From 8a4211ca1a897e060c54fd20733b292157251e6d Mon Sep 17 00:00:00 2001 From: Hearot Date: Tue, 18 Jan 2022 20:40:44 +0100 Subject: [PATCH] Aggiunge nuovi appunti di Fisica --- .gitignore | 2 + docs/CNAME => CNAME | 0 Fisica/fisica.pdf | Bin 0 -> 129578 bytes Fisica/fisica.tex | 89 ++++++++++++++++++++++++++++++++++ docs/index.html => index.html | 0 5 files changed, 91 insertions(+) rename docs/CNAME => CNAME (100%) create mode 100644 Fisica/fisica.pdf create mode 100644 Fisica/fisica.tex rename docs/index.html => index.html (100%) diff --git a/.gitignore b/.gitignore index 9ff04ec..7571e32 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,5 @@ *.aux *.log +*.fdb_latexmk +*.fls *.synctex.gz \ No newline at end of file diff --git a/docs/CNAME b/CNAME similarity index 100% rename from docs/CNAME rename to CNAME diff --git a/Fisica/fisica.pdf b/Fisica/fisica.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3c43115cb79b579c5da1f58f21657742bcd58bc1 GIT binary patch literal 129578 zcmc$`bzD_nw=Ya7t#qeINp5k?aba!`mNOwp{2r5WPcXxw=bVy5gm+#seeSV(% zoO92)_x|zn`K-xYV~#QAoMVhRzH_a;)}mGr6K4W3bD~gx{oXZ&!cM_TVQXN4!q1Pw zB4cc0>SRU%;$ow?|3hIBH@9*!cA#Jpx6*eq7Be=qH8MsK6hv`!axm7nMsb^A8g4^r zXGQZ{y3Tykb5>ga)N+!HmZ#0}@CjM&yH~L`X5PMqr#MKLLglC9CKRYs^dj>CEwI_I znb;{uB6C_%SBF?5!A`zwTudSG)LG{z?Lr9gb2HC2*i_0Lw; z2-hX#*vCyvvCYHu=_3qN))Rfy?nDR^&_njnj7m(Lf<@Wb&51%AV)5VVz<;Ux?Jl0* z&Z40B@7)Ct1N_1MyHR-lQv0781=8<-FbelQ;s4Gk5aB;Y`Cq2|_hdnT`|4l83FiEt z24|C+Y{Hm0M$>-DS0)F4+GBwa%J!5`UuQ4I_GiM8;AkpHpOi_S1+TW+j=Xz39q&4^ z9fU&Lcl5d8r}OzXw}+4S>Fr3oX*yPMUH_LKrjZr~&T-~#$RGF{7EEl9$OqneOmg2^ zFh%xHZ_S?$9ArN2CR$(kFs%U+`GjJ7gOyZ$`{j`=;mE`VaDWQ z#BnN%irrktC)ZPV>Y%;>F_}m#`ds6Y9Lgl~R|NXEaKazorcyk>*B^JG#$kN+;#l*% zeO!K0mAr%?@@u4V0IGrBE4(DNPZhGBr|YCc)fdOc;$d`FXEnMrCP_%!Ufk2Rsx3MK zuDIoPOtDU|*rU6~4$UvE+Lz@h#pn%=yx{ox$FW*xackVy`cWrkn>=5Fb?H%zMsmy* z(CH$n($a#Oe!NI1lj!K+UK@+7#|F; z+L&A%^qe*)V{$6_D=%Zq;l|mD+Al@!aU~~2rrZ$i&#uD83tq0Th6BRA#$p=EHSH7j zRTxX!rIX*LDIy0D(M_<6(rG?&$A}wTJiR*@vOB@yEA{{ zDuPYq*poMBzU6?JM2B6hM-tDKphCIXbvY-+x|FKoNB_Z?#{Tt{))4_!w^^2ez}uxX z;&)2PT`7@m_7tP`5zNB_lr#yN$SwwwG*m(1b^CMm-kRvQ8+ur5u8BX%xq5s3C2tw9 z<4~lY3Sn*fOY7FTtis%^G^cN%3$=Y+$~{%y-rHia~>W;Lv+OKH~qF6gH$dA7oqdV z7-bE_!atWrXqwqo$j{#P*sA`*AZ6wudXG$lnMd9GHGA?EnvvnVAh128Ly;Yx&yfW;@$bDp)7rImAASz}l{*>7VSGM;1b1kEa7xGxc zH}k98TuU#p2&8H?)Z&`QO(I;RNSF*03Tcs5B}tXK(tFecU_L+TW$E;P*JV0GZi1#+ z{i}Vp4Wo-SRR6ehp;USs?3mmaX;;kR-}g~L<4ur=eV~YZ4n6KzJ!@!BS$G?J_22@Q zWANrll;tG9f_!7`XP31P7Bw2@5QcsG^^ zRESFqGE!}zC>ly08pUALqP|sY8(adex}ClB-qYI=3npY5y*B2A(PnRmfue`yBp< zHY~G2bnPvScltAPA3`XKBi)^d@UpYpFOpwy1y%Mw!+X|+_w;RPcNk{gYUPH$(-2kv z_V&eY&NSoj(QMjEk={3U3L_`yviF4!KT+ZffDj_;XzGsh&&Hg+uzaPr_q?r`M{$2^ z^*d&!^@mf+JC}k{?O8h*G+InLJ-YTg(XY{#!O`&!^a1wD=6W>a&-8Y4kj92)P$Q@& zy7QdgnVB>1CP-X1$YKww9uJhK|B8v-XV7qN@%r{ADDCynCwaXY;J5CsJ!dQM5{Ps1 zQt8+h-`9$-{fbnQE5Fp2I=7GL{u=0TW1;6>(p+_%pc-dK7#R|57EGElKS;?X5&sT|V|QJI_zW6$Ik!1V;BYA*nR@ z7qUN|qq*7oUNDY_ycp+E5xuF|^RQFIy(1_9&E(Hk&rJABlvzZgHomuSnZLZOb|L3J zCZ*y<2rlzkrC-A)`#uai@tyQLiv0=J35&Lt)p+y zEM}Py8{?pxOoP%mV0o&wc~A_tn3=pKt^vKT3^SU>P~rO>d`qB?%+xL7)z~|(e+OaE z-+P7s6osLH_#a>x1lfxKl>a*%hD!ed;(vB09BdRI=q?D@o`Ap{J2LI)~<_y@>ds6ja=&6F7i7v`X+aVl}on_60(hC1)EK-cG2A1|wUf#oY!EE_5PbckXX%*A? 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+\thispagestyle{empty} + +\newcommand{\gfrac}[2]{\displaystyle \frac{#1}{#2}} + +\newpage + +\chapter{I moti principali della fisica} + +\section{Moto rettilineo uniforme (m.u.a.)} + +Conoscendo le definizioni di accelerazione ($\vec{a} = \frac{d\vec{v}}{dt}$) +e di velocità ($\vec{v} = \frac{d\vec{x}}{dt}$) è possibile, ponendo l'accelerazione +costante (i.e. il \textit{jerk} è nullo, $\frac{d\vec{a}}{dt} = 0$), ricavare numerose formule. + +\subsection{Le equazioni del moto in un sistema di riferimento unidimensionale} + +Le equazioni del moto sono le seguenti: + +\begin{equation} + \begin{cases} + x(t)=x_0+v_0t+\frac{1}{2}a_0t^2 \\ + v(t)=v_0+at + \end{cases} +\end{equation} + +\begin{proof} + Da $a=\frac{dv}{dt}$, si ricava $dv=a\cdot dt$, da cui: + + \begin{equation*} + \int dv=\int a\, dt = a \int dt \Rightarrow v=v_0+at + \end{equation*} + + Dimostrata questa prima equazione, è possibile dimostrare in modo analogo l'altra: + + \begin{equation*} + \int dx=\int v\cdot dt = \int v_0\, dt + \int at\, dt = x_0+v_0t+\frac12at^2 + \end{equation*} + + La dimostrazione può essere inoltre resa immediata se si sviluppano $x(t)$ e + $v(t)$ come serie di Taylor-Maclaurin. + +\end{proof} + +\subsection{Lo spostamento in funzione della velocità e dell'accelerazione} + +Senza ricorrere alla variabile di tempo $t$, è possibile +esprimere lo spostamento in funzione della velocità e dell'accelerazione +mediante le seguente formula: + +\begin{equation} + x-x_0=\frac{v^2-v_0^2}{2a} +\end{equation} + +\begin{proof} + + Considerando $a=\frac{dv}{dt}$, è possibile riscrivere mediante l'impiego + delle formule di derivazione delle funzioni composte quest'ultima formula in + + \begin{equation*} + a=\frac{dv}{dt}=\frac{dx}{dt}\frac{dv}{dx}=v\,\frac{dv}{dx} + \end{equation*} + + Da ciò si può ricavare infine l'ultima formula: + + \begin{equation*} + a\,dx=v\,dv \Rightarrow a \int dx = \int v \, dv + \end{equation*} + + E quindi: + + \begin{equation*} + a(x-x_0)=\frac{v^2-v_0^2}{2} \Rightarrow x-x_0=\frac{v^2-v_0^2}{2a} + \end{equation*} + +\end{proof} + + +\end{document} \ No newline at end of file diff --git a/docs/index.html b/index.html similarity index 100% rename from docs/index.html rename to index.html