adjustments to cheatsheet after LM & PTTT practice exams

diff --git a/physics/final.pdf b/physics/final.pdf
index db09fd38933f3916809395c7219d207e928d36a7..904bb0126cbaade84fa9bd6f2271d8003e71b759 100644 (file)
Binary files a/physics/final.pdf and b/physics/final.pdf differ

diff --git a/physics/final.tex b/physics/final.tex
index 4628ed0ac6ef18b0fcfa57a0311519543c000455..64240ea9160ea07817fc46098025368bd033a03e 100644 (file)
--- a/physics/final.tex
+++ b/physics/final.tex
@@ -120,7 +120,7 @@
 % -----------------------
   \subsection*{Hooke's law}
 
 % -----------------------
   \subsection*{Hooke's law}
 

-  $F=-kx$
+  $F=-kx$ (intercepts origin)

 
   $\text{elastic potential energy} = {1 \over 2}kx^2$
 
 
   $\text{elastic potential energy} = {1 \over 2}kx^2$
 


@@ -212,9 +212,9 @@
 
   \subsection*{Non-contact forces}
     \begin{itemize}
 
   \subsection*{Non-contact forces}
     \begin{itemize}

-      {\item electric fields (dipoles \& monopoles)}
-      {\item magnetic fields (dipoles only)}
-      {\item gravitational fields (monopoles only)}
+      {\item electric (dipoles \& monopoles)}
+      {\item magnetic (dipoles only)}
+      {\item gravitational (monopoles only, $F_g=0$ at mid, attractive only)}

     \end{itemize}
 
     \vspace{1em}
     \end{itemize}
 
     \vspace{1em}


@@ -244,9 +244,9 @@
 % -----------------------
   \subsection*{Satellites}
 
 % -----------------------
   \subsection*{Satellites}
 

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

 
 

-    \[T={\sqrt{4 \pi^2 r^3} \over {GM_\text{planet}}}\tag{period}\]
+    \[T={\sqrt{4 \pi^2 r^3 \over {GM}}}\tag{period}\]

 
     \[r = \sqrt[3]{{GMT^2}\over{4\pi^2}}\tag{radius}\]
 
 
     \[r = \sqrt[3]{{GMT^2}\over{4\pi^2}}\tag{radius}\]
 


@@ -271,13 +271,13 @@
 % -----------------------
   \subsection*{Electric fields}
 
 % -----------------------
   \subsection*{Electric fields}
 

-    \[F=qE \tag{$E$ = strength} \]
+    \[F=qE(=ma) \tag{strength} \]

     \[F=k{{q_1q_2}\over r^2}\tag{force between $q_{1,2}$} \]
     \[E=k{q \over r^2} \tag{field on point charge} \]
     \[E={V \over d} \tag{field between plates}\]
     \[F=BInl \tag{force on a coil} \]
     \[\Phi = B_{\perp}A\tag{magnetic flux} \]
     \[F=k{{q_1q_2}\over r^2}\tag{force between $q_{1,2}$} \]
     \[E=k{q \over r^2} \tag{field on point charge} \]
     \[E={V \over d} \tag{field between plates}\]
     \[F=BInl \tag{force on a coil} \]
     \[\Phi = B_{\perp}A\tag{magnetic flux} \]

-    \[\mathcal{E} = -N{{\Delta \Phi}\over{\Delta t}} \tag{induced emf} \]
+    \[\mathcal{E} = -N{{\Delta \Phi}\over{\Delta t}} = Blv\tag{induced emf} \]

     \[{V_p \over V_s}={N_p \over N_s}={I_s \over I_p} \tag{xfmr coil ratios} \]
 
     \textbf{Lenz's law:}  $I_{\operatorname{emf}}$ opposes $\Delta \Phi$ \\
     \[{V_p \over V_s}={N_p \over N_s}={I_s \over I_p} \tag{xfmr coil ratios} \]
 
     \textbf{Lenz's law:}  $I_{\operatorname{emf}}$ opposes $\Delta \Phi$ \\


@@ -298,7 +298,7 @@
     \textbf{Flux-time graphs:} $m \times n = \operatorname{emf}.$
     If $f$ increases, ampl. \& $f$ of $\mathcal{E}$ increase
 
     \textbf{Flux-time graphs:} $m \times n = \operatorname{emf}.$
     If $f$ increases, ampl. \& $f$ of $\mathcal{E}$ increase
 

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

 
 % -----------------------
   \subsection*{Particle acceleration}
 
 % -----------------------
   \subsection*{Particle acceleration}


@@ -310,7 +310,6 @@
     \[W={1\over2}mv^2=qV \tag{field or points}\]
     \[v=\sqrt{{2qV} \over {m}}\tag{velocity of particle}\]
 
     \[W={1\over2}mv^2=qV \tag{field or points}\]
     \[v=\sqrt{{2qV} \over {m}}\tag{velocity of particle}\]
 

-

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


@@ -380,7 +379,7 @@
   \includegraphics[width=4.5cm]{graphics/poissons-spot.png} \\
   Poissons's spot supports wave theory (circular diffraction)
 
   \includegraphics[width=4.5cm]{graphics/poissons-spot.png} \\
   Poissons's spot supports wave theory (circular diffraction)
 

-  \textbf{Standing waves} - constructive int. at resonant freq
+  \textbf{Standing waves} - constructive int. at resonant freq. Rebound from ends.

 
   \textbf{Coherent } - identical frequency, phase, direction (ie strong & directional). e.g. laser
 
 
   \textbf{Coherent } - identical frequency, phase, direction (ie strong & directional). e.g. laser
 


@@ -409,7 +408,8 @@
 
   % -----------------------
   \subsection*{Polarisation}
 
   % -----------------------
   \subsection*{Polarisation}

-  \includegraphics[height=3.5cm]{graphics/polarisation.png}
+  \includegraphics[height=3.5cm]{graphics/polarisation.png} \\
+  Reduces total amplitude

 
   % -----------------------
   \subsection*{Diffraction}
 
   % -----------------------
   \subsection*{Diffraction}


@@ -458,9 +458,10 @@
 
   \subsection*{De Broglie's theory}
 
 
   \subsection*{De Broglie's theory}
 

-  \[ \lambda = {h \over \rho} = {h \over mv} \]
+  \[ \lambda = {h \over \rho} = {h \over mv} = {h \over {m \sqrt{2W \over m}}}\]

   \[ \rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c \]
   \[ v = \sqrt{2E_K \div m} \]
   \[ \rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c \]
   \[ v = \sqrt{2E_K \div m} \]

+

   \begin{itemize}
     \item cannot confirm with double-slit (slit $< r_{\operatorname{proton}}$)
     \item confirmed by e- and x-ray patterns
   \begin{itemize}
     \item cannot confirm with double-slit (slit $< r_{\operatorname{proton}}$)
     \item confirmed by e- and x-ray patterns


@@ -513,6 +514,7 @@
   \subsubsection*{Stopping potential $V_0$ for min $I$}
 
   $$V_0=h_{\text{eV}}(f-f_0)$$
   \subsubsection*{Stopping potential $V_0$ for min $I$}
 
   $$V_0=h_{\text{eV}}(f-f_0)$$

+  Opposes induced photocurrent

 
   \subsubsection*{Graph features}
 
 
   \subsubsection*{Graph features}
 


@@ -555,6 +557,7 @@ $f \cdot V$ & ${h \over q}$ & $f_0$ & $-\phi \over q$ &
     \item predicts delay between incidence and ejection
     \item speed depends on medium
     \item supported by bright spot in centre
     \item predicts delay between incidence and ejection
     \item speed depends on medium
     \item supported by bright spot in centre

+    \item $\lambda = {hc \over E}$

   \end{itemize}
 
   \subsubsection*{particle model}
   \end{itemize}
 
   \subsubsection*{particle model}


@@ -567,6 +570,7 @@ $f \cdot V$ & ${h \over q}$ & $f_0$ & $-\phi \over q$ &
     \item light exerts force
     \item light bent by gravity
     \item quantised energy
     \item light exerts force
     \item light bent by gravity
     \item quantised energy

+    \item $\lambda = {h \over \rho}$

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