From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Mon, 2 Sep 2019 01:11:33 +0000 (+1000)
Subject: [spec] minor formatting improvements
X-Git-Tag: yr12~47
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/97cc94dd9d1067c24a3f6fbac83cfe81bca340cb?ds=sidebyside

[spec] minor formatting improvements
---

diff --git a/spec/dynamics.tex b/spec/dynamics.tex
index b6a1af8..7856ca9 100644
--- a/spec/dynamics.tex
+++ b/spec/dynamics.tex
@@ -22,13 +22,17 @@ To find angle of an \(a\boldsymbol{i} + b\boldsymbol{j}\) vector, use \(\theta =
 
 The resolved part of a force \(P\) at angle \(\theta\) is has magnitude \(P \cos \theta\)
 
-To convert force \(||\vec{OA}\) to angle-magnitude form, find component \(\perp\vec{OA}\) then \(|\boldsymbol{r}|=\sqrt{\left(||\vec{OA}\right)^2 + \left(\perp\vec{OA}\right)^2},\quad \theta = \tan^{-1}\dfrac{\perp\vec{OA}}{||\vec{OA}}\)
+To convert force \(||\vec{OA}\) to angle-magnitude form, find component \(\perp\vec{OA}\) then:
+\begin{align*}
+  |\boldsymbol{r}| &= \sqrt{\left(||\vec{OA}\right)^2 + \left(\perp\vec{OA}\right)^2} \\
+  \theta &= \tan^{-1}\dfrac{\perp\vec{OA}}{||\vec{OA}}
+\end{align*}
 
 \subsection*{Newton's laws}
 
 \begin{tcolorbox}
   \begin{enumerate}[leftmargin=1mm]
-    \item Velocity is constant without a net external force
+    \item Velocity is constant without \(\Sigma F\)
     \item \(\frac{d}{dt} \rho \propto \Sigma F \implies \boldsymbol{F}=m\boldsymbol{a}\)
     \item Equal and opposite forces
   \end{enumerate}