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Corrected on-site errors: (1) Javascript was not loading (2) MathJax …

…was not loading (3) Custom dependencies reduced (subject –> docs again, per theme)

To-do: (1) Get rid of normalize.min.css.map 404 error (2) Minor beautification (3) Test github links from live site (4) Think about inviting contributions more openly
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V.H. Belvadi V.H. Belvadi
V.H. Belvadi authored and V.H. Belvadi committed Apr 23, 2019
1 parent 16668fa commit 3ebeea937b0f43843643d2a7bc6d5c4d4d82eb56
@@ -20,7 +20,7 @@ pygmentsCodeFences = true
BookEnableJS = true
BookMenuBundle = "/menu"
BookMenuBundleActiveLinkColor = "#de0303"
BookRepo = "https://github.com/alex-shpak/hugo-book"
BookEditPath = "edit/master/exampleSite/content"
BookRepo = "https://github.com/physicscapsule/physicscapsule.github.io"
# BookEditPath = "edit/master/content"
BookDateFormat = "2 January 2006"
enableGitInfo = true
@@ -41,15 +41,15 @@ This was a powerful idea because in Newton's time it was largely believed that o

However, the idea of ***friction*** must rightly be attributed to Galileo who believed that such a force existed and worked towards bringing moving things to rest. It is interesting how Galileo arrived at his idea ***empirically***, i.e. using experiments rather than a logical thought process.

{{< figure src="galileo-experiment-1-3.png" title="Galileo's experiment" caption="Fig. 1: All things considered equal a ball released at A goes up to, and no more or less that, B at the same height above ground as A." >}}
{{< figure src="/images/galileo-experiment-1-3.png" title="Galileo's experiment" caption="Fig. 1: All things considered equal a ball released at A goes up to, and no more or less that, B at the same height above ground as A." >}}

From fig. 1 it is clear that an object released at position A on some container would reach position B at the same height as A — under ideal circumstances. Galileo observed as much.

{{< figure src="galileo-experiment-2-3.png" alt="Galileo's experiment" caption="Fig. 1: All things considered equal a ball released at A goes up to, and no more or less that, B at the same height above ground as A." >}}
{{< figure src="/images/galileo-experiment-2-3.png" alt="Galileo's experiment" caption="Fig. 2: All things considered equal a ball released at A goes up to, and no more or less that, B at the same height above ground as A." >}}

As in fig. 2, Galileo modified his experiment and found that this height would be reached regardless of the angle of inclination, i.e. no matter how wide or narrow the container got or how asymmetric his set-up was.

{{<figure caption="Fig. 3: Logic dictates then that in this case the ball must keep traveling—perhaps infinitely—until it reaches the same height as A, yet we know from experience that the ball will eventually come to a halt. Why?" src="galileo-experiment-3-3.png" alt="Galileo's experiment">}}
{{<figure caption="Fig. 3: Logic dictates then that in this case the ball must keep traveling—perhaps infinitely—until it reaches the same height as A, yet we know from experience that the ball will eventually come to a halt. Why?" src="/images/galileo-experiment-3-3.png" alt="Galileo's experiment">}}

Finally, in fig. 3, the genius of Galileo shows: he reasoned that if the angle was a full 180 degrees, meaning that if the slope never brought the object up to its initial position, the object should keep moving, never being able to attain its desired height. Unsurprisingly he found the object does stop. So, he reasoned, there must be some unseen force in whose nature it is to stop moving objects. This is the force we now call friction.

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@@ -23,7 +23,7 @@ Although we saw the acceleration definiton first, we will be looking at the seco

Let us call our force F, our object's mass m and let us assume it moves as a result of this force (see [Newton's first law](/newton-first-law-mass-inertia)) proportional to a velocity v. It is important to understand why we use the term proportional: the body actually accelerates, as we will see, hence its motion will be an acceleration of, say, a, proportional to its velocity v, i.e. as velocity increases, so does its acceleration and vice versa.

{{<figure caption="A force $ \vec{F} $ acting on a mass m and causing it to accelerate at $ \vec{a} $." src="newton-second-law.png">}}
{{<figure caption="A force $ \vec{F} $ acting on a mass m and causing it to accelerate at $ \vec{a} $." src="/images/newton-second-law.png">}}

Then, following the second form of the law stated above, we realise that the momentum, $p$, of this body, defined as a product of its mass and velocity at any time t, is proportional to the force. In other words, we know the definition of linear momentum as, $$\begin{equation}\mathbf{P}=\mathit{m}\mathbf{v}\label{eq:Pmv}\end{equation} $$

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@@ -23,7 +23,7 @@ Our aim now is to see how we can use our reference axes to describe, mathematica

Think of a set of three reference axes as shown in the figure below. An arbitrary plane $ ABC $ can be drawn connecting points on the three axes. Let $ OA = a $, $ OB = b $, and $ OC = c $.

{{< figure src="miller-indices.png" title="Reference axes set-up" caption="An arbitrary set of three reference axes along with a pair of crystallographic planes drawn on them." class="left" >}}
{{< figure src="/images/miller-indices.png" title="Reference axes set-up" caption="An arbitrary set of three reference axes along with a pair of crystallographic planes drawn on them." class="left" >}}

We know that to get to a point $ (X, Y, Z) $ on our plane we need to travel a length of $ X $ along the x-axis, a length of $ Y $ parallel to the Y-axis, and a length $Z$ in the z-direction.

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@@ -0,0 +1,38 @@
<script type="text/javascript">
//var allSpan = document.getElementsByClassName('entries');
//
//for(var x = 0; x < allSpan.length; x++)
//{
// allSpan[x].onclick=function()
// {
// if(this.parentNode)
// {
// var childList = this.parentNode.getElementsByClassName('listing');
// for(var y = 0; y< childList.length;y++)
// {
// var currentState = childList[y].style.display;
// if(currentState=="none")
// {
// childList[y].style.display="block";
// }
// else
// {
// childList[y].style.display="none";
// }
// }
// }
// }
//}
$(document).ready(function() {
$('.book-menu ul li.entries').click(function(e) {
$('.book-menu ul li ul.listing').slideUp();
$(this).children('.book-menu ul li ul.listing').slideDown();
});
// $('.book-menu ul li.entries').click(function(e) {
// var newText = $(this).text();
// $(this).parents('.book-menu ul li.entries').find('strong').text(newText);
// e.stopPropagation();
// });
});
</script>
@@ -0,0 +1,36 @@
<script type="text/x-mathjax-config">
var font = "Gyre-Pagella";
MathJax.Hub.Config({
tex2jax: {
inlineMath: [['$','$'], ['\\(','\\)']],
displayMath: [['$$','$$'], ['\[','\]']],
processEscapes: true,
processEnvironments: true,
skipTags: ['script', 'noscript', 'style', 'textarea', 'pre','code'],
TeX: { equationNumbers: { autoNumber: "AMS" },
extensions: ["AMSmath.js", "AMSsymbols.js", "enclose.js"] },
Macros: {
ham: "{\\mathscr{H}}",
lag: "{\\mathscr{L}}",
kam: "{\\mathscr{K}}",
d: "{\\textrm{d}}"
},
},
"SVG":{
font:font
},
"HTML-CSS": {
webFont: font,
imageFont: font,
preferredFont: font,
availableFonts: [],
scale: 95,
linebreaks: { automatic: true, width: "article" },
mtextFontInherit: true
}
});
</script>
<script type="text/javascript" async
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.4/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
@@ -0,0 +1,7 @@
{{- template "hrefhack" . -}}
{{ with .Site.GetPage .Site.Params.BookMenuBundle }}
{{ .Content | replaceRE "<ul>" "<ul class=\"listing\">" | replaceRE "<li>" "<li class=\"entries\">" | safeHTML }}
{{ end }}
{{ if .Site.Params.BookEnableJS }}
{{- template "jsmenu" . -}}
{{ end }}
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