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}