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\n

Fisica

\n

Vettori

\n \n \n

\n Componenti cartesiane\n

\n

\n Usa le regole base della trigonometria:\n

\n

\n {r`\\vec{v} = \\vec{v}_x + \\vec{v}_y`}\n

\n

\n {r`\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha`}\n

\n

\n {r`\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha`}\n

\n \n \n

\n Somma\n

\n

\n Scomponi in componenti, poi sommali:\n

\n

\n {r`\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)`}\n

\n

\n Produce il vettore risultante dall'applicazione della regola del parallelogramma.\n

\n \n \n

\n Differenza\n

\n

\n Alla fine è sempre una somma:\n

\n

\n {r`\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)`}\n

\n

\n Produce il vettore che parte da w e arriva a v.\n

\n \n \n

\n Prodotto scalare\n

\n

\n Si chiama scalare perchè il risultato è uno scalare, non un vettore.\n

\n

\n {r`\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha`}\n

\n

\n Produce il modulo della proiezione di {r`\\vec{a}`} su {r`\\vec{b}`}.\n

\n \n \n

\n Leggi di Newton\n

\n \n \n

\n 1ᵃ: Inerzia\n

\n

\n Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia.\n

\n

\n {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0`}\n

\n \n \n

\n 2ᵃ: Proporzionalità\n

\n

\n La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la massa.\n

\n

\n {r`\\Sigma \\vec{F} = m \\vec{a}`}\n

\n \n \n

\n 3ᵃ: Azione e reazione\n

\n

\n Due corpi esercitano forze uguali e opposte uno sull'altro. \n

\n

\n {r`\\vec{F}_{21} = -\\vec{F}_{12}`}\n

\n \n \n

\n Forza di gravità\n

\n \n \n

\n Tra due corpi\n

\n

\n Due corpi puntiformi si attirano uno verso l'altro con forza:\n

\n

\n {r`\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}`}\n

\n

\n G è la costante di gravitazione universale e vale:\n

\n

\n {r`G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}`}\n

\n \n \n

\n Verso la Terra\n

\n

\n Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza peso uguale a:\n

\n

\n {r`\\left | \\vec{F} \\right | = g m`}\n

\n

\n g è la costante di gravità della Terra, e vale:\n

\n

\n {r`g = 9.81 \\frac{m}{s^2}`}\n

\n \n \n

\n Su pianeti diversi\n

\n

\n Per pianeti diversi dalla Terra vale la stessa regola:\n

\n

\n {r`\\left | \\vec{F} \\right | = g m`}\n

\n

\n L'unica differenza è che cambia la costante di gravità:\n

\n

\n {r`g_{luna} = 1.62 \\frac{m}{s^2}`}\n

\n

\n {r`g_{marte} = 3.71 \\frac{m}{s^2}`}\n

\n \n \n

\n Forze di contatto\n

\n \n \n

\n Normale\n

\n

\n Si oppone alle forze applicate alla superficie di contatto.\n

\n

\n Un libro appoggiato su un tavolo ha la forza di gravità che lo attira verso il terreno e la forza normale che lo trattiene dal cadere. \n

\n \n \n

\n Attrito statico\n

\n

\n Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:\n

\n

\n {r`\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |`}\n

\n \n \n

\n Attrito dinamico\n

\n

\n Rallenta i corpi che si stanno muovendo finchè essi non si fermano:\n

\n

\n {r`\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |`}\n

\n \n \n

\n Tensione\n

\n

\n E' forza trasmessa tra due estremi di una fune.\n

\n

\n Può essere redirezionata per mezzo di carrucole.\n

\n \n \n

\n Elastica\n

\n

\n Una molla cerca sempre di tornare alla sua posizione indeformata con forza:\n

\n

\n {r`F = -k x`}\n

\n

\n (E' negativa perchè la forza è opposta a quella applicata per deformarla.)\n

\n \n \n

\n Cinematica\n

\n \n \n

\n Spostamento\n

\n

\n È un vettore che indica la posizione di un corpo rispetto a un'origine.\n

\n

\n {r`\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)`}\n

\n \n \n

\n Velocità\n

\n

\n È un vettore che misura la variazione di posizione nel tempo.\n

\n

\n {r`\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}`}\n

\n

\n Se si considera un intervallo di tempo infinitesimale si dice velocità istantanea:\n

\n

\n {r`\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}`}\n

\n \n \n

\n Accelerazione\n

\n

\n È un vettore che misura la variazione di velocità nel tempo.\n

\n

\n {r`\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}`}\n

\n

\n Se si considera un intervallo di tempo infinitesimale si dice accelerazione istantanea:\n

\n

\n {r`\\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}`}\n

\n \n \n

\n Quantità di moto (momento lineare)\n

\n

\n La quantità di moto è una proprietà vettoriale dei corpi:\n

\n

\n {r`\\vec{p} = m \\vec{v}`}\n

\n

\n Se la forza risultante è nulla, la quantità di moto non cambia.\n

\n

\n {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0`}\n

\n \n \n

\n Moto rettilineo uniforme\n

\n \n \n

\n Spostamento\n

\n

\n La legge oraria è:\n

\n

\n {r`s(t) = v \\cdot \\Delta t + s(0)`}\n

\n \n \n

\n Velocità\n

\n

\n È costante:\n

\n

\n {r`v(t) = k`}\n

\n \n \n

\n Accelerazione\n

\n

\n La velocità non varia:\n

\n

\n {r`a(t) = 0`}\n

\n \n \n

\n Forze\n

\n

\n Si applica la prima legge di Newton:\n

\n

\n f(t) = 0\n

\n \n \n

\n Moto rettilineo uniformemente accelerato\n

\n \n \n

\n Spostamento\n

\n

\n La legge oraria è:\n

\n

\n {r`s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)`}\n

\n \n \n

\n Velocità\n

\n

\n È una retta:\n

\n

\n {r`v(t) = a \\Delta t + v(0)`}\n

\n \n \n

\n Accelerazione\n

\n

\n È costante:\n

\n

\n {r`a(t) = k`}\n

\n \n \n

\n Forze\n

\n

\n Si applica la prima legge di Newton:\n

\n

\n f(t) = m a\n

\n \n \n

\n Moto armonico semplice\n

\n \n \n

\n Ampiezza\n

\n

\n E' la distanza dal centro massima che raggiunge il corpo.\n

\n

\n (L'ampiezza di una sinusoide.)\n

\n \n \n

\n Velocità angolare\n

\n

\n Indica quanto in fretta cambia la posizione del corpo. \n

\n

\n Dipende dal periodo:\n

\n

\n {r`\\omega = \\frac{2 \\pi}{T}`}\n

\n \n \n

\n Spostamento\n

\n

\n E' una sinusoide:\n

\n

\n {r`s(t) = A \\sin (\\omega \\cdot t + \\phi)`}\n

\n \n \n

\n Velocità\n

\n

\n E' la sinusoide dello spostamento, sfasata di {r`\\frac{\\pi}{2}`}:\n

\n

\n {r`s(t) = A \\sin (\\omega \\cdot t + \\phi + \\frac{\\pi}{2})`}\n

\n \n \n

\n Accelerazione\n

\n

\n E' la sinusoide della velocità, sfasata di {r`\\frac{\\pi}{2}`}:\n

\n

\n {r`s(t) = A \\sin (\\omega \\cdot t + \\phi + \\pi)`}\n

\n \n \n

\n Forze\n

\n

\n Si applica la prima legge di Newton:\n

\n

\n f(t) = m a\n

\n \n \n

\n Moti composti\n

\n \n \n

\n Moto parabolico\n

\n

\n Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.\n

\n \n \n

\n Moto circolare uniforme\n

\n

\n Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di {r`\\frac{\\pi}{2}`}, sull'asse Y.\n

\n \n \n

\n Moto circolare uniforme\n

\n \n \n

\n Velocità angolare\n

\n

\n Quanto cambia la fase nel tempo.\n

\n

\n {r`\\omega = \\frac{2 \\pi}{T}`}\n

\n \n \n

\n Fase\n

\n

\n E' l'angolo percorso dal corpo rispetto alla posizione iniziale.\n

\n

\n Si indica con {r`\\phi`}, e generalmente si usa in radianti.\n

\n \n \n

\n Velocità\n

\n

\n Si applicano le formule per la circonferenza:\n

\n

\n {r`v = \\frac{\\Delta s}{t} = \\frac{2 \\pi \\cdot r}{T}`}\n

\n \n \n

\n Accelerazione\n

\n

\n Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto: \n

\n

\n {r`a = \\frac{v^2}{r} = r \\cdot \\omega^2 = v \\cdot \\omega`}\n

\n \n \n

\n Forza centripeta\n

\n

\n È verso il centro e si calcola con:\n

\n

\n {r`F = m \\cdot a`}\n

\n \n \n

\n Lavoro ed energia\n

\n \n \n

\n Lavoro\n

\n

\n E' compiuto da una forza che sposta un corpo.\n

\n

\n {r`W = \\vec{F} \\cdot \\vec{s} = F \\cdot \\Delta s \\cdot cos(\\alpha )`}\n

\n

\n (Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)\n

\n \n \n

\n Energia cinetica\n

\n

\n Un corpo ha energia cinetica in ogni momento uguale a:\n

\n

\n {r`E_c = \\frac{1}{2} m v^2`}\n

\n

\n Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:\n

\n

\n {r`\\Delta E_c = W`}\n

\n \n \n

\n Energia potenziale gravitazionale\n

\n

\n Un corpo ha energia potenziale in ogni momento pari a: \n

\n

\n {r`E_{p_g} = m \\cdot g \\cdot h`}\n

\n

\n (Con h uguale a un altezza scelta come punto di riferimento.)\n

\n \n \n

\n Energia potenziale elastica\n

\n

\n Una molla ha sempre energia potenziale elastica pari a:\n

\n

\n {r`E_{p_e} = \\frac{1}{2} k x^2`}\n

\n \n \n

\n Forze conservative\n

\n

\n Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo.\n

\n

\n Ad esempio, è conservativa la forza di gravità, ma non è conservativa la forza di attrito.\n

\n

\n Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:\n

\n

\n {r`E = E_k + E_p`}\n

\n \n \n

\n Potenza\n

\n

\n È la velocità di trasferimento di energia:\n

\n

\n {r`P = \\frac{\\Delta E}{\\Delta t}`}\n

\n \n \n
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\n\t\t);\n\t}\n}\n\n\n\n// WEBPACK FOOTER //\n// ./index.js","!function(){\"use strict\";function e(e,t){var n,o,r,i,l=W;for(i=arguments.length;i-- >2;)P.push(arguments[i]);t&&null!=t.children&&(P.length||P.push(t.children),delete t.children);while(P.length)if((o=P.pop())&&void 0!==o.pop)for(i=o.length;i--;)P.push(o[i]);else\"boolean\"==typeof o&&(o=null),(r=\"function\"!=typeof e)&&(null==o?o=\"\":\"number\"==typeof o?o+=\"\":\"string\"!=typeof o&&(r=!1)),r&&n?l[l.length-1]+=o:l===W?l=[o]:l.push(o),n=r;var a=new T;return a.nodeName=e,a.children=l,a.attributes=null==t?void 0:t,a.key=null==t?void 0:t.key,void 0!==M.vnode&&M.vnode(a),a}function t(e,t){for(var n in t)e[n]=t[n];return e}function n(e,t){e&&(\"function\"==typeof e?e(t):e.current=t)}function o(n,o){return e(n.nodeName,t(t({},n.attributes),o),arguments.length>2?[].slice.call(arguments,2):n.children)}function r(e){!e.__d&&(e.__d=!0)&&1==V.push(e)&&(M.debounceRendering||D)(i)}function i(){var e;while(e=V.pop())e.__d&&x(e)}function l(e,t,n){return\"string\"==typeof t||\"number\"==typeof t?void 0!==e.splitText:\"string\"==typeof t.nodeName?!e._componentConstructor&&a(e,t.nodeName):n||e._componentConstructor===t.nodeName}function a(e,t){return e.__n===t||e.nodeName.toLowerCase()===t.toLowerCase()}function u(e){var n=t({},e.attributes);n.children=e.children;var o=e.nodeName.defaultProps;if(void 0!==o)for(var r in o)void 0===n[r]&&(n[r]=o[r]);return n}function c(e,t){var n=t?document.createElementNS(\"http://www.w3.org/2000/svg\",e):document.createElement(e);return n.__n=e,n}function p(e){var t=e.parentNode;t&&t.removeChild(e)}function s(e,t,o,r,i){if(\"className\"===t&&(t=\"class\"),\"key\"===t);else if(\"ref\"===t)n(o,null),n(r,e);else if(\"class\"!==t||i)if(\"style\"===t){if(r&&\"string\"!=typeof r&&\"string\"!=typeof o||(e.style.cssText=r||\"\"),r&&\"object\"==typeof r){if(\"string\"!=typeof o)for(var l in o)l in r||(e.style[l]=\"\");for(var l in r)e.style[l]=\"number\"==typeof r[l]&&!1===E.test(l)?r[l]+\"px\":r[l]}}else if(\"dangerouslySetInnerHTML\"===t)r&&(e.innerHTML=r.__html||\"\");else if(\"o\"==t[0]&&\"n\"==t[1]){var a=t!==(t=t.replace(/Capture$/,\"\"));t=t.toLowerCase().substring(2),r?o||e.addEventListener(t,_,a):e.removeEventListener(t,_,a),(e.__l||(e.__l={}))[t]=r}else if(\"list\"!==t&&\"type\"!==t&&!i&&t in e){try{e[t]=null==r?\"\":r}catch(e){}null!=r&&!1!==r||\"spellcheck\"==t||e.removeAttribute(t)}else{var u=i&&t!==(t=t.replace(/^xlink:?/,\"\"));null==r||!1===r?u?e.removeAttributeNS(\"http://www.w3.org/1999/xlink\",t.toLowerCase()):e.removeAttribute(t):\"function\"!=typeof r&&(u?e.setAttributeNS(\"http://www.w3.org/1999/xlink\",t.toLowerCase(),r):e.setAttribute(t,r))}else e.className=r||\"\"}function _(e){return this.__l[e.type](M.event&&M.event(e)||e)}function f(){var e;while(e=A.shift())M.afterMount&&M.afterMount(e),e.componentDidMount&&e.componentDidMount()}function d(e,t,n,o,r,i){H++||(R=null!=r&&void 0!==r.ownerSVGElement,B=null!=e&&!(\"__preactattr_\"in e));var l=h(e,t,n,o,i);return r&&l.parentNode!==r&&r.appendChild(l),--H||(B=!1,i||f()),l}function h(e,t,n,o,r){var i=e,l=R;if(null!=t&&\"boolean\"!=typeof t||(t=\"\"),\"string\"==typeof t||\"number\"==typeof t)return e&&void 0!==e.splitText&&e.parentNode&&(!e._component||r)?e.nodeValue!=t&&(e.nodeValue=t):(i=document.createTextNode(t),e&&(e.parentNode&&e.parentNode.replaceChild(i,e),v(e,!0))),i.__preactattr_=!0,i;var u=t.nodeName;if(\"function\"==typeof u)return N(e,t,n,o);if(R=\"svg\"===u||\"foreignObject\"!==u&&R,u+=\"\",(!e||!a(e,u))&&(i=c(u,R),e)){while(e.firstChild)i.appendChild(e.firstChild);e.parentNode&&e.parentNode.replaceChild(i,e),v(e,!0)}var p=i.firstChild,s=i.__preactattr_,_=t.children;if(null==s){s=i.__preactattr_={};for(var f=i.attributes,d=f.length;d--;)s[f[d].name]=f[d].value}return!B&&_&&1===_.length&&\"string\"==typeof _[0]&&null!=p&&void 0!==p.splitText&&null==p.nextSibling?p.nodeValue!=_[0]&&(p.nodeValue=_[0]):(_&&_.length||null!=p)&&m(i,_,n,o,B||null!=s.dangerouslySetInnerHTML),y(i,t.attributes,s),R=l,i}function m(e,t,n,o,r){var i,a,u,c,s,_=e.childNodes,f=[],d={},m=0,b=0,y=_.length,g=0,w=t?t.length:0;if(0!==y)for(var C=0;C