{"id":786,"date":"2026-10-04T11:13:28","date_gmt":"2026-10-04T10:13:28","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-momentu-sily\/"},"modified":"2026-10-04T11:13:28","modified_gmt":"2026-10-04T10:13:28","slug":"kalkulator-momentu-sily","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-momentu-sily\/","title":{"rendered":"Kalkulator momentu si\u0142y"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Oblicz moment si\u0142y, si\u0142\u0119 lub rami\u0119 d\u017awigni<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"786\" data-favorite-title=\"Moment si\u0142y\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-momentu-sily\/\" data-favorite-excerpt=\"Oblicz moment si\u0142y, si\u0142\u0119 lub d\u0142ugo\u015b\u0107 ramienia d\u017awigni ze wzoru \u03c4 = r \u00b7 F \u00b7 sin(\u03b8). Wprowad\u017a dowolne dwie wielko\u015bci oraz k\u0105t, a wynik otrzymasz w N\u00b7m, lb\u00b7ft lub kgf\u00b7m.\" aria-label=\"Dodaj do ulubionych\" data-favorite-icon=\"icon icon-physic\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-momentu-sily\/\" method=\"POST\" class=\"calculator\" id=\"calculator-786\" data-post=\"786\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Co obliczy\u0107<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"co_obliczy\"><option value=\"torque\" selected>Moment si\u0142y (\u03c4)<\/option><option value=\"force\">Si\u0142a (F)<\/option><option value=\"length\">Rami\u0119 d\u017awigni (r)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field is-single\" id=\"input-2\" hidden><label for=\"field-2\">Moment si\u0142y (\u03c4)<\/label><div class=\"field-group\"><input type=\"text\" name=\"moment_siy_\" id=\"field-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 25\" min=\"0\" value=\"25\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"N\u00b7m\" selected>N\u00b7m<\/option><option value=\"lb\u00b7ft\">lb\u00b7ft<\/option><option value=\"kgf\u00b7m\">kgf\u00b7m<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field is-single has-term\" id=\"input-3\"><label for=\"field-4\">Si\u0142a (F)<\/label><div class=\"term\">F<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"sia_f\" id=\"field-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 100\" min=\"0\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"N\" selected>N<\/option><option value=\"lbf\">lbf<\/option><option value=\"kgf\">kgf<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field is-single has-term\" id=\"input-4\"><label for=\"field-6\">D\u0142ugo\u015b\u0107 ramienia d\u017awigni (r)<\/label><div class=\"term\">r<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"dugo_ramienia_dwigni_r\" id=\"field-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.25\" min=\"0\" value=\"0.25\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"m\" selected>m<\/option><option value=\"cm\">cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field is-single has-term\" id=\"input-5\"><label for=\"field-8\">K\u0105t mi\u0119dzy si\u0142\u0105 a ramieniem (\u03b8)<\/label><div class=\"term\">\u03b8<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"kt_midzy_si_a_ramieniem_\" id=\"field-8\" aria-describedby=\"calc-unit-8 calc-info-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 90\" min=\"0\" max=\"180\" value=\"90\"\/><div class=\"unit\" id=\"calc-unit-8\">\u00b0<\/div><small id=\"calc-info-8\">90\u00b0 oznacza, \u017ce si\u0142a dzia\u0142a prostopadle do ramienia d\u017awigni.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"786\">Oblicz<\/button><button type=\"reset\">Wyczy\u015b\u0107<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Obliczaj automatycznie<\/label><small>Po w\u0142\u0105czeniu wynik aktualizuje si\u0119 automatycznie po zmianie dowolnej warto\u015bci.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Wyniki oblicze\u0144<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Wyznaczona wielko\u015b\u0107<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Wszystkie wielko\u015bci w tym obliczeniu<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Kopiuj link do tego obliczenia<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Zostaw komentarz<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"786\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Jak oceniasz ten wynik?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Lubi\u0119 to <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Pomocne <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Niejasne <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Rozczarowanie <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Niedok\u0142adne <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Wz\u00f3r na moment si\u0142y<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Wz\u00f3r<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ \\tau = r \\cdot F \\cdot \\sin(\\theta) \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Gdzie:<\/strong><\/p>\n<ul>\n<li>\\(\\tau\\) \u2014 moment si\u0142y (N\u00b7m)<\/li>\n<li>\\(r\\) \u2014 d\u0142ugo\u015b\u0107 ramienia d\u017awigni, czyli odleg\u0142o\u015b\u0107 prostopad\u0142a od osi obrotu do punktu przy\u0142o\u017cenia si\u0142y (m)<\/li>\n<li>\\(F\\) \u2014 przy\u0142o\u017cona si\u0142a (N)<\/li>\n<li>\\(\\theta\\) \u2014 k\u0105t mi\u0119dzy ramieniem d\u017awigni a kierunkiem si\u0142y (stopnie lub radiany)<\/li>\n<\/ul>\n<p>Wz\u00f3r wyra\u017ca obrotowe dzia\u0142anie si\u0142y: moment ro\u015bnie wraz ze wzrostem d\u0142ugo\u015bci ramienia d\u017awigni i si\u0142y, a najwi\u0119kszy jest, gdy si\u0142a dzia\u0142a prostopadle do ramienia (\\(\\theta = 90^\\circ\\)).<\/p>\n<p>T\u0119 sam\u0105 zale\u017cno\u015b\u0107 mo\u017cna przekszta\u0142ci\u0107, aby obliczy\u0107 si\u0142\u0119 lub rami\u0119 d\u017awigni:<\/p>\n<p>\\[ F = \\frac{\\tau}{r \\cdot \\sin(\\theta)} \\qquad r = \\frac{\\tau}{F \\cdot \\sin(\\theta)} \\]<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Moment si\u0142y \u2013 przyk\u0142ad obliczenia<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> naciskasz na klucz si\u0142\u0105 100 N w punkcie odleg\u0142ym o 0,25 m od \u015bruby, prostopadle do trzonka.<\/p>\n<p>\\[ \\tau = r \\cdot F \\cdot \\sin(\\theta) = 0.25 \\times 100 \\times \\sin(90^\\circ) \\]<\/p>\n<p>\\[ \\tau = 0.25 \\times 100 \\times 1 = 25 \\text{ N\u00b7m} \\]<\/p>\n<p><strong>Wynik:<\/strong> moment si\u0142y wynosi 25 N\u00b7m (\u2248 18,44 lb\u00b7ft, \u2248 2,55 kgf\u00b7m).<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora momentu si\u0142y<\/h2>\n<ol>\n<li>W rozwijanym menu <strong>Oblicz<\/strong> wybierz, czy chcesz obliczy\u0107 <strong>moment si\u0142y (\u03c4)<\/strong>, <strong>si\u0142\u0119 (F)<\/strong> czy <strong>rami\u0119 d\u017awigni (r)<\/strong>. Pole wybranej wielko\u015bci znika \u2014 wpisujesz pozosta\u0142e dwie.<\/li>\n<li>Wprowad\u017a znan\u0105 warto\u015b\u0107 <strong>momentu si\u0142y (\u03c4)<\/strong> i wybierz jego jednostk\u0119 (N\u00b7m, lb\u00b7ft lub kgf\u00b7m) \u2014 widoczne tylko przy obliczaniu si\u0142y lub ramienia.<\/li>\n<li>Wprowad\u017a znan\u0105 warto\u015b\u0107 <strong>si\u0142y (F)<\/strong> wraz z jednostk\u0105 (N, lbf lub kgf).<\/li>\n<li>Wprowad\u017a <strong>d\u0142ugo\u015b\u0107 ramienia d\u017awigni (r)<\/strong> i wybierz jednostk\u0119 (m, cm, mm, ft lub in).<\/li>\n<li>Wprowad\u017a <strong>k\u0105t mi\u0119dzy si\u0142\u0105 a ramieniem (\u03b8)<\/strong> w stopniach. U\u017cyj 90\u00b0, je\u015bli si\u0142a dzia\u0142a prostopadle do d\u017awigni.<\/li>\n<li>Odczytaj wynik w wybranej jednostce wraz z warto\u015bciami w innych popularnych jednostkach oraz tabel\u0105 zbiorcz\u0105 wszystkich wielko\u015bci.<\/li>\n<\/ol>\n<h2>Czym jest moment si\u0142y?<\/h2>\n<p>Moment si\u0142y (nazywany te\u017c momentem obrotowym) to obrotowy odpowiednik si\u0142y. Podczas gdy <a href=\"https:\/\/wpcalc.com\/pl\/fizyka\/sila-fizyka\/\">si\u0142a<\/a> dzia\u0142aj\u0105ca liniowo pcha obiekt po prostej, moment si\u0142y mierzy, jak skutecznie si\u0142a powoduje obr\u00f3t obiektu wok\u00f3\u0142 punktu obrotu \u2014 osi \u015bruby, zawiasu drzwi, piasty ko\u0142a czy stawu w ciele cz\u0142owieka. To w\u0142a\u015bnie moment si\u0142y dokr\u0119ca \u015brub\u0119, otwiera drzwi i obraca wa\u0142 korbowy.<\/p>\n<p>Warto\u015b\u0107 momentu zale\u017cy od trzech rzeczy: jak mocno naciskasz (si\u0142a), gdzie naciskasz (d\u0142ugo\u015b\u0107 ramienia d\u017awigni) i w jakim kierunku naciskasz (k\u0105t). Rami\u0119 d\u017awigni to odleg\u0142o\u015b\u0107 od osi obrotu do punktu przy\u0142o\u017cenia si\u0142y, a do obrotu przyczynia si\u0119 tylko sk\u0142adowa si\u0142y prostopad\u0142a do tego ramienia \u2014 st\u0105d w\u0142a\u015bnie czynnik \\(\\sin(\\theta)\\). Przy 90\u00b0 dzia\u0142a ca\u0142a si\u0142a; przy 0\u00b0 lub 180\u00b0, gdy si\u0142a skierowana jest wzd\u0142u\u017c ramienia, nie powstaje \u017caden obr\u00f3t.<\/p>\n<p>Dlatego w\u0142a\u015bnie klamki drzwi umieszcza si\u0119 daleko od zawias\u00f3w, d\u0142ugie przed\u0142u\u017cki (tzw. \u201e\u0142amaki\u201d) poluzowuj\u0105 oporne \u015bruby, a klucz \u0142atwiej obraca\u0107, naciskaj\u0105c go na ko\u0144cu, a nie przy g\u0142owie. Podwojenie d\u0142ugo\u015bci ramienia podwaja moment przy tym samym wysi\u0142ku \u2014 i odwrotnie.<\/p>\n<p>Jednostk\u0105 momentu si\u0142y w uk\u0142adzie SI jest niutonometr (N\u00b7m). Zwr\u00f3\u0107 uwag\u0119, \u017ce cho\u0107 N\u00b7m jest wymiarowo to\u017csame z d\u017culem, momentu si\u0142y nigdy nie wyra\u017ca si\u0119 w d\u017culach \u2014 to wielko\u015b\u0107 obrotowa, a nie energia. W praktyce imperialnej moment podaje si\u0119 zwykle w funto-stopach (lb\u00b7ft). Je\u015bli chcesz powi\u0105za\u0107 moment z energi\u0105 lub ruchem, pami\u0119taj, \u017ce praca wykonana przez sta\u0142y moment przy danym k\u0105cie obrotu to \\(W = \\tau \\varphi\\); odpowiedniki liniowe znajdziesz w kalkulatorach <a href=\"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-pracy\/\">Praca<\/a> i <a href=\"https:\/\/wpcalc.com\/en\/physics\/power\/\">Moc<\/a>.<\/p>\n<h2>Za\u0142o\u017cenia, ograniczenia i praktyczne wskaz\u00f3wki<\/h2>\n<ul>\n<li><strong>Jedna si\u0142a, jedna o\u015b obrotu.<\/strong> Kalkulator zak\u0142ada jedn\u0105 si\u0142\u0119 dzia\u0142aj\u0105c\u0105 w jednym punkcie na sztywnej d\u017awigni wok\u00f3\u0142 sta\u0142ej osi. Rzeczywiste uk\u0142ady z wieloma si\u0142ami lub obci\u0105\u017ceniami roz\u0142o\u017conymi wymagaj\u0105 osobnego sumowania moment\u00f3w.<\/li>\n<li><strong>K\u0105t ma znaczenie.<\/strong> Wiele os\u00f3b zak\u0142ada, \u017ce si\u0142a dzia\u0142a zawsze prostopadle. Je\u015bli ci\u0105gniesz klucz pod ma\u0142ym k\u0105tem, efektywny moment szybko spada \u2014 przy 30\u00b0 uzyskujesz tylko po\u0142ow\u0119 momentu w por\u00f3wnaniu z ci\u0105gni\u0119ciem pod k\u0105tem 90\u00b0.<\/li>\n<li><strong>Kierunek obrotu nie jest pokazany.<\/strong> Wynik to warto\u015b\u0107 bezwzgl\u0119dna. Zgodnie z konwencj\u0105 moment przeciwny do ruchu wskaz\u00f3wek zegara uznaje si\u0119 cz\u0119sto za dodatni, a zgodny z nimi za ujemny; znaki przypisz samodzielnie przy r\u00f3wnowa\u017ceniu wielu moment\u00f3w.<\/li>\n<li><strong>Sytuacje statyczne i dynamiczne.<\/strong> To narz\u0119dzie oblicza sam moment, a nie wynikaj\u0105ce z niego przyspieszenie k\u0105towe. Dla maszyn wiruj\u0105cych moment wi\u0105\u017ce si\u0119 z przyspieszeniem k\u0105towym poprzez moment bezw\u0142adno\u015bci: \\(\\tau = I\\alpha\\).<\/li>\n<li><strong>Sp\u00f3jno\u015b\u0107 jednostek.<\/strong> Kalkulator przelicza jednostki wewn\u0119trznie, wi\u0119c mo\u017cesz np. miesza\u0107 lbf z metrami. Przy obliczeniach r\u0119cznych trzymaj si\u0119 jednego sp\u00f3jnego uk\u0142adu.<\/li>\n<li><strong>Klucze dynamometryczne i warto\u015bci zadane.<\/strong> Specyfikacje dokr\u0119cania \u015brub podaje si\u0119 w jednostkach momentu (np. N\u00b7m lub lb\u00b7ft). Aby osi\u0105gn\u0105\u0107 zadany moment r\u0119cznie, oblicz si\u0142\u0119, aby wiedzie\u0107, jak mocno ci\u0105gn\u0105\u0107 przy znanej d\u0142ugo\u015bci ramienia.<\/li>\n<\/ul>\n<p>W zadaniach dotycz\u0105cych si\u0142 w uk\u0142adzie wiruj\u0105cym lub ograniczonym \u2014 np. liny przerzuconej przez bloczek lub obiektu na r\u00f3wni pochy\u0142ej \u2014 przydatne mog\u0105 by\u0107 te\u017c kalkulatory <a href=\"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-naciagu-lin\/\">Naci\u0105g lin<\/a> i <a href=\"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-rownia-pochylego\/\">R\u00f3wnia pochy\u0142a<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Oblicz moment si\u0142y, si\u0142\u0119 lub d\u0142ugo\u015b\u0107 ramienia d\u017awigni ze wzoru \u03c4 = r \u00b7 F \u00b7 sin(\u03b8). Wprowad\u017a dowolne dwie wielko\u015bci oraz k\u0105t, a wynik otrzymasz w N\u00b7m, lb\u00b7ft lub kgf\u00b7m.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[10],"tags":[54],"class_list":["post-786","post","type-post","status-publish","format-standard","hentry","category-fizyka","tag-mechanika"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/786","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/comments?post=786"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/786\/revisions"}],"predecessor-version":[{"id":1781,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/786\/revisions\/1781"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}