rendered physics stuff

diff --git a/physics/midyear.fdb_latexmk b/physics/midyear.fdb_latexmk
index 8d8598fed636cc879e0f11ec6608f0f1cdd3427f..48a4005022a2216298b4bddac29a5c7859bd6dd7 100644 (file)
--- a/physics/midyear.fdb_latexmk
+++ b/physics/midyear.fdb_latexmk
@@ -1,5 +1,5 @@
 # Fdb version 3
 # Fdb version 3

-["pdflatex"] 1531987725 "midyear.tex" "midyear.pdf" "midyear" 1531987726
+["pdflatex"] 1532049248 "midyear.tex" "midyear.pdf" "midyear" 1532049249

   "/mnt/andrew/graphics/ac-generator.png" 1529320281 28991 f74a831edcaed66632e709a6b2e2ebfd ""
   "/mnt/andrew/graphics/ac-motor.png" 1529313736 18626 d0f4943be26fdce44a4ce45ccb01633c ""
   "/mnt/andrew/graphics/banked-track.png" 1531025364 51228 cc5d8f3f8efb06a64aca4afabfd63eed ""
   "/mnt/andrew/graphics/ac-generator.png" 1529320281 28991 f74a831edcaed66632e709a6b2e2ebfd ""
   "/mnt/andrew/graphics/ac-motor.png" 1529313736 18626 d0f4943be26fdce44a4ce45ccb01633c ""
   "/mnt/andrew/graphics/banked-track.png" 1531025364 51228 cc5d8f3f8efb06a64aca4afabfd63eed ""


@@ -70,9 +70,9 @@
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   "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1530607795 2586890 ddabbb88c498d59d5daa7919afb0a27f ""
   "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1530607774 7906415 c2bc2a1e85cbebe301ae391211242f7e ""
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   "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1530607774 7906415 c2bc2a1e85cbebe301ae391211242f7e ""

-  "midyear.aux" 1531987726 223 c9c8cc73e6c5d1c4bae220d8eb29b53c ""
-  "midyear.tex" 1531987725 9117 4a1990d0b0ea8d63b7cd19f496ac4706 ""
+  "midyear.aux" 1532049249 223 c9c8cc73e6c5d1c4bae220d8eb29b53c ""
+  "midyear.tex" 1532049248 9329 b74d77b1da90c209352ffa9ba1392fc8 ""

   (generated)
   (generated)

-  "midyear.log"
-  "midyear.pdf"

   "midyear.aux"
   "midyear.aux"

+  "midyear.pdf"
+  "midyear.log"

diff --git a/physics/midyear.fls b/physics/midyear.fls
index fd1ed4eb3a581ed1895f82a4a1935bae6bdca46b..a75a253687ab48673a186444ceeacc038ebe7144 100644 (file)
--- a/physics/midyear.fls
+++ b/physics/midyear.fls
@@ -76,8 +76,6 @@ INPUT /usr/share/texmf-dist/fonts/map/fontname/texfonts.map
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 INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr17.tfm
 INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm
 INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm

-INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm
-INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm

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 INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
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 INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
 INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd


@@ -90,6 +88,8 @@ INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd
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 INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm
 INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm
 INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
 INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm
 INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm

+INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm
+INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm

 INPUT /mnt/andrew/graphics/banked-track.png
 INPUT /mnt/andrew/graphics/banked-track.png
 OUTPUT midyear.pdf
 INPUT /mnt/andrew/graphics/banked-track.png
 INPUT /mnt/andrew/graphics/banked-track.png
 OUTPUT midyear.pdf

diff --git a/physics/midyear.log b/physics/midyear.log
index 60f4e250f28d8ad2145f14f3724db705b29abe6b..26cfccd392b94e412da4429234e9f99d3f90648b 100644 (file)
--- a/physics/midyear.log
+++ b/physics/midyear.log
@@ -1,4 +1,4 @@
-This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018/Arch Linux) (preloaded format=pdflatex 2018.7.3)  19 JUL 2018 18:08
+This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018/Arch Linux) (preloaded format=pdflatex 2018.7.3)  20 JUL 2018 11:14

 entering extended mode
  restricted \write18 enabled.
  file:line:error style messages enabled.
 entering extended mode
  restricted \write18 enabled.
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 File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live
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 File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live
 ))

-LaTeX Font Info:    Try loading font information for U+msa on input line 28.
+LaTeX Font Info:    Try loading font information for U+msa on input line 27.

  (/usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd
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-LaTeX Font Info:    Try loading font information for U+msb on input line 28.
+LaTeX Font Info:    Try loading font information for U+msb on input line 27.

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 <use /mnt/andrew/graphics/banked-track.png>

-Package pdftex.def Info: /mnt/andrew/graphics/banked-track.png  used on input line 33.
+Package pdftex.def Info: /mnt/andrew/graphics/banked-track.png  used on input line 35.

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 Package amsmath Warning: Foreign command \over;
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-Overfull \hbox (0.85123pt too wide) in paragraph at lines 94--95
+Overfull \hbox (0.85123pt too wide) in paragraph at lines 96--97

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@@ -285,50 +285,60 @@ Overfull \hbox (0.85123pt too wide) in paragraph at lines 94--95
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-Package pdftex.def Info: /mnt/andrew/graphics/field-lines.png  used on input line 267.
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-Overfull \hbox (8.70474pt too wide) in paragraph at lines 267--268
+Overfull \hbox (8.70474pt too wide) in paragraph at lines 222--223

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+./midyear.tex:301: Missing $ inserted.
+<inserted text> 
+                $
+l.301       P_
+              {\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \ov...
+I've inserted a begin-math/end-math symbol since I think
+you left one out. Proceed, with fingers crossed.
+
+./midyear.tex:304: Missing $ inserted.
+<inserted text> 
+                $
+l.304 
+      
+I've inserted a begin-math/end-math symbol since I think
+you left one out. Proceed, with fingers crossed.
+

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+[2 </mnt/andrew/graphics/field-lines.png> </mnt/andrew/graphics/ac-generator.png> </mnt/andrew/graphics/dc-motor-2.png (PNG copy)> </mnt/andrew/graphics/ac-motor.png>] (./midyear.aux) ) 

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+Output written on midyear.pdf (2 pages, 331326 bytes).

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diff --git a/physics/midyear.pdf b/physics/midyear.pdf
index e86882ba66806f2dd5c28b40119e0f4113a4b84d..fe8f6a48a32ac9efbddb859c0490f5a580067368 100644 (file)
Binary files a/physics/midyear.pdf and b/physics/midyear.pdf differ

diff --git a/physics/midyear.synctex.gz b/physics/midyear.synctex.gz
index 353f42d6e3f26f5b92f0398f3b5692c7a6cc6980..d23c75ce5e4fd68e7b30dacf0c4d8912ddc3d204 100644 (file)
Binary files a/physics/midyear.synctex.gz and b/physics/midyear.synctex.gz differ

diff --git a/physics/midyear.tex b/physics/midyear.tex
index 865a0abf2639036ec068a71f831e1c6853071051..d52268657c4de0074723ad074871d31b85cd06b7 100644 (file)
--- a/physics/midyear.tex
+++ b/physics/midyear.tex
@@ -18,12 +18,14 @@
 \begin{multicols}{3}
 
 % +++++++++++++++++++++++
 \begin{multicols}{3}
 
 % +++++++++++++++++++++++

-  
+

 {\huge Physics}\hfill Andrew Lorimer\hspace{2em}
 
 % +++++++++++++++++++++++
 \section{Motion}
 
 {\huge Physics}\hfill Andrew Lorimer\hspace{2em}
 
 % +++++++++++++++++++++++
 \section{Motion}
 

+  $\operatorname{m/s} \times 3.6 = \operatorname{km/h}$
+

   \subsection*{Inclined planes}
     $F = m g \sin\theta - F_{frict} = m a$
 
   \subsection*{Inclined planes}
     $F = m g \sin\theta - F_{frict} = m a$
 


@@ -32,11 +34,11 @@
 
     \includegraphics[height=4cm]{/mnt/andrew/graphics/banked-track.png}
 
 
     \includegraphics[height=4cm]{/mnt/andrew/graphics/banked-track.png}
 

-    $\theta = \tan^{-1} {{v^2} \over rg}$ (also for objects on string)
+    $$\theta = \tan^{-1} {{v^2} \over rg}$$

 
     $\Sigma F$ always acts towards centre, but not necessarily horizontally
 
 
     $\Sigma F$ always acts towards centre, but not necessarily horizontally
 

-    $\Sigma F = {{mv^2} \over r} = mg \tan \theta$
+    $\Sigma F = F_{\operatorname{norm}} + F_{\operatorname{g}}={{mv^2} \over r} = mg \tan \theta$

 
     Design speed $v = \sqrt{gr\tan\theta}$
 
 
     Design speed $v = \sqrt{gr\tan\theta}$
 


@@ -52,9 +54,7 @@
     $\Sigma E = {1 \over 2} mv^2 + mgh$ (energy transfer)
 
 % -----------------------
     $\Sigma E = {1 \over 2} mv^2 + mgh$ (energy transfer)
 
 % -----------------------

-  \subsection*{Horizontal motion}
-
-    $\operatorname{m/s} \times 3.6 = \operatorname{km/h}$
+  \subsection*{Horizontal circular motion}

 
     $v = {{2 \pi r} \over T}$
 
 
     $v = {{2 \pi r} \over T}$
 


@@ -62,7 +62,7 @@
 
     $a_{centrip} = {v^2 \over r} = {{4 \pi^2 r} \over T^2}$
 
 
     $a_{centrip} = {v^2 \over r} = {{4 \pi^2 r} \over T^2}$
 

-    $\Sigma F$ towards centre, $v$ tangential
+    $\Sigma F, a$ towards centre, $v$ tangential

 
     $F_{centrip} = {{mv^2} \over r} = {{4 \pi^2 rm} \over T^2}$
 
 
     $F_{centrip} = {{mv^2} \over r} = {{4 \pi^2 rm} \over T^2}$
 


@@ -87,7 +87,9 @@
     \begin{align*}
       v=\sqrt{v^2_x + v^2_y} \tag{vectors} \\
       h={{u^2\sin \theta ^2}\over 2g} \tag{max height}\\
     \begin{align*}
       v=\sqrt{v^2_x + v^2_y} \tag{vectors} \\
       h={{u^2\sin \theta ^2}\over 2g} \tag{max height}\\

-      y=ut \sin \theta-{1 \over 2}gt^2 \tag{time of flight} \\
+      x=ut\cos\theta \tag{$\Delta x$ at $t$} \\
+      y=ut \sin \theta-{1 \over 2}gt^2 \tag{height at $t$} \\
+      t={{2u\sin\theta}\over g} \tag{time of flight}\\

       d={v^2 \over g}\sin \theta \tag{horiz. range} \\
     \end{align*}
 
       d={v^2 \over g}\sin \theta \tag{horiz. range} \\
     \end{align*}
 


@@ -135,7 +137,7 @@
 
     $\operatorname{impulse} = \Delta \rho, \quad F \Delta t = m \Delta v$
 
 
     $\operatorname{impulse} = \Delta \rho, \quad F \Delta t = m \Delta v$
 

-    Momentum is conserved.
+    $\Sigma mv_0=\Sigma mv_1$ (conservation)

 
     $\Sigma E_{K \operatorname{before}} = \Sigma E_{K \operatorname{after}}$ if elastic
 
 
     $\Sigma E_{K \operatorname{before}} = \Sigma E_{K \operatorname{after}}$ if elastic
 


@@ -190,20 +192,11 @@
 
     $$v={\rho \over {m\sqrt{1+{p^2 \over {m^2 c^2}}}}}$$
 
 
     $$v={\rho \over {m\sqrt{1+{p^2 \over {m^2 c^2}}}}}$$
 

-% -----------------------
-  \subsection*{Fusion and fission}
-
-    $1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$
-
-    e- accelerated with $x$ V is given $x$ eV
-

 % -----------------------
   \subsection*{High-altitude muons}
     \begin{itemize}
       {\item $t$ dilation - more muons reach Earth than expected}
 % -----------------------
   \subsection*{High-altitude muons}
     \begin{itemize}
       {\item $t$ dilation - more muons reach Earth than expected}

-      {\item normal half-life is $2.2 \operatorname{\mu s}$ in stationary frame}
-      {\item at $v \approx c$, muons observed from Earth have halflife $> 2.2 \operatorname{\mu s}$}
-      {\item slower time - more time to travel, so muons reach surface}
+      {\item normal half-life $2.2 \operatorname{\mu s}$ in stationary frame, $> 2.2 \operatorname{\mu s}$ observed from Earth}

     \end{itemize}
 
 % +++++++++++++++++++++++
     \end{itemize}
 
 % +++++++++++++++++++++++


@@ -222,27 +215,27 @@
       \item monopoles: lines towards centre
       \item dipoles: field lines $+ \rightarrow -$ or $\operatorname{N} \rightarrow \operatorname{S}$ (or perpendicular to wire)
       \item closer field lines means larger force
       \item monopoles: lines towards centre
       \item dipoles: field lines $+ \rightarrow -$ or $\operatorname{N} \rightarrow \operatorname{S}$ (or perpendicular to wire)
       \item closer field lines means larger force

-      \item dot means out of page, cross means into page
+      \item dot: out of page, cross: into page

       \item +ve corresponds to N pole
     \end{itemize}
 
       \item +ve corresponds to N pole
     \end{itemize}
 

+    \includegraphics[height=2cm]{/mnt/andrew/graphics/field-lines.png}
+

 % -----------------------
   \subsection*{Gravity}
 
     \[F_g=G{{m_1m_2}\over r^2}\tag{grav. force}\]
 % -----------------------
   \subsection*{Gravity}
 
     \[F_g=G{{m_1m_2}\over r^2}\tag{grav. force}\]

-
-    \[g={F_g \over m}=G{M_{\operatorname{planet}} \over r^2}\tag{grav. acc.}\]
-
+    \[g={F_g \over m_2}=G{m_{1} \over r^2}\tag{field of $m_1$}\]

     \[E_g = mg \Delta h\tag{gpe}\]
     \[E_g = mg \Delta h\tag{gpe}\]

-

     \[W = \Delta E_g = Fx\tag{work}\]
     \[W = \Delta E_g = Fx\tag{work}\]

-

     \[w=m(g-a) \tag{app. weight}\]
 
     \[w=m(g-a) \tag{app. weight}\]
 

+    % \columnbreak
+

 % -----------------------
   \subsection*{Satellites}
 
 % -----------------------
   \subsection*{Satellites}
 

-    \[v=\sqrt{GM \over r} = \sqrt{gr} = {{2 \pi r} \over T}\]
+    \[v=\sqrt{Gm_{\operatorname{planet}} \over r} = \sqrt{gr} = {{2 \pi r} \over T}\]

 
     \[T={\sqrt{4 \pi^2 r^2} \over {GM}}\tag{period}\]
 
 
     \[T={\sqrt{4 \pi^2 r^2} \over {GM}}\tag{period}\]
 


@@ -257,54 +250,63 @@
       \item emf $\mathcal{E}$ measured in volts
     \end{itemize}
 
       \item emf $\mathcal{E}$ measured in volts
     \end{itemize}
 

-    \[{E_1 \over E_2}={r_1 \over r_2}^2\]
+    % \[{E_1 \over E_2}={r_1 \over r_2}^2\]

 
 

-    \[F=qvB\tag{force on moving charged particles}\]
+    \[F=qvB\tag{$F$ on moving $q$}\]
+    \[F=IlB\tag{$F$ of $B$ on $I$}\]
+    \[r={mv \over qB} \tag{radius of $q$ in $B$}\]

 
     if $B {\not \perp} A, \Phi \rightarrow 0$ \hspace{1em}, \hspace{1em} if $B \parallel A, \Phi = 0$
 
 
     if $B {\not \perp} A, \Phi \rightarrow 0$ \hspace{1em}, \hspace{1em} if $B \parallel A, \Phi = 0$
 

-
-    \includegraphics[height=2cm]{/mnt/andrew/graphics/field-lines.png}
-

 % -----------------------
   \subsection*{Electric fields}
 
 % -----------------------
   \subsection*{Electric fields}
 

-    \begin{align*}
-      F=qE \tag{$E$ = strength} \\
-      W=q_{\operatorname{point}}\Delta V \tag{in field or points} \\
-      F=k{{q_1q_2}\over r^2}\tag{force between $q_{1,2}$} \\
-      E=k{Q \over r^2} \tag{$r=||EQ||$} \\
-      F=BInl \tag{force on a coil} \\
-      \Phi = B_{\perp}A\tag{magnetic flux} \\
-      \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} \\
-    \end{align*}
+    \[F=qE \tag{$E$ = strength} \]
+    \[F=k{{q_1q_2}\over r^2}\tag{force between $q_{1,2}$} \]
+    \[E=k{q \over r^2} \tag{field on point charge} \]
+    \[E={V \over d} \tag{field between plates}\]
+    \[F=BInl \tag{force on a coil} \]
+    \[\Phi = B_{\perp}A\tag{magnetic flux} \]
+    \[\mathcal{E} = -N{{\Delta \Phi}\over{\Delta t}} \tag{induced emf} \]
+    \[{V_p \over V_s}={N_p \over N_s}={I_s \over I_p} \tag{xfmr coil ratios} \]

 
 

-    \textbf{Lenz's law:}  ``$-n$'' in Faraday - emf opposes $\Delta \Phi$
+    \textbf{Lenz's law:}  $I_{\operatorname{emf}}$ opposes $\Delta \Phi$

 
     \textbf{Eddy currents:} counter movement within a field
 
 
     \textbf{Eddy currents:} counter movement within a field
 

-    \textbf{Right hand grip:} thumb points to north or $I$
+    \textbf{Right hand grip:} thumb points to $I$ (single wire) or N (solenoid / coil)

 
 

-    \textbf{Right hand slap:} field, current, force are $\perp$
+    \textbf{Right hand slap:} $B \perp I \perp F$

 
 

-    \textbf{Flux-time graphs:} gradient $\times n = \operatorname{emf}$
+    \textbf{Flux-time graphs:} $m \times n = \operatorname{emf}$

 
     \textbf{Transformers:} core strengthens \& focuses $\Phi$
 
 
     \textbf{Transformers:} core strengthens \& focuses $\Phi$
 

+% -----------------------
+  \subsection*{Particle acceleration}
+
+    $1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$
+
+    e- accelerated with $x$ V is given $x$ eV
+
+    \[W={1\over2}mv^2=qV \tag{field or points}\]
+    \[v=\sqrt{{2qV} \over {m}}\tag{velocity of particle}\]
+
+

 % -----------------------
   \subsection*{Power transmission}
 
 % -----------------------
   \subsection*{Power transmission}
 

-    \begin{align*}
-      V_{\operatorname{rms}}={V_{\operatorname{p\rightarrow p}}\over \sqrt{2}} \\
+    % \begin{align*}
+      $$V_{\operatorname{rms}}={V_{\operatorname{p\rightarrow p}}\over \sqrt{2}}$$

       P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R} \\
       P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R} \\

-    \end{align*}
+      V_{\operatorname{loss}}=IR
+    % \end{align*}

 
     Use high-$V$ side for correct $|V_{drop}|$
 
     \begin{itemize}
 
     Use high-$V$ side for correct $|V_{drop}|$
 
     \begin{itemize}

-      {\item Parallel - voltage is constant}
-      {\item Series - voltage is shared within branch}
+      {\item Parallel - $V$ is constant}
+      {\item Series - $V$ shared within branch}

     \end{itemize}
 
     \includegraphics[height=4cm]{/mnt/andrew/graphics/ac-generator.png}
     \end{itemize}
 
     \includegraphics[height=4cm]{/mnt/andrew/graphics/ac-generator.png}