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}
 
-  $F=-kx$
+  $F=-kx$ (intercepts origin)
 
   $\text{elastic potential energy} = {1 \over 2}kx^2$
 
@@ -212,9 +212,9 @@
 
   \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}
@@ -244,9 +244,9 @@
 % -----------------------
   \subsection*{Satellites}
 
-    \[v=\sqrt{Gm_{\operatorname{planet}} \over r} = \sqrt{gr} = {{2 \pi r} \over T}\]
+    \[v=\sqrt{GM \over r} = \sqrt{gr} = {{2 \pi r} \over T}\]
 
-    \[T={\sqrt{4 \pi^2 r^3} \over {GM_\text{planet}}}\tag{period}\]
+    \[T={\sqrt{4 \pi^2 r^3 \over {GM}}}\tag{period}\]
 
     \[r = \sqrt[3]{{GMT^2}\over{4\pi^2}}\tag{radius}\]
 
@@ -271,13 +271,13 @@
 % -----------------------
   \subsection*{Electric fields}
 
-    \[F=qE \tag{$E$ = strength} \]
+    \[F=qE(=ma) \tag{strength} \]
     \[F=k{{q_1q_2}\over r^2}\tag{force between $q_{1,2}$} \]
     \[E=k{q \over r^2} \tag{field on point charge} \]
     \[E={V \over d} \tag{field between plates}\]
     \[F=BInl \tag{force on a coil} \]
     \[\Phi = B_{\perp}A\tag{magnetic flux} \]
-    \[\mathcal{E} = -N{{\Delta \Phi}\over{\Delta t}} \tag{induced emf} \]
+    \[\mathcal{E} = -N{{\Delta \Phi}\over{\Delta t}} = Blv\tag{induced emf} \]
     \[{V_p \over V_s}={N_p \over N_s}={I_s \over I_p} \tag{xfmr coil ratios} \]
 
     \textbf{Lenz's law:}  $I_{\operatorname{emf}}$ opposes $\Delta \Phi$ \\
@@ -298,7 +298,7 @@
     \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}
@@ -310,7 +310,6 @@
     \[W={1\over2}mv^2=qV \tag{field or points}\]
     \[v=\sqrt{{2qV} \over {m}}\tag{velocity of particle}\]
 
-
 % -----------------------
   \subsection*{Power transmission}
 
@@ -380,7 +379,7 @@
   \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
 
@@ -409,7 +408,8 @@
 
   % -----------------------
   \subsection*{Polarisation}
-  \includegraphics[height=3.5cm]{graphics/polarisation.png}
+  \includegraphics[height=3.5cm]{graphics/polarisation.png} \\
+  Reduces total amplitude
 
   % -----------------------
   \subsection*{Diffraction}
@@ -458,9 +458,10 @@
 
   \subsection*{De Broglie's theory}
 
-  \[ \lambda = {h \over \rho} = {h \over mv} \]
+  \[ \lambda = {h \over \rho} = {h \over mv} = {h \over {m \sqrt{2W \over m}}}\]
   \[ \rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c \]
   \[ v = \sqrt{2E_K \div m} \]
+
   \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 $I$}
 
   $$V_0=h_{\text{eV}}(f-f_0)$$
+  Opposes induced photocurrent
 
   \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 $\lambda = {hc \over E}$
   \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 $\lambda = {h \over \rho}$
   \end{itemize}
 
   % +++++++++++++++++++++++