update cheatsheet from Neap 2017 exam

diff --git a/physics/final.pdf b/physics/final.pdf
index 375bdb14fee6b7e408157c3c4dc9c45944a9bf42..8d0ab7876b83f8d89168cfd080969a9ac57e1719 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 fabaceff42984213d4aeeb6c305c14811ab84f8a..1db6640019b9d718215d93388e5e256d4307b714 100644 (file)
--- a/physics/final.tex
+++ b/physics/final.tex
@@ -68,18 +68,18 @@
 
     $\Sigma F, a$ towards centre, $v$ tangential
 
-    $F_{centrip} = {{mv^2} \over r} = {{4 \pi^2 rm} \over T^2}$
+    $\Sigma F = F_{centrip} = {{mv^2} \over r} = {{4 \pi^2 rm} \over T^2}=T \sin \theta = mg \tan \theta$
 
     \includegraphics[height=4cm]{graphics/circ-forces.png}
 
 % -----------------------
   \subsection*{Vertical circular motion}
 
-    $T =$ tension, e.g. circular pendulum
+    % $T =$ tension, e.g. circular pendulum
 
-    $T+mg = {{mv^2}\over r}$ at highest point
+    $T+mg = {{mv^2}\over r}, v = \sqrt{rg}$ (top)
 
-    $T-mg = {{mv^2} \over r}$ at lowest point
+    $T-mg = {{mv^2} \over r}, v = \sqrt{2rg}$ (bottom)
 
     $E_K_{\text{bottom}}=E_K_{\text{top}}+mgh$
 
@@ -115,7 +115,7 @@
       \item{Force-time: $A=\Delta \rho$}
       \item{Force-disp: $A=W$}
       \item{Force-ext: $m=k,\quad A=E_{spr}$}
-      \item{Force-dist: $A=\Delta \operatorname{gpe}$}
+      \item{$F_g$-dist: $A=\Delta \operatorname{gpe}$}
       \item{Field-dist: $A=\Delta \operatorname{gpe} / \operatorname{kg}$}
     \end{itemize}
 
@@ -340,7 +340,7 @@
     \includegraphics[height=4cm]{graphics/dc-motor-2.png}
     \includegraphics[height=3cm]{graphics/ac-motor.png} \\
 
-    Force on current-carying wire, not copper \\
+    Force on I-carying wire, not Cu \\
     $F=0$ for front & back of coil (parallel) \\
     Any angle $> 0$ will produce force \\
 % \end{wrapfigure}
@@ -428,9 +428,10 @@
     % \(\Delta x\) = fringe spacing \\
     \(l\) = distance from source to observer\\
     \(d\) = separation between each wave source (e.g. slit) \(=S_1-S_2\)
-    \item diffraction $\propto {\lambda \over d}$
+    \item diffraction $\propto {\lambda \over d} \propto$ fringe spacing
+    \item $d(|\overrightarrow{S_1W}|-|\overrightarrow{S_2W}|)=d \Delta x = \lambda l$
     \item significant diffraction when ${\lambda \over \Delta x} \ge 1$
-    \item diffraction creates distortion (electron $>$ optical microscopes)
+    \item diffraction creates distortion (electron $\gt$ optical microscopes)
   \end{itemize}
 
 
@@ -553,7 +554,9 @@ $f \cdot V$ & ${h \over q}$ & $f_0$ & $-\phi \over q$ &
 
   \subsection*{Uncertainty principle}
 
-  measuring location of an e- requires hitting it with a photon, but this causes $\rho$ to be transferred to electron, moving it.
+  $\Delta x \approx {\text{slit width} \over 2$}
+
+  measurement: $\rho$ transferred to e-\\ slit: possibility of diff. before slit
 
   \subsection*{Wave-particle duality}