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2018/2019.")),Object(le.h)(je,null,Object(le.h)("h2",null,Object(le.h)("a",{href:"/vldigeometria"},"Videolezioni di Geometria")),Object(le.h)("p",null,"Ottime videolezioni di Geometria con licenza ",Object(le.h)("a",{href:"https://creativecommons.org/licenses/by-nc-sa/4.0/"},"CC BY-NC-SA 4.0")," che ho trovato sul ",Object(le.h)("a",{href:"https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0"},"portale Dolly 2018")," dell'",Object(le.h)("a",{href:"https://www.unimore.it/"},"Unimore"),".")),Object(le.h)(je,null,Object(le.h)("h2",null,Object(le.h)("a",{href:"/mingwinstall"},"Come installare MinGW")),Object(le.h)("p",null,"Un breve tutorial con immagini su come installare e configurare ",Object(le.h)("a",{href:"https://it.wikipedia.org/wiki/MinGW"},"MinGW")," per compilare programmi C e C++ su Windows."))),Object(le.h)("h2",null,"Altre collegamenti utili"),Object(le.h)(ye,null,Object(le.h)(je,null,Object(le.h)("h2",null,Object(le.h)("a",{href:"https://t.me/unimoreinfo"},"@unimoreinfo")),Object(le.h)("p",null,"Il gruppo ",Object(le.h)("a",{href:"https://telegram.org/"},"Telegram")," del corso di Informatica dell'Unimore!")),Object(le.h)(je,null,Object(le.h)("h2",null,Object(le.h)("a",{href:"https://calendar.google.com/calendar?cid=MmYza2o2M3VuZWQ1cmZqaGpmOGY0MWFrNmdAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ"},"Calendario Lezioni")),Object(le.h)("p",null,"Calendario Google ",Object(le.h)("small",null,"quasi")," sempre aggiornato delle lezioni e degli esami del secondo anno dell'",Object(le.h)("a",{href:"https://www.unimore.it/"},"Unimore")," durante l'Anno Accademico 2019/2020.")),Object(le.h)(je,null,Object(le.h)("h2",null,Object(le.h)("a",{href:"http://erre2.fermitech.info/dashboard"},"Erre2")),Object(le.h)("p",null,"Portale contenente appunti e riassunti mantenuto da ",Object(le.h)("a",{href:"https://github.com/LBindustries"},"Lorenzo Balugani"),".")),Object(le.h)(je,null,Object(le.h)("h2",null,Object(le.h)("a",{href:"https://github.com/vezzalinistefano/Appunti-Algoritmi"},"vezzalinistefano/Appunti-Algoritmi")),Object(le.h)("p",null,"Appunti di Algoritmi e Strutture Dati mantenuti da ",Object(le.h)("a",{href:"https://github.com/vezzalinistefano/"},"Vezzalini Stefano"),".")))),xe=function(e){function t(){return E(this,t),A(this,e.apply(this,arguments))}return M(t,e),t.prototype.render=function(){return Ce},t}(le.Component),Se=(n("0lnO"),n("+uq9")),Ee=n.n(Se),Ae=function(e){function t(){return L(this,t),T(this,e.apply(this,arguments))}return I(t,e),t.prototype.render=function(){var e="{\\color{White} "+this.props.children+" }";return Object(le.h)("img",{src:"https://latex.codecogs.com/png.latex?"+e,alt:this.props.children,title:this.props.children,class:Ee.a.latex})},t}(le.Component),Me=n("ddTt"),Le=n.n(Me),Te=function(e){function t(){return D(this,t),B(this,e.apply(this,arguments))}return 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(\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)"]),Ue=H(["\vec{v} cdot \vec{w} = left | \vec{v} \right | left | \vec{w} \right | cos alpha"],["\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha"]),Ve=H(["\vec{a}"],["\\vec{a}"]),We=H(["\vec{b}"],["\\vec{b}"]),$e=H(["\vec{c} = \vec{a} \times \vec{b}"],["\\vec{c} = \\vec{a} \\times \\vec{b}"]),Ge=H(["left | \vec{c} \right | = left | \vec{a} \right | cdot left | \vec{b} \right | cdot sin(alpha)"],["\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)"]),Ke=H(["Sigma \vec{F} = 0 Longleftrightarrow Delta v = 0"],["\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0"]),Ze=H(["Sigma \vec{F} = m \vec{a}"],["\\Sigma \\vec{F} = m \\vec{a}"]),Ye=H(["\vec{F}_{21} = -\vec{F}_{12}"],["\\vec{F}_{21} = -\\vec{F}_{12}"]),Qe=H(["left | \vec{F} \right | = G \frac{m_1 m_2}{s^2}"],["\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}"]),Xe=H(["G = 6.67 cdot 10^{-11} \frac{N m^2}{{kg}^2}"],["G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}"]),Je=H(["left | \vec{F} \right | = g m"],["\\left | \\vec{F} \\right | = g m"]),et=H(["g = 9.81 \frac{m}{s^2}"],["g = 9.81 \\frac{m}{s^2}"]),tt=H(["g_{luna} = 1.62 \frac{m}{s^2}"],["g_{luna} = 1.62 \\frac{m}{s^2}"]),nt=H(["g_{marte} = 3.71 \frac{m}{s^2}"],["g_{marte} = 3.71 \\frac{m}{s^2}"]),rt=H(["left | \vec{F} \right | leq mu_{s} left | \vec{F}_{normale} \right |"],["\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |"]),at=H(["left | \vec{F} \right | leq mu_{d} left | \vec{F}_{normale} \right |"],["\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |"]),ot=H(["F = -k x"],["F = -k x"]),it=H(["Delta \vec{s} = \vec{s}(fine) - \vec{s}(inizio)"],["\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)"]),lt=H(["\vec{v} = \frac{Delta \vec{s}}{Delta t}"],["\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}"]),ct=H(["\vec{v} = lim_{Delta t \to 0} \frac{Delta \vec{s}}{Delta t} = \frac{d \vec{s}}{dt}"],["\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}"]),st=H(["\vec{a} = \frac{Delta \vec{v}}{Delta t}"],["\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}"]),ut=H(["\vec{a} = lim_{Delta v \to 0} \frac{Delta \vec{v}}{Delta t} = \frac{d \vec{v}}{d t} = \frac{d^2 \vec{s}}{d t^2}"],["\\vec{a} = \\lim_{\\Delta v \\to 0} \\frac{\\Delta \\vec{v}}{\\Delta t} = \\frac{d \\vec{v}}{d t} = \\frac{d^2 \\vec{s}}{d t^2}"]),ht=H(["\vec{p} = m \vec{v}"],["\\vec{p} = m \\vec{v}"]),pt=H(["Sigma \vec{F} = 0 Longleftrightarrow Delta \vec{p} = 0"],["\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0"]),dt=H(["s(t) = v cdot Delta t + s(0)"],["s(t) = v \\cdot \\Delta t + s(0)"]),bt=H(["v(t) = k"],["v(t) = k"]),ft=H(["a(t) = 0"],["a(t) = 0"]),mt=H(["s(t) = \frac{1}{2} a cdot (Delta t)^2 + v(0) cdot (Delta t) + s(0)"],["s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)"]),gt=H(["v(t) = a Delta t + v(0)"],["v(t) = a \\Delta t + v(0)"]),_t=H(["a(t) = k"],["a(t) = k"]),vt=H(["omega = \frac{2 pi}{T}"],["\\omega = \\frac{2 \\pi}{T}"]),jt=H(["s(t) = A sin (omega cdot t + phi)"],["s(t) = A \\sin (\\omega \\cdot t + \\phi)"]),wt=H(["\frac{pi}{2}"],["\\frac{\\pi}{2}"]),Ot=H(["v(t) = A sin (omega cdot t + phi + \frac{pi}{2})"],["v(t) = A \\sin (\\omega \\cdot t + \\phi + \\frac{\\pi}{2})"]),yt=H(["pi"],["\\pi"]),kt=H(["a(t) = A sin (omega cdot t + phi + pi)"],["a(t) = A \\sin (\\omega \\cdot t + \\phi + \\pi)"]),zt=H(["phi"],["\\phi"]),Pt=H(["v = \frac{Delta s}{t} = \frac{2 pi cdot r}{T} = omega r"],["v = \\frac{\\Delta s}{t} = \\frac{2 \\pi \\cdot r}{T} = \\omega r"]),Ct=H(["a = \frac{v^2}{r} = r cdot omega^2 = v cdot omega"],["a = \\frac{v^2}{r} = r \\cdot \\omega^2 = v \\cdot \\omega"]),xt=H(["F = m cdot a"],["F = m \\cdot a"]),St=H(["W = \vec{F} cdot \vec{s} = F cdot Delta s cdot cos(alpha )"],["W = \\vec{F} \\cdot \\vec{s} = F \\cdot 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I"]),en=H(["R"],["R"]),tn=H(["Omega"],["\\Omega"]),nn=H(["R = \rho \frac{L_{unghezza}}{A_{rea}}"],["R = \\rho \\frac{L_{unghezza}}{A_{rea}}"]),rn=H(["\rho"],["\\rho"]),an=H(["\rho = \rho_0 (1 + alpha(T - T_0))"],["\\rho = \\rho_0 (1 + \\alpha(T - T_0))"]),on=H(["C = \frac{q_{massima}}{Delta V}"],["C = \\frac{q_{massima}}{\\Delta V}"]),ln=H(["C_{nuova} = kappa cdot \frac{epsilon_0 cdot A}{s}"],["C_{nuova} = \\kappa \\cdot \\frac{\\epsilon_0 \\cdot A}{s}"]),cn=H(["kappa"],["\\kappa"]),sn=H(["d"],["d"]),un=H(["Fa"],["Fa"]),hn=H(["R_{serie} = sum_{i=1}^{n} R_i"],["R_{serie} = \\sum_{i=1}^{n} R_i"]),pn=H(["R_{parallelo} = \frac{1}{sum_{i=1}^{n} \frac{1}{R_i}}"],["R_{parallelo} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{R_i}}"]),dn=H(["C_{serie} = \frac{1}{sum_{i=1}^{n} \frac{1}{C_i}}"],["C_{serie} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{C_i}}"]),bn=H(["C_{parallelo} = sum_{i=1}^{n} C_n"],["C_{parallelo} = \\sum_{i=1}^{n} C_n"]),fn=H(["mu_0 = 4 pi cdot 10^{-7} \frac{H}{m}"],["\\mu_0 = 4 \\pi \\cdot 10^{-7} \\frac{H}{m}"]),mn=H(["\frac{N}{A^2}"],["\\frac{N}{A^2}"]),gn=H(["B"],["B"]),_n=H(["Phi_B"],["\\Phi_B"]),vn=H(["Wb = T cdot m^2"],["Wb = T \\cdot m^2"]),jn=H(["\vec{F}_{magnetica} = q cdot (\vec{v} \times \vec{B})"],["\\vec{F}_{magnetica} = q \\cdot (\\vec{v} \\times \\vec{B})"]),wn=H(["\vec{B}"],["\\vec{B}"]),On=H(["\vec{v}"],["\\vec{v}"]),yn=H(["\vec{F}_{magnetica} = I cdot (\vec{L} \times \vec{B})"],["\\vec{F}_{magnetica} = I \\cdot (\\vec{L} \\times \\vec{B})"]),kn=H(["\vec{L}"],["\\vec{L}"]),zn=H(["left | \vec{B} \right | = mu_0 cdot I cdot \frac{A_{vvolgimenti}}{L_{unghezzafilo}}"],["\\left | \\vec{B} \\right | = \\mu_0 \\cdot I \\cdot \\frac{A_{vvolgimenti}}{L_{unghezzafilo}}"]),Pn=H(["left | \vec{B} \right | = \frac{mu cdot I}{2 pi r}"],["\\left | \\vec{B} \\right | = \\frac{\\mu \\cdot I}{2 \\pi r}"]),Cn=H(["Delta V_{indotta} = v cdot B cdot L"],["\\Delta V_{indotta} = v \\cdot B \\cdot L"]),xn=H(["Phi_B = \vec{B} cdot \vec{A} = B cdot A cdot cos(alpha)"],["\\Phi_B = \\vec{B} \\cdot \\vec{A} = B \\cdot A \\cdot \\cos(\\alpha)"]),Sn=String.raw,En=Object(le.h)("h1",null,"Fisica"),An=Object(le.h)("h2",null,"Vettori"),Mn=Object(le.h)("h3",null,"Componenti cartesiane"),Ln=Object(le.h)("p",null,"Usa le regole base della trigonometria:"),Tn=Object(le.h)("h3",null,"Somma"),In=Object(le.h)("p",null,"Scomponi in componenti, poi sommali:"),Dn=Object(le.h)("p",null,"Produce il vettore risultante dall'applicazione della regola del parallelogramma."),Bn=Object(le.h)("h3",null,"Differenza"),qn=Object(le.h)("p",null,"Alla fine è sempre una somma:"),Fn=Object(le.h)("p",null,"Produce il vettore che parte da ",Object(le.h)(Ae,null,"w")," e arriva a ",Object(le.h)(Ae,null,"v"),"."),Nn=Object(le.h)("h3",null,"Prodotto scalare"),Rn=Object(le.h)("p",null,"Si chiama scalare perchè il risultato è uno scalare, non un vettore."),Hn=Object(le.h)("h3",null,"Prodotto vettoriale"),Un=Object(le.h)("p",null,"Si chiama vettoriale perchè il risultato è un altro vettore."),Vn=Object(le.h)("li",null,Object(le.h)("a",{href:"https://it.wikipedia.org/wiki/Regola_della_mano_destra"},"Regola della mano destra")),Wn=Object(le.h)("p",null,"Non è commutativo!"),$n=Object(le.h)("h2",null,"Leggi di Newton"),Gn=Object(le.h)("h3",null,"1ᵃ: Inerzia"),Kn=Object(le.h)("p",null,"Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia."),Zn=Object(le.h)("h3",null,"2ᵃ: Proporzionalità"),Yn=Object(le.h)("p",null,"La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la ",Object(le.h)("i",null,"massa"),"."),Qn=Object(le.h)("h3",null,"3ᵃ: Azione e reazione"),Xn=Object(le.h)("p",null,"Due corpi esercitano forze uguali e opposte uno sull'altro."),Jn=Object(le.h)("h2",null,"Forza di gravità"),er=Object(le.h)("h3",null,"Tra due corpi"),tr=Object(le.h)("p",null,"Due corpi puntiformi si attirano uno verso l'altro con forza:"),nr=Object(le.h)("p",null,Object(le.h)(Ae,null,"G")," è la ",Object(le.h)("i",null,"costante di gravitazione universale")," e vale:"),rr=Object(le.h)("h3",null,"Verso la Terra"),ar=Object(le.h)("p",null,"Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza ",Object(le.h)("i",null,"peso")," uguale a:"),or=Object(le.h)("p",null,Object(le.h)(Ae,null,"g")," è la ",Object(le.h)("i",null,"costante di gravità")," della Terra, e vale:"),ir=Object(le.h)("h3",null,"Su pianeti diversi"),lr=Object(le.h)("p",null,"Per pianeti diversi dalla Terra vale la stessa regola:"),cr=Object(le.h)("p",null,"L'unica differenza è che cambia la ",Object(le.h)("i",null,"costante di gravità"),":"),sr=Object(le.h)("h2",null,"Forze di contatto"),ur=Object(le.h)(je,null,Object(le.h)("h3",null,"Normale"),Object(le.h)("p",null,"Si oppone alle forze applicate alla superficie di contatto."),Object(le.h)("p",null,"Un libro appoggiato su un tavolo ha la ",Object(le.h)("b",null,"forza di gravità")," che lo attira verso il terreno e la ",Object(le.h)("b",null,"forza normale")," che lo trattiene dal cadere.")),hr=Object(le.h)("h3",null,"Attrito statico"),pr=Object(le.h)("p",null,"Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:"),dr=Object(le.h)("h3",null,"Attrito dinamico"),br=Object(le.h)("p",null,"Rallenta i corpi che si stanno muovendo finchè essi non si fermano:"),fr=Object(le.h)(je,null,Object(le.h)("h3",null,"Tensione"),Object(le.h)("p",null,"E' forza trasmessa tra due estremi di una fune."),Object(le.h)("p",null,"Può essere redirezionata per mezzo di carrucole.")),mr=Object(le.h)("h3",null,"Elastica"),gr=Object(le.h)("p",null,"Una molla cerca sempre di tornare alla sua posizione indeformata con forza:"),_r=Object(le.h)("p",null,"(E' negativa perchè la forza è opposta a quella applicata per deformarla.)"),vr=Object(le.h)("h2",null,"Cinematica"),jr=Object(le.h)("h3",null,"Spostamento"),wr=Object(le.h)("p",null,"È un vettore che indica la posizione di un corpo rispetto a un'origine."),Or=Object(le.h)("h3",null,"Velocità"),yr=Object(le.h)("p",null,"È un vettore che misura la variazione di posizione nel tempo."),kr=Object(le.h)("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",Object(le.h)("i",null,"velocità istantanea"),":"),zr=Object(le.h)("h3",null,"Accelerazione"),Pr=Object(le.h)("p",null,"È un vettore che misura la variazione di velocità nel tempo."),Cr=Object(le.h)("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",Object(le.h)("i",null,"accelerazione istantanea"),":"),xr=Object(le.h)("h3",null,"Quantità di moto ",Object(le.h)("small",null,"(momento lineare)")),Sr=Object(le.h)("p",null,"La quantità di moto è una proprietà vettoriale dei corpi:"),Er=Object(le.h)("p",null,"Se la forza risultante è nulla, la quantità di moto non cambia."),Ar=Object(le.h)("h2",null,"Moto rettilineo uniforme"),Mr=Object(le.h)("h3",null,"Spostamento"),Lr=Object(le.h)("p",null,"La ",Object(le.h)("i",null,"legge oraria")," è:"),Tr=Object(le.h)("h3",null,"Velocità"),Ir=Object(le.h)("p",null,"È costante:"),Dr=Object(le.h)("h3",null,"Accelerazione"),Br=Object(le.h)("p",null,"La velocità non varia:"),qr=Object(le.h)(je,null,Object(le.h)("h3",null,"Forze"),Object(le.h)("p",null,"Si applica la prima legge di Newton:"),Object(le.h)("p",null,Object(le.h)(Ae,null,"f(t) = 0"))),Fr=Object(le.h)("h2",null,"Moto rettilineo uniformemente accelerato"),Nr=Object(le.h)("h3",null,"Spostamento"),Rr=Object(le.h)("p",null,"La ",Object(le.h)("i",null,"legge oraria")," è:"),Hr=Object(le.h)("h3",null,"Velocità"),Ur=Object(le.h)("p",null,"È una retta:"),Vr=Object(le.h)("h3",null,"Accelerazione"),Wr=Object(le.h)("p",null,"È costante:"),$r=Object(le.h)(je,null,Object(le.h)("h3",null,"Forze"),Object(le.h)("p",null,"Si applica la prima legge di Newton:"),Object(le.h)("p",null,Object(le.h)(Ae,null,"f(t) = m a"))),Gr=Object(le.h)("h2",null,"Moto armonico semplice"),Kr=Object(le.h)(je,null,Object(le.h)("h3",null,"Ampiezza"),Object(le.h)("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),Object(le.h)("p",null,"(L'ampiezza di una sinusoide.)")),Zr=Object(le.h)("h3",null,"Velocità angolare"),Yr=Object(le.h)("p",null,"Indica quanto in fretta cambia la posizione del corpo."),Qr=Object(le.h)("p",null,"Dipende dal periodo:"),Xr=Object(le.h)("h3",null,"Spostamento"),Jr=Object(le.h)("p",null,"E' una sinusoide:"),ea=Object(le.h)("h3",null,"Velocità"),ta=Object(le.h)("h3",null,"Accelerazione"),na=Object(le.h)(je,null,Object(le.h)("h3",null,"Forze"),Object(le.h)("p",null,"Si applica la prima legge di Newton:"),Object(le.h)("p",null,Object(le.h)(Ae,null,"f(t) = m a"))),ra=Object(le.h)("h2",null,"Moti composti"),aa=Object(le.h)(je,null,Object(le.h)("h3",null,"Moto parabolico"),Object(le.h)("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),oa=Object(le.h)("h3",null,"Moto circolare uniforme"),ia=Object(le.h)("h2",null,"Moto circolare uniforme"),la=Object(le.h)("h3",null,"Velocità angolare"),ca=Object(le.h)("p",null,"Quanto cambia la fase nel tempo."),sa=Object(le.h)("h3",null,"Fase"),ua=Object(le.h)("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),ha=Object(le.h)("h3",null,"Velocità"),pa=Object(le.h)("p",null,"Si applicano le formule per la circonferenza:"),da=Object(le.h)("h3",null,"Accelerazione"),ba=Object(le.h)("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),fa=Object(le.h)("h3",null,"Forza centripeta"),ma=Object(le.h)("p",null,"È verso il centro e si calcola con:"),ga=Object(le.h)("h2",null,"Lavoro ed energia"),_a=Object(le.h)("h3",null,"Lavoro"),va=Object(le.h)("p",null,"E' compiuto da una forza che sposta un corpo."),ja=Object(le.h)("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)"),wa=Object(le.h)("h3",null,"Energia cinetica"),Oa=Object(le.h)("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),ya=Object(le.h)("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),ka=Object(le.h)("h3",null,"Energia potenziale gravitazionale"),za=Object(le.h)("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),Pa=Object(le.h)("p",null,"(Con ",Object(le.h)(Ae,null,"h")," uguale a un altezza scelta come punto di riferimento.)"),Ca=Object(le.h)("h3",null,"Energia potenziale elastica"),xa=Object(le.h)("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),Sa=Object(le.h)("h3",null,"Forze conservative"),Ea=Object(le.h)("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),Aa=Object(le.h)("p",null,"Ad esempio, è conservativa la ",Object(le.h)("i",null,"forza di gravità"),", ma ",Object(le.h)("b",null,"non")," è conservativa la forza di attrito."),Ma=Object(le.h)("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),La=Object(le.h)("h3",null,"Potenza"),Ta=Object(le.h)("p",null,"È la velocità di trasferimento di energia:"),Ia=Object(le.h)("h2",null,"Elettrostatica"),Da=Object(le.h)("h3",null,"Carica elettrica"),Ba=Object(le.h)("p",null,"È una proprietà dei corpi che può essere ",Object(le.h)(Te,null,"positiva")," o ",Object(le.h)(Be,null,"negativa"),"."),qa=Object(le.h)("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),Fa=Object(le.h)("p",null,"Cariche ",Object(le.h)(Te,null,"opp"),Object(le.h)(Be,null,"oste")," si attraggono; cariche ",Object(le.h)(Te,null,"uguali")," si respingono."),Na=Object(le.h)(je,null,Object(le.h)("h3",null,"Conduttori e isolanti"),Object(le.h)("p",null,"Più ",Object(le.h)("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),Object(le.h)("p",null,"I corpi in cui la carica si muove bene sono ",Object(le.h)("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",Object(le.h)("i",null,"isolanti"),"."),Object(le.h)("p",null,"Il corpo umano è un buon conduttore.")),Ra=Object(le.h)("h2",null,"Polarizzazione"),Ha=Object(le.h)(ye,null,Object(le.h)(je,null,Object(le.h)("h3",null,"Polarizzazione"),Object(le.h)("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),Ua=Object(le.h)(ye,null,Object(le.h)(je,null,Object(le.h)("h3",null,"Messa a terra"),Object(le.h)("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",Object(le.h)("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",Object(le.h)(Te,null,"cariche positive")," e ",Object(le.h)(Be,null,"negative")," all'interno)."))),Va=Object(le.h)(ye,null,Object(le.h)(je,null,Object(le.h)("h3",null,"Polarizzazione per strofinio"),Object(le.h)("p",null,"Strofinando tra loro due corpi isolanti, essi si ",Object(le.h)("i",null,"polarizzeranno per strofinio"),".")),Object(le.h)(je,null,Object(le.h)("h3",null,"Polarizzazione per contatto"),Object(le.h)("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",Object(le.h)("i",null,"polarizzarsi per contatto"),".")),Object(le.h)(je,null,Object(le.h)("h3",null,"Polarizzazione per induzione"),Object(le.h)("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',Object(le.h)(Te,null,"certo segno")," vicino, esso avrà tutte le cariche del ",Object(le.h)(Be,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",Object(le.h)(Te,null,"stesso segno")," più lontano possibile da esse."),Object(le.h)("p",null,"Mettendo a terra il conduttore, nuove cariche del ",Object(le.h)(Be,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),Object(le.h)("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",Object(le.h)(Be,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),Wa=Object(le.h)("h2",null,"Forza elettrica"),$a=Object(le.h)("h3",null,"Legge di Coulomb"),Ga=Object(le.h)("p",null,"Due corpi carichi si attraggono tra loro con forza:"),Ka=Object(le.h)("i",null,"costante di Coulomb"),Za=Object(le.h)("h3",null,"Permeabilità dello spazio vuoto"),Ya=Object(le.h)("i",null,"permeabilità del vuoto"),Qa=Object(le.h)("h3",null,"Campo elettrico"),Xa=Object(le.h)("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),Ja=Object(le.h)("h3",null,"Flusso elettrico"),eo=Object(le.h)("p",null,'È la differenza tra "quanto" campo elettrico ',Object(le.h)(Te,null,"entra")," e quanto campo elettrico ",Object(le.h)(Be,null,"esce")," da una certa area."),to=Object(le.h)("p",null,"È proporzionale alla intensità del campo, alla dimensione dell'area scelta e a come l'area è disposta rispetto alla direzione del campo."),no=Object(le.h)("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),ro=Object(le.h)("h3",null,"Legge di Gauss"),ao=Object(le.h)("p",null,"Il flusso elettrico uscente da una superficie è proporzionale alla carica presente al suo interno."),oo=Object(le.h)("p",null,"E' equivalente alla Legge di Coulomb."),io=Object(le.h)("h2",null,"Energia elettrica"),lo=Object(le.h)("h3",null,"Energia potenziale elettrica"),co=Object(le.h)("i",null,"energia potenziale elettrica"),so=Object(le.h)("h2",null,"Circuiti elettrici"),uo=Object(le.h)("h3",null,"Potenziale elettrico (Tensione)"),ho=Object(le.h)("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),po=Object(le.h)("p",null,"In una batteria è detto ",Object(le.h)("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli."),bo=Object(le.h)("h3",null,"Corrente elettrica (Intensità)"),fo=Object(le.h)("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),mo=Object(le.h)("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),go=Object(le.h)(je,null,Object(le.h)("h3",null,"Corrente continua (",Object(le.h)("abbr",{title:"Direct Current"},"DC"),")"),Object(le.h)("p",null,"Quando in un circuito la direzione della corrente è costante.")),_o=Object(le.h)(je,null,Object(le.h)("h3",null,"Corrente alternata (",Object(le.h)("abbr",{title:"Alternate Current"},"AC"),")"),Object(le.h)("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),vo=Object(le.h)("h3",null,"Potenza elettrica"),jo=Object(le.h)("p",null,"Possiamo calcolare la potenza di un circuito:"),wo=Object(le.h)("h2",null,"Elementi di un circuito"),Oo=Object(le.h)("h3",null,"Resistore"),yo=Object(le.h)("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),ko=Object(le.h)("p",null,"Il potenziale utilizzato è pari a:"),zo=Object(le.h)("i",null,"resistenza"),Po=Object(le.h)("p",null,"La resistenza di un conduttore vale:"),Co=Object(le.h)("i",null,"resistività"),xo=Object(le.h)("h3",null,"Condensatore"),So=Object(le.h)("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),Eo=Object(le.h)("p",null,"Per farlo, cattura cariche ",Object(le.h)(Te,null,"positive")," e ",Object(le.h)(Be,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),Ao=Object(le.h)("p",null,"Ha una ",Object(le.h)("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),Mo=Object(le.h)("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),Lo=Object(le.h)("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),To=Object(le.h)("i",null,"costante dielettrica relativa"),Io=Object(le.h)("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",Object(le.h)("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",Object(le.h)("i",null,"breakdown"),"."),Do=Object(le.h)(je,null,Object(le.h)("h3",null,"Amperometro"),Object(le.h)("p",null,"Misura la corrente elettrica se messo in serie."),Object(le.h)("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),Bo=Object(le.h)(je,null,Object(le.h)("h3",null,"Voltmetro"),Object(le.h)("p",null,"Misura la differenza di potenziale se messo in parallelo."),Object(le.h)("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)")),qo=Object(le.h)("h2",null,"Principi di Kirchhoff"),Fo=Object(le.h)(ye,null,Object(le.h)(je,null,Object(le.h)("h3",null,"Legge dei nodi"),Object(le.h)("p",null,"Per nodo si intende un qualsiasi punto del circuito."),Object(le.h)("p",null,"Da un nodo entra ed esce la stessa corrente.")),Object(le.h)(je,null,Object(le.h)("h3",null,"Legge delle maglie"),Object(le.h)("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),Object(le.h)("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),No=Object(le.h)("h2",null,"Serie e Parallelo"),Ro=Object(le.h)(ye,null,Object(le.h)(je,null,Object(le.h)("h3",null,"Circuito in serie"),Object(le.h)("p",null,"Più parti di circuito sono ",Object(le.h)("i",null,"in serie")," se sono consecutive e senza biforcazioni."),Object(le.h)("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),Object(le.h)(je,null,Object(le.h)("h3",null,"Circuito in parallelo"),Object(le.h)("p",null,"Più parti di circuito sono ",Object(le.h)("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),Object(le.h)("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),Ho=Object(le.h)("h2",null,"Resistenze equivalenti"),Uo=Object(le.h)("h3",null,"Circuiti in serie"),Vo=Object(le.h)("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dal valore della somma di tutte le quelle sostituite:"),Wo=Object(le.h)("h3",null,"Circuiti in parallelo"),$o=Object(le.h)("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dal valore di:"),Go=Object(le.h)("h2",null,"Condensatori equivalenti"),Ko=Object(le.h)("h3",null,"Circuiti in serie"),Zo=Object(le.h)("p",null,"Nei circuiti in serie, tutte i condensatori possono essere sostituiti con uno equivalente dal valore di:"),Yo=Object(le.h)("h3",null,"Circuiti in parallelo"),Qo=Object(le.h)("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dal valore della somma della capacità di tutti quelli sostituiti:"),Xo=Object(le.h)("h2",null,"Magnetismo"),Jo=Object(le.h)("h3",null,"Permeabilità magnetica dello spazio vuoto"),ei=Object(le.h)("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),ti=Object(le.h)("h3",null,"Campo magnetico"),ni=Object(le.h)("p",null,"Come un campo elettrico, ma per i magneti."),ri=Object(le.h)(Ae,null,"T"),ai=Object(le.h)("h3",null,"Flusso magnetico"),oi=Object(le.h)("p",null,"Come il flusso elettrico, ma per campi magnetici."),ii=Object(le.h)(je,null,Object(le.h)("h3",null,"Legge di Gauss per il magnetismo"),Object(le.h)("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo.")),li=Object(le.h)("h2",null,"Forze magnetiche"),ci=Object(le.h)("h3",null,"Forza magnetica su carica puntiforme ",Object(le.h)("small",null,"(Forza di Lorentz)")),si=Object(le.h)("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),ui=Object(le.h)("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),hi=Object(le.h)("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme."),pi=Object(le.h)("h3",null,"Forza magnetica in un filo"),di=Object(le.h)("p",null,"I campi magnetici influenzano anche le cariche presenti in un conduttore:"),bi=Object(le.h)("p",null,Object(le.h)(Pe,null,"Modulo di L?")),fi=Object(le.h)("h2",null,"Campi magnetici"),mi=Object(le.h)(je,null,Object(le.h)("h3",null,"Campo magnetico in una spira"),Object(le.h)("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),gi=Object(le.h)("h3",null,"Campo magnetico di un solenoide"),_i=Object(le.h)("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),vi=Object(le.h)("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),ji=Object(le.h)("h3",null,"Legge di Oersted"),wi=Object(le.h)("p",null,Object(le.h)("i",null,"Caso particolare della ",Object(le.h)("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),Oi=Object(le.h)("p",null,"Il modulo del campo magnetico ",Object(le.h)(Ae,null,"B")," prodotto da un filo in cui passa una corrente continua ",Object(le.h)(Ae,null,"I")," alla distanza ",Object(le.h)(Ae,null,"s")," è:"),yi=Object(le.h)("p",null,Object(le.h)(Pe,null,"Verso di B?")),ki=Object(le.h)("h2",null,"Induzione elettromagnetica"),zi=Object(le.h)("h3",null,"Forza elettromotrice indotta"),Pi=Object(le.h)("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),Ci=Object(le.h)("p",null,"La differenza di potenziale si crea a 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[Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\n11. [Proprietà delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\n13. [Proprietà e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\n20. [Teorema diagonalizzabilità](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\n23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)\n24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)\n25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)\n26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)\n27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\n\nNell'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\n                    "],["\nTutte le videolezioni sono state pubblicate sotto licenza [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) dalla Prof.ssa Beatrice Ruini nell'anno accademico 2018/2019 sul [portale Dolly 2018](https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0) (Moodle).\n\nPer comodità, ho estratto l'url sorgente del video dall'embed presente nella rispettiva pagina.\n\n1. [Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\n11. [Proprietà delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\n13. [Proprietà e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\n20. [Teorema diagonalizzabilità](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\n23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)\n24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)\n25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)\n26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)\n27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\n\nNell'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\n                    "]),qi=String.raw,Fi=Object(le.h)("h1",null,"Videolezioni di Geometria"),Ni=function(e){function t(){return Z(this,t),Y(this,e.apply(this,arguments))}return Q(t,e),t.prototype.render=function(){return Object(le.h)("div",null,Fi,Object(le.h)(je,null,Object(le.h)(Di,null,qi(Bi))))},t}(le.Component),Ri=(String,Object(le.h)("div",null,Object(le.h)("h1",null,"Come installare MinGW"),Object(le.h)(je,null,Object(le.h)("p",null," Scaricate ",Object(le.h)("a",{href:"https://osdn.net/projects/mingw/downloads/68260/mingw-get-setup.exe/"},"l'installer ufficiale"),", ed eseguitelo."),Object(le.h)("img",{src:"https://i.imgur.com/mDZSqjV.png"}),Object(le.h)("p",null," Dovrebbe comparire questa schermata. 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