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class="vector-toc-numb">2</span> <span>Lever History</span> </div> </a> <ul id="toc-Lever_History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Force_and_levers" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Force_and_levers"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Force and levers</span> </div> </a> <ul id="toc-Force_and_levers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Types_of_levers" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Types_of_levers"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Types of levers</span> </div> </a> <ul id="toc-Types_of_levers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Compound_lever" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Compound_lever"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Compound lever</span> </div> </a> <ul id="toc-Compound_lever-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Law_of_the_lever" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Law_of_the_lever"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Law of the lever</span> </div> </a> <ul id="toc-Law_of_the_lever-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Virtual_work_and_the_law_of_the_lever" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Virtual_work_and_the_law_of_the_lever"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Virtual work and the law of the lever</span> </div> </a> <ul id="toc-Virtual_work_and_the_law_of_the_lever-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Lever</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 97 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-97" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">97 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Hefboom" title="Hefboom – Afrikaans" lang="af" hreflang="af" data-title="Hefboom" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Hebel_(Physik)" title="Hebel (Physik) – Alemannic" lang="gsw" hreflang="gsw" data-title="Hebel (Physik)" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%98%E1%8D%88%E1%8A%95%E1%89%85%E1%88%8D" title="መፈንቅል – Amharic" lang="am" hreflang="am" data-title="መፈንቅል" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%89%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A5%8B%E0%A4%B2%E0%A4%95" title="उत्तोलक – Angika" lang="anp" hreflang="anp" data-title="उत्तोलक" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D8%A7%D9%81%D8%B9%D8%A9" title="رافعة – Arabic" lang="ar" hreflang="ar" data-title="رافعة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Palanca" title="Palanca – Aragonese" lang="an" hreflang="an" data-title="Palanca" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Palanca" title="Palanca – Asturian" lang="ast" hreflang="ast" data-title="Palanca" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Ling" title="Ling – Azerbaijani" lang="az" hreflang="az" data-title="Ling" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B2%E0%A6%BF%E0%A6%AD%E0%A6%BE%E0%A6%B0_(%E0%A6%AF%E0%A6%A8%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A6%B0)" title="লিভার (যন্ত্র) – Bangla" lang="bn" hreflang="bn" data-title="লিভার (যন্ত্র)" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A0%D1%8B%D1%87%D0%B0%D0%B3" title="Рычаг – Belarusian" lang="be" hreflang="be" data-title="Рычаг" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A0%D1%8B%D1%87%D0%B0%D0%B3" title="Рычаг – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Рычаг" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9B%D0%BE%D1%81%D1%82" title="Лост – Bulgarian" lang="bg" hreflang="bg" data-title="Лост" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Poluga" title="Poluga – Bosnian" lang="bs" hreflang="bs" data-title="Poluga" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Palanca" title="Palanca – Catalan" lang="ca" hreflang="ca" data-title="Palanca" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D3%B3%D1%81%D0%B5%D0%BA" title="Кӳсек – Chuvash" lang="cv" hreflang="cv" data-title="Кӳсек" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/P%C3%A1ka" title="Páka – Czech" lang="cs" hreflang="cs" data-title="Páka" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Trosol" title="Trosol – Welsh" lang="cy" hreflang="cy" data-title="Trosol" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/V%C3%A6gtstangsprincip" title="Vægtstangsprincip – Danish" lang="da" hreflang="da" data-title="Vægtstangsprincip" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Hebel_(Physik)" title="Hebel (Physik) – German" lang="de" hreflang="de" data-title="Hebel (Physik)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kang" title="Kang – Estonian" lang="et" hreflang="et" data-title="Kang" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%BF%CF%87%CE%BB%CF%8C%CF%82" title="Μοχλός – Greek" lang="el" hreflang="el" data-title="Μοχλός" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Palanca" title="Palanca – Spanish" lang="es" hreflang="es" data-title="Palanca" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Levilo" title="Levilo – Esperanto" lang="eo" hreflang="eo" data-title="Levilo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Palanka" title="Palanka – Basque" lang="eu" hreflang="eu" data-title="Palanka" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%87%D8%B1%D9%85" title="اهرم – Persian" lang="fa" hreflang="fa" data-title="اهرم" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Levier_(m%C3%A9canique)" title="Levier (mécanique) – French" lang="fr" hreflang="fr" data-title="Levier (mécanique)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Luamh%C3%A1n" title="Luamhán – Irish" lang="ga" hreflang="ga" data-title="Luamhán" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Panca" title="Panca – Galician" lang="gl" hreflang="gl" data-title="Panca" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A7%80%EB%A0%88" title="지레 – Korean" lang="ko" hreflang="ko" data-title="지레" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BC%D5%AE%D5%A1%D5%AF" title="Լծակ – Armenian" lang="hy" hreflang="hy" data-title="Լծակ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%89%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A5%8B%E0%A4%B2%E0%A4%95" title="उत्तोलक – Hindi" lang="hi" hreflang="hi" data-title="उत्तोलक" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Poluga" title="Poluga – Croatian" lang="hr" hreflang="hr" data-title="Poluga" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Levero" title="Levero – Ido" lang="io" hreflang="io" data-title="Levero" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Tuas" title="Tuas – Indonesian" lang="id" hreflang="id" data-title="Tuas" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Vogarst%C3%B6ng" title="Vogarstöng – Icelandic" lang="is" hreflang="is" data-title="Vogarstöng" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Leva_(fisica)" title="Leva (fisica) – Italian" lang="it" hreflang="it" data-title="Leva (fisica)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A0%D7%95%D7%A3_(%D7%9E%D7%9B%D7%A0%D7%99%D7%A7%D7%94)" title="מנוף (מכניקה) – Hebrew" lang="he" hreflang="he" data-title="מנוף (מכניקה)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AE%E0%B3%80%E0%B2%9F%E0%B3%81%E0%B2%97%E0%B3%8B%E0%B2%B2%E0%B3%81" title="ಮೀಟುಗೋಲು – Kannada" lang="kn" hreflang="kn" data-title="ಮೀಟುಗೋಲು" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%91%E1%83%94%E1%83%A0%E1%83%99%E1%83%94%E1%83%A2%E1%83%98" title="ბერკეტი – Georgian" lang="ka" hreflang="ka" data-title="ბერკეტი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%98%D1%96%D0%BD%D1%82%D1%96%D1%80%D0%B5%D0%BA" title="Иінтірек – Kazakh" lang="kk" hreflang="kk" data-title="Иінтірек" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Kolpes" title="Kolpes – Cornish" lang="kw" hreflang="kw" data-title="Kolpes" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Wenzo" title="Wenzo – Swahili" lang="sw" hreflang="sw" data-title="Wenzo" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Levye" title="Levye – Haitian Creole" lang="ht" hreflang="ht" data-title="Levye" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A0%D1%8B%D1%87%D0%B0%D0%B3" title="Рычаг – Kyrgyz" lang="ky" hreflang="ky" data-title="Рычаг" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Vectis" title="Vectis – Latin" lang="la" hreflang="la" data-title="Vectis" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Svira" title="Svira – Latvian" lang="lv" hreflang="lv" data-title="Svira" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Svertas" title="Svertas – Lithuanian" lang="lt" hreflang="lt" data-title="Svertas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Leva_(fixica)" title="Leva (fixica) – Ligurian" lang="lij" hreflang="lij" data-title="Leva (fixica)" data-language-autonym="Ligure" data-language-local-name="Ligurian" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/vraga" title="vraga – Lojban" lang="jbo" hreflang="jbo" data-title="vraga" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Emel%C5%91" title="Emelő – Hungarian" lang="hu" hreflang="hu" data-title="Emelő" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9B%D0%BE%D1%81%D1%82" title="Лост – Macedonian" lang="mk" hreflang="mk" data-title="Лост" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%89%E0%B4%A4%E0%B5%8D%E0%B4%A4%E0%B5%8B%E0%B4%B2%E0%B4%95%E0%B4%82" title="ഉത്തോലകം – Malayalam" lang="ml" hreflang="ml" data-title="ഉത്തോലകം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tuas" title="Tuas – Malay" lang="ms" hreflang="ms" data-title="Tuas" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hefboom" title="Hefboom – Dutch" lang="nl" hreflang="nl" data-title="Hefboom" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%89%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A5%8B%E0%A4%B2%E0%A4%95" title="उत्तोलक – Nepali" lang="ne" hreflang="ne" data-title="उत्तोलक" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%A5%E0%A4%BF%E0%A4%81%E0%A4%AD%E0%A4%83" title="थिँभः – Newari" lang="new" hreflang="new" data-title="थिँभः" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%81%A6%E3%81%93" title="てこ – Japanese" lang="ja" hreflang="ja" data-title="てこ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%97%D0%B5%D1%80%D0%B0%D0%B7%D0%B0%D0%BA%D1%8A" title="Зеразакъ – Chechen" lang="ce" hreflang="ce" data-title="Зеразакъ" data-language-autonym="Нохчийн" data-language-local-name="Chechen" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Heebelreegel" title="Heebelreegel – Northern Frisian" lang="frr" hreflang="frr" data-title="Heebelreegel" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Vektstang" title="Vektstang – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Vektstang" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Vektstong" title="Vektstong – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Vektstong" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Aigre" title="Aigre – Occitan" lang="oc" hreflang="oc" data-title="Aigre" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Fonqolcha" title="Fonqolcha – Oromo" lang="om" hreflang="om" data-title="Fonqolcha" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Richag" title="Richag – Uzbek" lang="uz" hreflang="uz" data-title="Richag" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Liiva" title="Liiva – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Liiva" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Leva" title="Leva – Piedmontese" lang="pms" hreflang="pms" data-title="Leva" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/D%C5%BAwignia" title="Dźwignia – Polish" lang="pl" hreflang="pl" data-title="Dźwignia" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Alavanca" title="Alavanca – Portuguese" lang="pt" hreflang="pt" data-title="Alavanca" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/P%C3%A2rghie" title="Pârghie – Romanian" lang="ro" hreflang="ro" data-title="Pârghie" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Wanqhana" title="Wanqhana – Quechua" lang="qu" hreflang="qu" data-title="Wanqhana" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D1%8B%D1%87%D0%B0%D0%B3" title="Рычаг – Russian" lang="ru" hreflang="ru" data-title="Рычаг" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A2%D3%A9%D2%BB%D2%AF%D2%AF" title="Төһүү – Yakut" lang="sah" hreflang="sah" data-title="Төһүү" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Llozi" title="Llozi – Albanian" lang="sq" hreflang="sq" data-title="Llozi" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Lever" title="Lever – Simple English" lang="en-simple" hreflang="en-simple" data-title="Lever" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/P%C3%A1ka" title="Páka – Slovak" lang="sk" hreflang="sk" data-title="Páka" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Vzvod" title="Vzvod – Slovenian" lang="sl" hreflang="sl" data-title="Vzvod" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%86%D9%88%DB%8E%DA%B5" title="نوێڵ – Central Kurdish" lang="ckb" hreflang="ckb" data-title="نوێڵ" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D1%83%D0%B3%D0%B0" title="Полуга – Serbian" lang="sr" hreflang="sr" data-title="Полуга" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Poluga" title="Poluga – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Poluga" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Vipu" title="Vipu – Finnish" lang="fi" hreflang="fi" data-title="Vipu" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/H%C3%A4vst%C3%A5ng" title="Hävstång – Swedish" lang="sv" hreflang="sv" data-title="Hävstång" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Dalawit" title="Dalawit – Tagalog" lang="tl" hreflang="tl" data-title="Dalawit" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AF%86%E0%AE%AE%E0%AF%8D%E0%AE%AA%E0%AF%81%E0%AE%95%E0%AF%8B%E0%AE%B2%E0%AF%8D" title="நெம்புகோல் – Tamil" lang="ta" hreflang="ta" data-title="நெம்புகோல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%A4%E0%B1%81%E0%B0%B2%E0%B0%BE%E0%B0%A6%E0%B0%82%E0%B0%A1%E0%B0%AE%E0%B1%81" title="తులాదండము – Telugu" lang="te" hreflang="te" data-title="తులాదండము" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%B2%E0%B8%99_(%E0%B8%81%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C)" title="คาน (กลศาสตร์) – Thai" lang="th" hreflang="th" data-title="คาน (กลศาสตร์)" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kald%C4%B1ra%C3%A7" title="Kaldıraç – Turkish" lang="tr" hreflang="tr" data-title="Kaldıraç" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D0%B0%D0%B6%D1%96%D0%BB%D1%8C" title="Важіль – Ukrainian" lang="uk" hreflang="uk" data-title="Важіль" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%84%DB%8C%D9%88%D8%B1" title="لیور – Urdu" lang="ur" hreflang="ur" data-title="لیور" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Leva" title="Leva – Venetian" lang="vec" hreflang="vec" data-title="Leva" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%C3%B2n_b%E1%BA%A9y" title="Đòn bẩy – Vietnamese" lang="vi" hreflang="vi" data-title="Đòn bẩy" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Dj%C3%AEsse_(lev%C3%AE)" title="Djîsse (levî) – Walloon" lang="wa" hreflang="wa" data-title="Djîsse (levî)" data-language-autonym="Walon" data-language-local-name="Walloon" class="interlanguage-link-target"><span>Walon</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%9D%A0%E6%9D%86" title="杠杆 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="杠杆" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Ligw%C3%A1t" title="Ligwát – Waray" lang="war" hreflang="war" data-title="Ligwát" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%9D%A0%E6%9D%86" title="杠杆 – Wu" lang="wuu" hreflang="wuu" data-title="杠杆" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%A7%93%E6%A1%BF" title="槓桿 – Cantonese" lang="yue" hreflang="yue" data-title="槓桿" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%9D%A0%E6%9D%86" title="杠杆 – Chinese" lang="zh" hreflang="zh" data-title="杠杆" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-bew mw-list-item"><a href="https://bew.wikipedia.org/wiki/Dongk%C3%A8l" title="Dongkèl – Betawi" lang="bew" hreflang="bew" data-title="Dongkèl" data-language-autonym="Betawi" data-language-local-name="Betawi" class="interlanguage-link-target"><span>Betawi</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q40164#sitelinks-wikipedia" title="Edit interlanguage 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data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Simple machine consisting of a beam pivoted at a fixed hinge</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the simple machine. For other uses, see <a href="/wiki/Lever_(disambiguation)" class="mw-disambig" title="Lever (disambiguation)">Lever (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above">Lever</th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Palanca-ejemplo.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Palanca-ejemplo.jpg/220px-Palanca-ejemplo.jpg" decoding="async" width="220" height="99" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Palanca-ejemplo.jpg/330px-Palanca-ejemplo.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Palanca-ejemplo.jpg/440px-Palanca-ejemplo.jpg 2x" data-file-width="888" data-file-height="398" /></a></span><div class="infobox-caption">Levers can be used to exert a large force over a small distance at one end by exerting only a small force (effort) over a greater distance at the other.</div></td></tr><tr><th scope="row" class="infobox-label">Classification</th><td class="infobox-data"><a href="/wiki/Simple_machine" title="Simple machine">Simple machine</a></td></tr><tr><th scope="row" class="infobox-label">Components</th><td class="infobox-data">fulcrum or pivot, load and effort</td></tr><tr><th scope="row" class="infobox-label">Examples</th><td class="infobox-data">see-saw, bottle opener, etc.</td></tr></tbody></table> <p>A <b>lever</b> is a <a href="/wiki/Simple_machine" title="Simple machine">simple machine</a> consisting of a <a href="/wiki/Beam_(structure)" title="Beam (structure)">beam</a> or rigid rod pivoted at a fixed <a href="/wiki/Hinge" title="Hinge">hinge</a>, or <i><a href="https://en.wiktionary.org/wiki/fulcrum" class="extiw" title="wikt:fulcrum">fulcrum</a></i>. A lever is a rigid body capable of <a href="/wiki/Rotating" class="mw-redirect" title="Rotating">rotating</a> on a point on itself. On the basis of the locations of fulcrum, load, and effort, the lever is divided into <a class="mw-selflink-fragment" href="#Types_of_levers">three types</a>. It is one of the six <a href="/wiki/Simple_machine" title="Simple machine">simple machines</a> identified by Renaissance scientists. A lever amplifies an input force to provide a greater output force, which is said to provide <b>leverage</b>, which is <a href="/wiki/Mechanical_advantage" title="Mechanical advantage">mechanical advantage</a> gained in the system, equal to the ratio of the output force to the input force. As such, the lever is a <a href="/wiki/Mechanical_advantage_device" title="Mechanical advantage device">mechanical advantage device</a>, trading off force against movement. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etymology">Etymology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lever&action=edit&section=1" title="Edit section: Etymology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The word "lever" entered <a href="/wiki/English_language" title="English language">English</a> around 1300 from <a href="/wiki/Old_French" title="Old French">Old French</a>: <i lang="fr">levier</i>. This sprang from the stem of the verb <i>lever</i>, meaning "to raise". The verb, in turn, goes back to <a href="/wiki/Latin_language" class="mw-redirect" title="Latin language">Latin</a>: <i lang="la">levare</i>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> itself from the adjective <i>levis</i>, meaning "light" (as in "not heavy"). The word's primary origin is the <a href="/wiki/Proto-Indo-European_language" title="Proto-Indo-European language">Proto-Indo-European</a> stem <span title="uncoded-language text"><i lang="mis">leg<sup>wh</sup>-</i></span>, meaning "light", "easy", or "nimble", among other things. The PIE stem also gave rise to the English-language antonym of "heavy", "light".<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Lever_History">Lever History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lever&action=edit&section=2" title="Edit section: Lever History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Autumn Stanley argues that the <a href="/wiki/Digging_stick" title="Digging stick">digging stick</a> can be considered the first lever, which would position prehistoric women as the inventors of lever technology.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The next earliest known cultural evidence of the application of the lever mechanism dates back to the <a href="/wiki/Ancient_Near_East" title="Ancient Near East">ancient Near East</a> <abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 5000 BC</span>, when it was used in a simple <a href="/wiki/Balance_scale" class="mw-redirect" title="Balance scale">balance scale</a>.<sup id="cite_ref-Paipetis_4-0" class="reference"><a href="#cite_note-Paipetis-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> In <a href="/wiki/Ancient_Egypt" title="Ancient Egypt">ancient Egypt</a> <abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 4400 BC</span>, a foot pedal was used for the earliest horizontal frame <a href="/wiki/Loom" title="Loom">loom</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In <a href="/wiki/Mesopotamia" title="Mesopotamia">Mesopotamia</a> (modern Iraq) <abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 3000 BC</span>, the <a href="/wiki/Shadouf" class="mw-redirect" title="Shadouf">shadouf</a>, a crane-like device that uses a lever mechanism, was invented.<sup id="cite_ref-Paipetis_4-1" class="reference"><a href="#cite_note-Paipetis-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> In <a href="/wiki/Ancient_Egyptian_technology" title="Ancient Egyptian technology">ancient Egypt</a>, workmen used the lever to move and uplift obelisks weighing more than 100 tons. This is evident from the recesses in the large blocks and the <a href="/wiki/Lifting_boss" title="Lifting boss">handling bosses</a> that could not be used for any purpose other than for levers.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>The earliest remaining writings regarding levers date from the third century BC and were provided, by common belief, by the Greek mathematician <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a>, who famously stated "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world". That statement has given rise to the phrase "an Archimedean lever" being adopted for use in many instances, not just regarding mechanics, including abstract concepts about the successful effect of a human behavior or action intended to achieve results that could not have occurred without it.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Force_and_levers">Force and levers</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lever&action=edit&section=3" title="Edit section: Force and levers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Lever_Principle_3D.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Lever_Principle_3D.png/250px-Lever_Principle_3D.png" decoding="async" width="220" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Lever_Principle_3D.png/330px-Lever_Principle_3D.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Lever_Principle_3D.png/500px-Lever_Principle_3D.png 2x" data-file-width="904" data-file-height="514" /></a><figcaption>A lever in balance</figcaption></figure> <p>A lever is a beam connected to ground by a hinge, or pivot, called a fulcrum. The ideal lever does not dissipate or store energy, which means there is no friction in the hinge or bending in the beam. In this case, the power into the lever equals the power out, and the ratio of output to input force is given by the ratio of the distances from the fulcrum to the points of application of these forces. This is known as the <b>law of the lever</b>. </p><p>The mechanical advantage of a lever can be determined by considering the balance of <a href="/wiki/Moment_(physics)" title="Moment (physics)">moments</a> or <a href="/wiki/Torque" title="Torque">torque</a>, <i>T</i>, about the fulcrum. If the distance traveled is greater, then the output force is lessened. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}T_{1}&=F_{1}a,\quad \\T_{2}&=F_{2}b\!\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>a</mi> <mo>,</mo> <mspace width="1em"></mspace> </mtd> </mtr> <mtr> <mtd> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>b</mi> <mspace width="negativethinmathspace"></mspace> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}T_{1}&=F_{1}a,\quad \\T_{2}&=F_{2}b\!\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dffb4ce75a65376d4e5ccdda6a46f7def32e8d7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.01ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}T_{1}&=F_{1}a,\quad \\T_{2}&=F_{2}b\!\end{aligned}}}" /></span> </p><p>where F<sub>1</sub> is the input force to the lever and F<sub>2</sub> is the output force. The distances <i>a</i> and <i>b</i> are the perpendicular distances between the forces and the fulcrum. </p><p>Since the moments of torque must be balanced, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{1}=T_{2}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{1}=T_{2}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c49234dc1d227881d75b0c44f6d7f1ae4e189199" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:7.922ex; height:2.509ex;" alt="{\displaystyle T_{1}=T_{2}\!}" /></span>. So, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{1}a=F_{2}b\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>a</mi> <mo>=</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>b</mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{1}a=F_{2}b\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc34c252fb9baceebcc55019dec09466f9fa5e4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.371ex; width:10.407ex; height:2.509ex;" alt="{\displaystyle F_{1}a=F_{2}b\!}" /></span>. </p><p>The mechanical advantage of a lever is the ratio of output force to input force. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle MA={\frac {F_{2}}{F_{1}}}={\frac {a}{b}}.\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>.</mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MA={\frac {F_{2}}{F_{1}}}={\frac {a}{b}}.\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a940c348bc1d63fe199b2d80488ebe23888d644d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.204ex; width:16.296ex; height:5.509ex;" alt="{\displaystyle MA={\frac {F_{2}}{F_{1}}}={\frac {a}{b}}.\!}" /></span> </p><p>This relationship shows that the mechanical advantage can be computed from ratio of the distances from the fulcrum to where the input and output forces are applied to the lever, assuming a weightless lever and no losses due to friction, flexibility, or wear. This remains true even though the "horizontal" distance (perpendicular to the pull of gravity) of both <i>a</i> and <i>b</i> change (diminish) as the lever changes to any position away from the horizontal. </p> <div class="mw-heading mw-heading2"><h2 id="Types_of_levers">Types of levers</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lever&action=edit&section=4" title="Edit section: Types of levers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Lever_(PSF).png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Lever_%28PSF%29.png/250px-Lever_%28PSF%29.png" decoding="async" width="220" height="203" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Lever_%28PSF%29.png/330px-Lever_%28PSF%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Lever_%28PSF%29.png/500px-Lever_%28PSF%29.png 2x" data-file-width="1028" data-file-height="950" /></a><figcaption>Three classes of levers</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Levers_of_the_Human_Body.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Levers_of_the_Human_Body.svg/220px-Levers_of_the_Human_Body.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Levers_of_the_Human_Body.svg/330px-Levers_of_the_Human_Body.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Levers_of_the_Human_Body.svg/440px-Levers_of_the_Human_Body.svg.png 2x" data-file-width="512" data-file-height="384" /></a><figcaption>The three classifications of levers with examples of the human body</figcaption></figure> <p>Levers are classified by the relative positions of the fulcrum, effort, and resistance (or load). It is common to call the input force "effort" and the output force "load" or "resistance". This allows the identification of three classes of levers by the relative locations of the fulcrum, the resistance and the effort:<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <ul><li><span class="anchor" id="Class_1_lever"></span> <b>Class I</b> – Fulcrum is located between the effort and the resistance: The effort is applied on one side of the fulcrum and the resistance (or load) on the other side. For example, a <a href="/wiki/Seesaw" title="Seesaw">seesaw</a>, a <a href="/wiki/Crowbar_(tool)" class="mw-redirect" title="Crowbar (tool)">crowbar</a>, a pair of <a href="/wiki/Scissors" title="Scissors">scissors</a>, a <a href="/wiki/Balance_scale" class="mw-redirect" title="Balance scale">balance scale</a>, a pair of <a href="/wiki/Pliers" title="Pliers">pliers</a>, and a <a href="/wiki/Claw_hammer" title="Claw hammer">claw hammer</a> (pulling a nail). With the fulcrum in the middle, the lever's mechanical advantage may be greater than, less than, or even equal to 1.</li> <li><span class="anchor" id="Class_2_lever"></span> <b>Class II</b> – Resistance (or load) is located between the effort and the fulcrum: The effort is applied on one side of the resistance and the fulcrum is located on the other side, e.g. a <a href="/wiki/Wheelbarrow" title="Wheelbarrow">wheelbarrow</a>, a <a href="/wiki/Nutcracker" title="Nutcracker">nutcracker</a>, a <a href="/wiki/Bottle_opener" title="Bottle opener">bottle opener</a>, a <a href="/wiki/Wrench" title="Wrench">wrench</a>, a pair of <a href="/wiki/Bellows" title="Bellows">bellows</a>, and the <a href="/wiki/Brake" title="Brake">brake</a> <a href="/wiki/Automobile_pedal" class="mw-redirect" title="Automobile pedal">pedal</a> of a car. Since the load arm is smaller than the effort arm, the lever's mechanical advantage is always greater than 1. It is also called a force multiplier lever.</li> <li><span class="anchor" id="Class_3_lever"></span> <b>Class III</b> – Effort is located between the resistance and the fulcrum: The resistance (or load) is applied on one side of the effort and the fulcrum is located on the other side, e.g. a <a href="/wiki/Hoe_(tool)" title="Hoe (tool)">hoe</a>, a pair of <a href="/wiki/Tweezers" title="Tweezers">tweezers</a>, a <a href="/wiki/Hammer" title="Hammer">hammer</a>, a pair of <a href="/wiki/Tongs" title="Tongs">tongs</a>, a <a href="/wiki/Fishing_rod" title="Fishing rod">fishing rod</a>, and the <a href="/wiki/Mandible" title="Mandible">mandible</a> of a human skull. Since the effort arm is smaller than the load arm, the lever's mechanical advantage is always less than 1. It is also called a speed multiplier lever.</li></ul> <p>These cases are described by the mnemonic <i>fre 123</i> where the <i>f</i> fulcrum is between <i>r</i> and <i>e</i> for the 1st class lever, the <i>r</i> resistance is between <i>f</i> and <i>e</i> for the 2nd class lever, and the <i>e</i> effort is between <i>f</i> and <i>r</i> for the 3rd class lever. </p> <div class="mw-heading mw-heading2"><h2 id="Compound_lever">Compound lever</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lever&action=edit&section=5" title="Edit section: Compound lever"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Compound_lever" title="Compound lever">Compound lever</a></div> <p>A <a href="/wiki/Compound_lever" title="Compound lever">compound lever</a> comprises several levers acting in series: the resistance from one lever in a system of levers acts as effort for the next, and thus the applied force is transferred from one lever to the next. Examples of compound levers include scales, nail clippers, and piano keys. </p><p>The <i><a href="/wiki/Malleus" title="Malleus">malleus</a></i>, <i><a href="/wiki/Incus" title="Incus">incus</a></i>, and <i><a href="/wiki/Stapes" title="Stapes">stapes</a></i> are small bones in the <a href="/wiki/Middle_ear" title="Middle ear">middle ear</a>, connected as compound levers, that transfer sound waves from the <a href="/wiki/Eardrum" title="Eardrum">eardrum</a> to the <a href="/wiki/Oval_window" title="Oval window">oval window</a> of the <a href="/wiki/Cochlea" title="Cochlea">cochlea</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Law_of_the_lever">Law of the lever <span class="anchor" id="Law"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lever&action=edit&section=6" title="Edit section: Law of the lever"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Mechanical_advantage#Lever" title="Mechanical advantage">Mechanical advantage § Lever</a></div> <p>The lever is a movable bar that pivots on a fulcrum attached to a fixed point. The lever operates by applying forces at different distances from the fulcrum, or a pivot. </p><p>As the lever rotates around the fulcrum, points farther from this pivot move faster than points closer to the pivot. Therefore, a force applied to a point farther from the pivot must be less than the force located at a point closer in, because power is the product of force and velocity.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>If <i>a</i> and <i>b</i> are distances from the fulcrum to points <i>A</i> and <i>B</i> and the force <i>F<sub>A</sub></i> applied to <i>A</i> is the input and the force <i>F<sub>B</sub></i> applied at <i>B</i> is the output, the ratio of the velocities of points <i>A</i> and <i>B</i> is given by <i>a/b</i>, so the ratio of the output force to the input force, or mechanical advantage, is given by: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4516522ccaaa831010fc757760110894929d202" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.905ex; height:5.676ex;" alt="{\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}}.}" /></span> </p><p>This is the <i>law of the lever</i>, which was proven by <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> using geometric reasoning.<sup id="cite_ref-Usher1954_10-0" class="reference"><a href="#cite_note-Usher1954-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> It shows that if the distance <i>a</i> from the fulcrum to where the input force is applied (point <i>A</i>) is greater than the distance <i>b</i> from fulcrum to where the output force is applied (point <i>B</i>), then the lever amplifies the input force. On the other hand, if the distance <i>a</i> from the fulcrum to the input force is less than the distance <i>b</i> from the fulcrum to the output force, then the lever reduces the input force. </p><p>The use of velocity in the static analysis of a lever is an application of the principle of <a href="/wiki/Virtual_work#Law_of_the_Lever" title="Virtual work">virtual work</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Virtual_work_and_the_law_of_the_lever">Virtual work and the law of the lever</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lever&action=edit&section=7" title="Edit section: Virtual work and the law of the lever"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A lever is modeled as a rigid bar connected to a ground frame by a hinged joint called a fulcrum. The lever is operated by applying an input force <b>F</b><sub><i>A</i></sub> at a point <i>A</i> located by the coordinate vector <b>r</b><sub><i>A</i></sub> on the bar. The lever then exerts an output force <b>F</b><sub><i>B</i></sub> at the point <i>B</i> located by <b>r</b><sub><i>B</i></sub>. The rotation of the lever about the fulcrum <i>P</i> is defined by the rotation angle <i>θ</i> in radians. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Archimedes_lever_(Small).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Archimedes_lever_%28Small%29.jpg/250px-Archimedes_lever_%28Small%29.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Archimedes_lever_%28Small%29.jpg/330px-Archimedes_lever_%28Small%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Archimedes_lever_%28Small%29.jpg/500px-Archimedes_lever_%28Small%29.jpg 2x" data-file-width="640" data-file-height="427" /></a><figcaption>Archimedes lever, Engraving from <i>Mechanics Magazine</i>, published in London in 1824</figcaption></figure> <p>Let the coordinate vector of the point <i>P</i> that defines the fulcrum be <b>r</b><sub><i>P</i></sub>, and introduce the lengths </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=|\mathbf {r} _{A}-\mathbf {r} _{P}|,\quad b=|\mathbf {r} _{B}-\mathbf {r} _{P}|,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>,</mo> <mspace width="1em"></mspace> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=|\mathbf {r} _{A}-\mathbf {r} _{P}|,\quad b=|\mathbf {r} _{B}-\mathbf {r} _{P}|,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2bc0ad7632446bfdb4a9b80e454422e5b266c8e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.981ex; height:2.843ex;" alt="{\displaystyle a=|\mathbf {r} _{A}-\mathbf {r} _{P}|,\quad b=|\mathbf {r} _{B}-\mathbf {r} _{P}|,}" /></span> </p><p>which are the distances from the fulcrum to the input point <i>A</i> and to the output point <i>B</i>, respectively. </p><p>Now introduce the unit vectors <b>e</b><sub><i>A</i></sub> and <b>e</b><sub><i>B</i></sub> from the fulcrum to the point <i>A</i> and <i>B</i>, so </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {r} _{A}-\mathbf {r} _{P}=a\mathbf {e} _{A},\quad \mathbf {r} _{B}-\mathbf {r} _{P}=b\mathbf {e} _{B}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mi>a</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>,</mo> <mspace width="1em"></mspace> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mi>b</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{A}-\mathbf {r} _{P}=a\mathbf {e} _{A},\quad \mathbf {r} _{B}-\mathbf {r} _{P}=b\mathbf {e} _{B}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1d38f48dbfe59125b440a4aa8f1739c5a828f54" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:33.789ex; height:2.509ex;" alt="{\displaystyle \mathbf {r} _{A}-\mathbf {r} _{P}=a\mathbf {e} _{A},\quad \mathbf {r} _{B}-\mathbf {r} _{P}=b\mathbf {e} _{B}.}" /></span> </p><p>The velocity of the points <i>A</i> and <i>B</i> are obtained as </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {v} _{A}={\dot {\theta }}a\mathbf {e} _{A}^{\perp },\quad \mathbf {v} _{B}={\dot {\theta }}b\mathbf {e} _{B}^{\perp },}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>θ</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mi>a</mi> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> </mrow> </msubsup> <mo>,</mo> <mspace width="1em"></mspace> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>θ</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mi>b</mi> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> </mrow> </msubsup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} _{A}={\dot {\theta }}a\mathbf {e} _{A}^{\perp },\quad \mathbf {v} _{B}={\dot {\theta }}b\mathbf {e} _{B}^{\perp },}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67e232b1ecbab63ceb34a59bd476eb192f971e0f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:26.378ex; height:3.509ex;" alt="{\displaystyle \mathbf {v} _{A}={\dot {\theta }}a\mathbf {e} _{A}^{\perp },\quad \mathbf {v} _{B}={\dot {\theta }}b\mathbf {e} _{B}^{\perp },}" /></span> </p><p>where <b>e</b><sub><i>A</i></sub><sup>⊥</sup> and <b>e</b><sub><i>B</i></sub><sup>⊥</sup> are unit vectors perpendicular to <b>e</b><sub><i>A</i></sub> and <b>e</b><sub><i>B</i></sub>, respectively. </p><p>The angle <i>θ</i> is the <a href="/wiki/Generalized_coordinate" class="mw-redirect" title="Generalized coordinate">generalized coordinate</a> that defines the configuration of the lever, and the <a href="/wiki/Generalized_force" class="mw-redirect" title="Generalized force">generalized force</a> associated with this coordinate is given by </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\theta }=\mathbf {F} _{A}\cdot {\frac {\partial \mathbf {v} _{A}}{\partial {\dot {\theta }}}}-\mathbf {F} _{B}\cdot {\frac {\partial \mathbf {v} _{B}}{\partial {\dot {\theta }}}}=a(\mathbf {F} _{A}\cdot \mathbf {e} _{A}^{\perp })-b(\mathbf {F} _{B}\cdot \mathbf {e} _{B}^{\perp })=aF_{A}-bF_{B},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>θ</mi> <mo>˙</mo> </mover> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>θ</mi> <mo>˙</mo> </mover> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>a</mi> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>⋅</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo>−</mo> <mi>b</mi> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>⋅</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>−</mo> <mi>b</mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\theta }=\mathbf {F} _{A}\cdot {\frac {\partial \mathbf {v} _{A}}{\partial {\dot {\theta }}}}-\mathbf {F} _{B}\cdot {\frac {\partial \mathbf {v} _{B}}{\partial {\dot {\theta }}}}=a(\mathbf {F} _{A}\cdot \mathbf {e} _{A}^{\perp })-b(\mathbf {F} _{B}\cdot \mathbf {e} _{B}^{\perp })=aF_{A}-bF_{B},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cd0dbe294e8ffecdc3537d633b5cd7a37b007f2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:69.851ex; height:6.009ex;" alt="{\displaystyle F_{\theta }=\mathbf {F} _{A}\cdot {\frac {\partial \mathbf {v} _{A}}{\partial {\dot {\theta }}}}-\mathbf {F} _{B}\cdot {\frac {\partial \mathbf {v} _{B}}{\partial {\dot {\theta }}}}=a(\mathbf {F} _{A}\cdot \mathbf {e} _{A}^{\perp })-b(\mathbf {F} _{B}\cdot \mathbf {e} _{B}^{\perp })=aF_{A}-bF_{B},}" /></span> </p><p>where <i>F</i><sub><i>A</i></sub> and <i>F</i><sub><i>B</i></sub> are components of the forces that are perpendicular to the radial segments <i>PA</i> and <i>PB</i>. The principle of <a href="/wiki/Virtual_work" title="Virtual work">virtual work</a> states that at equilibrium the generalized force is zero, that is </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\theta }=aF_{A}-bF_{B}=0.\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> </msub> <mo>=</mo> <mi>a</mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>−</mo> <mi>b</mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mn>0.</mn> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\theta }=aF_{A}-bF_{B}=0.\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6360f0ca624d83eac4e3c4ed234361a5bd5da0f2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:21.893ex; height:2.509ex;" alt="{\displaystyle F_{\theta }=aF_{A}-bF_{B}=0.\,\!}" /></span> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Seesaw1902.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Seesaw1902.jpg/250px-Seesaw1902.jpg" decoding="async" width="220" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Seesaw1902.jpg/330px-Seesaw1902.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Seesaw1902.jpg/500px-Seesaw1902.jpg 2x" data-file-width="640" data-file-height="453" /></a><figcaption>Simple lever, fulcrum, and vertical posts</figcaption></figure> <p>Thus, the ratio of the output force <i>F</i><sub><i>B</i></sub> to the input force <i>F</i><sub><i>A</i></sub> is obtained as </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/475093e00f8cca0f2987e6a73db6b1ff3cd76d29" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.905ex; height:5.676ex;" alt="{\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}},}" /></span> </p><p>which is the <a href="/wiki/Mechanical_advantage" title="Mechanical advantage">mechanical advantage</a> of the lever. </p><p>This equation shows that if the distance <i>a</i> from the fulcrum to the point <i>A</i> where the input force is applied is greater than the distance <i>b</i> from fulcrum to the point <i>B</i> where the output force is applied, then the lever amplifies the input force. If the opposite is true that the distance from the fulcrum to the input point <i>A</i> is less than from the fulcrum to the output point <i>B</i>, then the lever reduces the magnitude of the input force. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lever&action=edit&section=8" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Applied_mechanics" title="Applied mechanics">Applied mechanics</a> – Practical application of mechanics</li> <li><a href="/wiki/Balance_lever_coupling" title="Balance lever coupling">Balance lever coupling</a></li> <li><a href="/wiki/Bascule_(disambiguation)" class="mw-redirect mw-disambig" title="Bascule (disambiguation)">bascule</a></li> <li><a href="/wiki/Linkage_(mechanical)" title="Linkage (mechanical)">Linkage (mechanical)</a> – Assembly of systems connected to manage forces and movement</li> <li><a href="/wiki/Mechanism_(engineering)" title="Mechanism (engineering)">Mechanism (engineering)</a> – Device which converts input forces and motion to output forces and motion</li> <li><a href="/wiki/On_the_Equilibrium_of_Planes" title="On the Equilibrium of Planes">On the Equilibrium of Planes</a> – Mechanical treatise by Archimedes</li> <li><a href="/wiki/Simple_machine" title="Simple machine">Simple machine</a> – Mechanical device that changes the direction or magnitude of a force</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lever&action=edit&section=9" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFChisholm1911" class="citation encyclopaedia cs1"><a href="/wiki/Hugh_Chisholm" title="Hugh Chisholm">Chisholm, Hugh</a>, ed. (1911). <span class="cs1-ws-icon" title="s:1911 Encyclopædia Britannica/Lever"><a class="external text" href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Lever">"Lever" </a></span>. <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i>. Vol. 16 (11th ed.). Cambridge University Press. p. 510.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Lever&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=510&rft.edition=11th&rft.pub=Cambridge+University+Press&rft.date=1911&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALever" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.etymonline.com/index.php?term=lever">"Etymology of the word "lever" in the Online Etymological"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150512104818/http://www.etymonline.com/index.php?term=lever">Archived</a> from the original on 2015-05-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-04-29</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Etymology+of+the+word+%22lever%22+in+the+Online+Etymological&rft_id=http%3A%2F%2Fwww.etymonline.com%2Findex.php%3Fterm%3Dlever&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALever" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFStanley1983" class="citation book cs1">Stanley, Autumn (1983). "<span class="cs1-kern-left"></span>"Women Hold Up Two-Thirds of the Sky: Notes for a Revised History of Technology."<span class="cs1-kern-right"></span>". In Rothschild, Joan (ed.). <i>Machina Ex Dea: Feminist Perspectives on Technology</i>. Pergamon Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=%22Women+Hold+Up+Two-Thirds+of+the+Sky%3A+Notes+for+a+Revised+History+of+Technology.%22&rft.btitle=Machina+Ex+Dea%3A+Feminist+Perspectives+on+Technology&rft.pub=Pergamon+Press&rft.date=1983&rft.aulast=Stanley&rft.aufirst=Autumn&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALever" class="Z3988"></span></span> </li> <li id="cite_note-Paipetis-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Paipetis_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Paipetis_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPaipetisCeccarelli2010" class="citation book cs1">Paipetis, S. A.; Ceccarelli, Marco (2010). <i>The Genius of Archimedes -- 23 Centuries of Influence on Mathematics, Science and Engineering: Proceedings of an International Conference held at Syracuse, Italy, June 8-10, 2010</i>. <a href="/wiki/Springer_Science_%26_Business_Media" class="mw-redirect" title="Springer Science & Business Media">Springer Science & Business Media</a>. p. 416. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9789048190911" title="Special:BookSources/9789048190911"><bdi>9789048190911</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Genius+of+Archimedes+--+23+Centuries+of+Influence+on+Mathematics%2C+Science+and+Engineering%3A+Proceedings+of+an+International+Conference+held+at+Syracuse%2C+Italy%2C+June+8-10%2C+2010&rft.pages=416&rft.pub=Springer+Science+%26+Business+Media&rft.date=2010&rft.isbn=9789048190911&rft.aulast=Paipetis&rft.aufirst=S.+A.&rft.au=Ceccarelli%2C+Marco&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALever" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBrunoOlendorf1997" class="citation book cs1">Bruno, Leonard C.; Olendorf, Donna (1997). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/sciencetechnolog0000brun"><i>Science and technology firsts</i></a></span>. <a href="/wiki/Gale_Research" class="mw-redirect" title="Gale Research">Gale Research</a>. p. <a rel="nofollow" class="external text" href="https://archive.org/details/sciencetechnolog0000brun/page/2">2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780787602567" title="Special:BookSources/9780787602567"><bdi>9780787602567</bdi></a>. <q>4400 B.C. Earliest evidence of the use of a horizontal loom is its depiction on a pottery dish found in Egypt and dated to this time. These first true frame looms are equipped with foot pedals to lift the warp threads, leaving the weaver's hands free to pass and beat the weft thread.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Science+and+technology+firsts&rft.pages=2&rft.pub=Gale+Research&rft.date=1997&rft.isbn=9780787602567&rft.aulast=Bruno&rft.aufirst=Leonard+C.&rft.au=Olendorf%2C+Donna&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsciencetechnolog0000brun&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALever" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFClarkeEngelbach1990" class="citation book cs1">Clarke, Somers; Engelbach, Reginald (1990). <i>Ancient Egyptian Construction and Architecture</i>. <a href="/wiki/Courier_Corporation" class="mw-redirect" title="Courier Corporation">Courier Corporation</a>. pp. <span class="nowrap">86–</span>90. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780486264851" title="Special:BookSources/9780486264851"><bdi>9780486264851</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ancient+Egyptian+Construction+and+Architecture&rft.pages=%3Cspan+class%3D%22nowrap%22%3E86-%3C%2Fspan%3E90&rft.pub=Courier+Corporation&rft.date=1990&rft.isbn=9780486264851&rft.aulast=Clarke&rft.aufirst=Somers&rft.au=Engelbach%2C+Reginald&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALever" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Alsop, Jon, <i><a rel="nofollow" class="external text" href="https://www.cjr.org/the_media_today/trump_musk_salute_gesture_attention.php">Trump, Musk, and the Limits of Attention</a></i>, <a href="/wiki/Columbia_Journalism_Review" title="Columbia Journalism Review">Columbia Journalism Review</a>, January 23, 2025</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFDavidovits2008" class="citation book cs1">Davidovits, Paul (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=e9hbt3xisb0C&pg=PA10">"Chapter 1"</a>. <i>Physics in Biology and Medicine</i> (3rd ed.). Academic Press. p. 10. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-369411-9" title="Special:BookSources/978-0-12-369411-9"><bdi>978-0-12-369411-9</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140103072006/http://books.google.com/books?id=e9hbt3xisb0C&pg=PA10">Archived</a> from the original on 2014-01-03<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-02-23</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+1&rft.btitle=Physics+in+Biology+and+Medicine&rft.pages=10&rft.edition=3rd&rft.pub=Academic+Press&rft.date=2008&rft.isbn=978-0-12-369411-9&rft.aulast=Davidovits&rft.aufirst=Paul&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3De9hbt3xisb0C%26pg%3DPA10&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALever" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFUickerPennockShigley2010" class="citation book cs1">Uicker, John; Pennock, Gordon; Shigley, Joseph (2010). <i>Theory of Machines and Mechanisms</i> (4th ed.). Oxford University Press USA. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-537123-9" title="Special:BookSources/978-0-19-537123-9"><bdi>978-0-19-537123-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+Machines+and+Mechanisms&rft.edition=4th&rft.pub=Oxford+University+Press+USA&rft.date=2010&rft.isbn=978-0-19-537123-9&rft.aulast=Uicker&rft.aufirst=John&rft.au=Pennock%2C+Gordon&rft.au=Shigley%2C+Joseph&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALever" class="Z3988"></span></span> </li> <li id="cite_note-Usher1954-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Usher1954_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFUsher,_A._P.1929" class="citation book cs1"><a href="/wiki/Abbott_Payson_Usher" title="Abbott Payson Usher">Usher, A. P.</a> (1929). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Zt4Aw9wKjm8C&pg=PA94"><i>A History of Mechanical Inventions</i></a>. Harvard University Press (reprinted by Dover Publications 1988). p. 94. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-14359-0" title="Special:BookSources/978-0-486-14359-0"><bdi>978-0-486-14359-0</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/514178">514178</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200726002155/https://books.google.com/books?id=Zt4Aw9wKjm8C&pg=PA94">Archived</a> from the original on 26 July 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">7 April</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Mechanical+Inventions&rft.pages=94&rft.pub=Harvard+University+Press+%28reprinted+by+Dover+Publications+1988%29&rft.date=1929&rft_id=info%3Aoclcnum%2F514178&rft.isbn=978-0-486-14359-0&rft.au=Usher%2C+A.+P.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DZt4Aw9wKjm8C%26pg%3DPA94&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALever" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lever&action=edit&section=10" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox 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srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/60px-Commons-logo.svg.png 1.5x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Levers" class="extiw" title="commons:Category:Levers">Levers</a></span>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735" /><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wiktionary-logo-en-v2.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/120px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/Special:Search/lever" class="extiw" title="wiktionary:Special:Search/lever">lever</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070114204336/http://www.diracdelta.co.uk/science/source/l/e/lever/source.html">Lever</a> at Diracdelta science and engineering encyclopedia</li> <li><i><a rel="nofollow" class="external text" href="http://demonstrations.wolfram.com/ASimpleLever/">A Simple Lever</a></i> by <a href="/wiki/Stephen_Wolfram" title="Stephen Wolfram">Stephen Wolfram</a>, <a href="/wiki/Wolfram_Demonstrations_Project" title="Wolfram Demonstrations Project">Wolfram Demonstrations Project</a>.</li> <li><a rel="nofollow" class="external text" href="http://www.enchantedlearning.com/physics/machines/Levers.shtml">Levers: Simple Machines</a> at EnchantedLearning.com</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output 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