiplication and division apply.
Scalars are in effect what I think most people think about in their every day lives.
Unfortunately scalars are rarely used in physics. Instead, most physics deals in vectors.
So what is a vector? A vector is defined as: a variable compromising both magnitude and direction.
Now I understand that for many this might sound confusing, I still remember (when I first are introduced to vectors) thinking how the hell can this work? Well let's see if I can explain.
Let's take the image to the right, the arrow is the vector hence forth I will refer to it as m. Now m could represent many thing from velocity, Newtonian force, acceleration, any of the 5 forces primary forces and much much more.
The vector has what are known as components these components represent the individual parts of the vector in space. Now I understand that such a wording might seem hard to understand so let's break this down a little. Our vector m has a direction both on x axis and on the y axis. It is the sum of those directions which makes the vector and it is those parts that we refer to as the components of a vector. The question is how do we represent these components?
The answer is simple simple and yet creates complications.
First we need to create what are known as unit vectors these vectors are parallel to each axis and will allow us to split up a vector into its components. By convention x and y are used but generally a little hat (it looks like this ^ ) goes on top of them. Due to the limits of font on DK I can not do so. So I will instead use the second accepted unit vectors, i and j (if we are in 3 dimensions the 3rd is k).
Thus according to the picture, m is equal to x * i + y * j (the spaces are to stop the 'smart' html reader) and with that we have a way to denote both direction and magnitude.
However there is a big problem with vectors and it is when we want to preform math on them. As I promised no calculus, I am going to have to hand wave a little here and will be a little brief. The basic problem is the unit vectors themselves. See when you (for example) try to multiple 2 vectors together it does not work like multiplying scalars. First the most obvious reason is because you have to use the FOIL rule to deal with multiplying what are essentially polynomials but even more importantly you can not just multiple unit vectors together.
Remember we are now dealing with spatial representation and since each unit vector (by definition) is parallel to the axis it is supposed to represent; it is also perpendicular to the other axises. This means that multiplying one unit vector by another will always equal zero and multiplying one unit vector by itself will always equal one (one assumption, both unit vectors have to be in the same coordinate system and dealing with different coordinate systems is a whole other can of worms). More over vectors thanks to their nature can be multiplied such that they give a scalar answer (a process known as the dot product) or a vector answer (the cross product). And these 2 processes are not the same; they give different answers and mean different things. And that's not even touching on the other peculiarities that arise from using vectors.
Thus we have a powerful and flexible mathematical way to talk about some of the most important concepts in physics. And yet at the same time it is still complicated.
I am going to end this here, I am tempted to take about vector operations but I think that would involve too much math in what I promised to be a diary math free.
If there is enough interest though, I can always come back to vector operations.