From: Andrew Lorimer Date: Sun, 21 Oct 2018 00:50:36 +0000 (+1100) Subject: lenz's law clarifications X-Git-Tag: yr11~12 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/52021e6627413b3e1a8d019461dcec1667c1b262 lenz's law clarifications --- diff --git a/physics/final.pdf b/physics/final.pdf index 904bb01..c1e9790 100644 Binary files a/physics/final.pdf and b/physics/final.pdf differ diff --git a/physics/final.tex b/physics/final.tex index b37f67c..4dbb0bd 100644 --- a/physics/final.tex +++ b/physics/final.tex @@ -91,14 +91,14 @@ \item vertical component gravity: $a_y = -g$ \end{itemize} - \begin{align*} - v=\sqrt{v^2_x + v^2_y} \tag{vectors} \\ - h={{u^2\sin \theta ^2}\over 2g} \tag{max height}\\ - 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*} + % \begin{align*} + $v=\sqrt{v^2_x + v^2_y}$ \hfill vectors \\ + $h={{u^2\sin \theta ^2}\over 2g}$ \hfill max height \\ + $x=ut\cos\theta$ \hfill $\Delta x$ at $t$ \\ + $y=ut \sin \theta-{1 \over 2}gt^2$ \hfill height at $t$ \\ + $t={{2u\sin\theta}\over g}$ \hfill time of flight \\ + $d={v^2 \over g}\sin \theta$ \hfill horiz. range \\ + % \end{align*} \includegraphics[height=3.2cm]{graphics/projectile-motion.png} @@ -128,6 +128,8 @@ $x={2mg \over k}$ + Vertical: $\Delta E = {1 \over 2}kx^2 + mgh + % ----------------------- \subsection*{Motion equations} @@ -177,7 +179,7 @@ % ----------------------- \subsection*{Lorentz factor} - $$\gamma = {1 \over {\sqrt{1-{v^2 \over c^2}}}}$$ + $$\gamma = {1 \over {\sqrt{1-{v^2 \over c^2}}}}, \quad v = c\sqrt{1-{1 \over \gamma^2}}$$ $t=t_0 \gamma$ ($t$ longer in moving frame) @@ -185,8 +187,6 @@ $m=m_0 \gamma$ (mass dilation) - $$v = c\sqrt{1-{1 \over \gamma^2}}$$ - % ----------------------- \subsection*{Energy and work} @@ -223,7 +223,7 @@ \begin{itemize} \item monopoles: lines towards centre - \item dipoles: field lines $+ \rightarrow -$ or $\operatorname{N} \rightarrow \operatorname{S}$ (or perpendicular to wire) + \item dipoles: field lines $+ \rightarrow -$ or $\operatorname{N} \rightarrow \operatorname{S}$ (two magnets) or $\rightarrow$ N (single) \item closer field lines means larger force \item dot: out of page, cross: into page \item +ve corresponds to N pole @@ -413,7 +413,7 @@ % ----------------------- \subsection*{Polarisation} \includegraphics[height=3.5cm]{graphics/polarisation.png} \\ - Reduces total amplitude (transverse only) + Transverse only. Reduces total $A$. % ----------------------- \subsection*{Diffraction} @@ -609,4 +609,8 @@ $f \cdot V$ & ${h \over q}$ & $f_0$ & $-\phi \over q$ & \end{multicols} +\begin{center} + \includegraphics[height=2.95cm]{graphics/spectrum.png} +\end{center} + \end{document}