From: Andrew Lorimer Date: Sun, 16 Sep 2018 23:38:50 +0000 (+1000) Subject: cheatsheet additions & tidy up sidecars X-Git-Tag: yr11~36^2~1 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/011103ef3dfaacc5ab96b6359186587943d59530?ds=inline cheatsheet additions & tidy up sidecars --- diff --git a/physics/final.fdb_latexmk b/physics/final.fdb_latexmk deleted file mode 100644 index 117fbf7..0000000 --- a/physics/final.fdb_latexmk +++ /dev/null @@ -1,89 +0,0 @@ -# Fdb version 3 -["pdflatex"] 1536577652 "final.tex" "final.pdf" "final" 1536578664 - "/usr/share/texmf-dist/fonts/map/fontname/texfonts.map" 1536122179 3332 103109f5612ad95229751940c61aada0 "" - "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1536122179 1004 54797486969f23fa377b128694d548df "" - "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm" 1536122179 916 f87d7c45f9c908e672703b83b72241a3 "" - "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam5.tfm" 1536122179 924 9904cf1d39e9767e7a3622f2a125a565 "" - 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[] - -[4] (./final.aux) ) -Here is how much of TeX's memory you used: - 2916 strings out of 492642 - 40185 string characters out of 6135567 - 126031 words of memory out of 5000000 - 6741 multiletter control sequences out of 15000+600000 - 7502 words of font info for 29 fonts, out of 8000000 for 9000 - 1141 hyphenation exceptions out of 8191 - 41i,10n,27p,272b,358s stack positions out of 5000i,500n,10000p,200000b,80000s - -Output written on final.pdf (4 pages, 595613 bytes). -PDF statistics: - 93 PDF objects out of 1000 (max. 8388607) - 53 compressed objects within 1 object stream - 0 named destinations out of 1000 (max. 500000) - 76 words of extra memory for PDF output out of 10000 (max. 10000000) - diff --git a/physics/final.pdf b/physics/final.pdf index 28ba95d..e027227 100644 Binary files a/physics/final.pdf and b/physics/final.pdf differ diff --git a/physics/final.synctex.gz b/physics/final.synctex.gz deleted file mode 100644 index 16fb978..0000000 Binary files a/physics/final.synctex.gz and /dev/null differ diff --git a/physics/final.tex b/physics/final.tex index 998e2a5..4fab03e 100644 --- a/physics/final.tex +++ b/physics/final.tex @@ -36,7 +36,7 @@ $\theta = \tan^{-1} {{v^2} \over rg}$ - $\Sigma F$ always acts towards centre, but not necessarily horizontally + $\Sigma F$ always acts towards centre (horizontally) $\Sigma F = F_{\operatorname{norm}} + F_{\operatorname{g}}={{mv^2} \over r} = mg \tan \theta$ @@ -121,6 +121,8 @@ $\text{elastic potential energy} = {1 \over 2}kx^2$ + $x={2mg \over k} + % ----------------------- \subsection*{Motion equations} @@ -241,7 +243,7 @@ \[v=\sqrt{Gm_{\operatorname{planet}} \over r} = \sqrt{gr} = {{2 \pi r} \over T}\] - \[T={\sqrt{4 \pi^2 r^2} \over {GM}}\tag{period}\] + \[T={\sqrt{4 \pi^2 r^3} \over {GM}}\tag{period}\] \[\sqrt[3]{{GMT^2}\over{4\pi^2}}\tag{radius}\] @@ -258,6 +260,7 @@ \[F=qvB\tag{$F$ on moving $q$}\] \[F=IlB\tag{$F$ of $B$ on $I$}\] + \[B={mv \over qr}\tag{field strength on e-}\] \[r={mv \over qB} \tag{radius of $q$ in $B$}\] if $B {\not \perp} A, \Phi \rightarrow 0$ \hspace{1em}, \hspace{1em} if $B \parallel A, \Phi = 0$ @@ -274,7 +277,8 @@ \[\mathcal{E} = -N{{\Delta \Phi}\over{\Delta t}} \tag{induced emf} \] \[{V_p \over V_s}={N_p \over N_s}={I_s \over I_p} \tag{xfmr coil ratios} \] - \textbf{Lenz's law:} $I_{\operatorname{emf}}$ opposes $\Delta \Phi$ + \textbf{Lenz's law:} $I_{\operatorname{emf}}$ opposes $\Delta \Phi$ \\ + % emf is gradient of flux-time graph \textbf{Eddy currents:} counter movement within a field @@ -324,7 +328,10 @@ % \begin{wrapfigure}{r}{-0.1\textwidth} \includegraphics[height=4cm]{graphics/dc-motor-2.png} - \includegraphics[height=3cm]{graphics/ac-motor.png} \\ + \includegraphics[height=3cm]{graphics/ac-motor.png} \\ + + $F=0$ for front & back of coil (parallel) \\ + Any angle $> 0$ will produce force \\ % \end{wrapfigure} \textbf{DC:} split ring (two halves) @@ -382,13 +389,13 @@ \includegraphics[width=6cm]{graphics/diffraction.jpg} \includegraphics[width=6cm]{graphics/diffraction-2.png} \begin{itemize} - \item \(pd = |S_1P-S_2P|\) for \(p\) on screen + % \item \(pd = |S_1P-S_2P|\) for \(p\) on screen \item Constructive: \(pd = n\lambda, n \in \mathbb{Z}\) \item Destructive: \(pd = (n-{1 \over 2})\lambda, n \in \mathbb{Z}\) - \item Fringe separation: \(\Delta x = {{\lambda l }\over d}\) where \\ - \(\Delta x\) = fringe spacing \\ - \(l\) = distance from slits to screen\\ - \(d\) = slit separation (\(=S_1-S_2\)) + \item Path difference: \(\Delta x = {{\lambda l }\over d}\) where \\ + % \(\Delta x\) = fringe spacing \\ + \(l\) = distance from source to observer\\ + \(d\) = separation between each wave source (e.g. slit) \(=S_1-S_2\) \item significant diffraction when ${\lambda \over \Delta x} \ge 1$ \end{itemize} @@ -533,7 +540,9 @@ Uncertainty of a measurement is $1 \over 2$ the smallest division \textbf{Precision} - concordance of values \\ - \textbf{Accuracy} - closeness to actual value + \textbf{Accuracy} - closeness to actual value\\ + \textbf{Random errors} - unpredictable, reduced by more tests \\ + \textbf{Systematic errors} - not reduced by more tests \columnbreak