{"id":100212,"date":"2026-02-15T20:27:40","date_gmt":"2026-02-15T20:27:40","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100212"},"modified":"2026-02-15T20:27:40","modified_gmt":"2026-02-15T20:27:40","slug":"rotor-moment-of-inertia","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/pt_br\/calculators\/rotor-moment-of-inertia\/","title":{"rendered":"Calculadora do Momento de In\u00e9rcia do Rotor | Ferramenta Gratuita #073"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Rotor Moment of Inertia Calculator\",\"description\":\"Calculate moment of inertia for various shapes.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/rotor-moment-of-inertia\/\",\"applicationCategory\":\"Engineering Calculator\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is mass moment of inertia?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Mass moment of inertia J is the rotational analog of mass. It determines resistance to angular acceleration: T = J * alpha.\"}},\n{\"@type\":\"Question\",\"name\":\"How to find J for complex rotors?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Break into simple shapes, calculate J for each, use parallel axis theorem: J = Jcm + md^2.\"}},\n{\"@type\":\"Question\",\"name\":\"What is radius of gyration?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"k = sqrt(J\/m). Distance where all mass could concentrate to give same J.\"}},\n{\"@type\":\"Question\",\"name\":\"Does length affect J?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Yes, J is proportional to length via mass for cylinders.\"}},\n{\"@type\":\"Question\",\"name\":\"How is J related to kinetic energy?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"KE = 0.5*J*omega^2. Used in flywheel and acceleration calculations.\"}}\n]}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Rotor Moment of Inertia\",\"item\":\"https:\/\/vibromera.eu\/calculators\/rotor-moment-of-inertia\/\"}]}<\/script>\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin>\n\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=DM+Sans:ital,opsz,wght@0,9..40,300;0,9..40,400;0,9..40,500;0,9..40,600;0,9..40,700;1,9..40,400&#038;family=JetBrains+Mono:wght@400;500;600&#038;family=Fraunces:opsz,wght@9..144,700;9..144,800&#038;display=swap\" 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print{.vc-section-body{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-presets,.vc-promo{display:none!important}}<\/style>\n\n<div class=\"vc-calculator\">\n<header class=\"vc-header\">\n<p class=\"vc-header-eyebrow\">Free Engineering Tool #073<\/p>\n<h1 class=\"vc-header-title\">Rotor Moment of Inertia Calculator<\/h1>\n<p class=\"vc-header-subtitle\">Calculate mass moment of inertia J for solid cylinder, hollow cylinder, disc, and sphere. Enter dimensions and material density.<\/p>\n<div class=\"vc-badges\"><span class=\"vc-badge\">Multiple Shapes<\/span><span class=\"vc-badge\">Material Density<\/span><span class=\"vc-badge\">Auto-Calc<\/span><\/div>\n<\/header>\n<div class=\"vc-card\">\n<div class=\"vc-unit-bar\"><button type=\"button\" class=\"vc-unit-btn vc-active\" data-system=\"metric\">Metric (mm, kg)<\/button><button type=\"button\" class=\"vc-unit-btn\" data-system=\"imperial\">Imperial (in, lb)<\/button><\/div>\n<form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid\">\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-shape\">Shape<\/label><select class=\"vc-select\" id=\"vc-shape\"><option value=\"solid\" selected>Solid Cylinder<\/option><option value=\"hollow\">Hollow Cylinder<\/option><option value=\"disc\">Thin Disc<\/option><option value=\"sphere\">Solid Sphere<\/option><\/select><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-rho\">Density <span class=\"vc-label-hint\">(kg\/m&sup3;)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-rho\" step=\"any\" min=\"1\" value=\"7850\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-od\">Outer Diameter D <span class=\"vc-label-hint\" id=\"vc-odu\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-od\" step=\"any\" min=\"1\" value=\"200\"><\/div>\n<div class=\"vc-field\" id=\"vc-fid\"><label class=\"vc-label\" for=\"vc-id\">Inner Diameter d <span class=\"vc-label-hint\" id=\"vc-idu\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-id\" step=\"any\" min=\"0\" value=\"100\"><\/div>\n<div class=\"vc-field\" id=\"vc-flen\"><label class=\"vc-label\" for=\"vc-len\">Length \/ Thickness <span class=\"vc-label-hint\" id=\"vc-lenu\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-len\" step=\"any\" min=\"1\" value=\"300\"><\/div>\n<\/div>\n<div class=\"vc-presets\"><div class=\"vc-presets-label\">Quick presets<\/div>\n<button type=\"button\" class=\"vc-preset-btn\" data-s=\"solid\" data-od=\"200\" data-id=\"0\" data-l=\"300\" data-r=\"7850\">Steel d200 L300<\/button>\n<button type=\"button\" class=\"vc-preset-btn\" data-s=\"hollow\" data-od=\"200\" data-id=\"100\" data-l=\"300\" data-r=\"7850\">Hollow 200\/100 L300<\/button>\n<button type=\"button\" class=\"vc-preset-btn\" data-s=\"disc\" data-od=\"400\" data-id=\"0\" data-l=\"20\" data-r=\"2700\">Alu Disc d400 t20<\/button>\n<\/div><\/form>\n<div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Results<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div>\n<div class=\"vc-result-grid\">\n<div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Moment of Inertia J<\/div><div class=\"vc-rcard-value\" id=\"vc-r-J\">&mdash;<\/div><\/div>\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Mass<\/div><div class=\"vc-rcard-value\" id=\"vc-r-mass\">&mdash;<\/div><\/div>\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Radius of Gyration k<\/div><div class=\"vc-rcard-value\" id=\"vc-r-rog\">&mdash;<\/div><\/div>\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">KE at 1000 RPM<\/div><div class=\"vc-rcard-value\" id=\"vc-r-ke\">&mdash;<\/div><\/div>\n<\/div><\/div><\/div>\n\n<div class=\"vc-section vc-open\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">&#x1F4D8;<\/span><span class=\"vc-section-title\">Theory &amp; Formulas<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n<div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\n<h3>Solid Cylinder<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n<h3>Hollow Cylinder<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n<h3>Solid Sphere<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n<table class=\"vc-table\"><thead><tr><th>Material<\/th><th>Density (kg\/m&sup3;)<\/th><\/tr><\/thead><tbody><tr><td>Steel<\/td><td>7850<\/td><\/tr><tr><td>Aluminum<\/td><td>2700<\/td><\/tr><tr><td>Cast Iron<\/td><td>7200<\/td><\/tr><tr><td>Brass<\/td><td>8500<\/td><\/tr><tr><td>Titanium<\/td><td>4500<\/td><\/tr><\/tbody><\/table>\n<div class=\"vc-warning-box\"><p style=\"margin:0;font-size:14px;color:var(--vc-ink-secondary)\">For complex rotors, sum individual section inertias using parallel axis theorem: J = &Sigma;(J<sub>i<\/sub> + m<sub>i<\/sub>r<sub>i<\/sub>&sup2;).<\/p><\/div>\n<\/div><\/div><\/div>\n\n<div class=\"vc-section\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">&#x1F517;<\/span><span class=\"vc-section-title\">Related Calculators<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n<div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\">\n<a class=\"vc-related-link\" href=\"\/calculators\/flywheel-energy-calculator\/\">Flywheel Energy<\/a>\n<a class=\"vc-related-link\" href=\"\/calculators\/rotor-acceleration-time\/\">Rotor Acceleration Time<\/a>\n<a class=\"vc-related-link\" href=\"\/calculators\/shaft-diameter-torsion\/\">Shaft Diameter<\/a>\n<a class=\"vc-related-link\" href=\"\/calculators\/residual-unbalance-iso1940\/\">Residual Unbalance<\/a>\n<\/div><\/div><\/div><\/div>\n\n<div class=\"vc-section\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">&#x2753;<\/span><span class=\"vc-section-title\">FAQ<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n<div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div><\/div>\n\n<div class=\"vc-promo\"><div class=\"vc-promo-text\"><strong>Vibromera<\/strong> &mdash; Portable Balancing &amp; Vibration Analysis. Used in 50+ countries.<\/div><a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/div>\n<footer class=\"vc-footer\"><p>&copy; 2024&ndash;2025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><div class=\"vc-footer-links\"><a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a><a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a><\/div><\/footer>\n<\/div>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>\n(function(){\n'use strict';var SLUG='rotor-moment-of-inertia',uS='metric';\nfunction $(id){return document.getElementById(id)}\nfunction fmt(n,d){if(isNaN(n)||!isFinite(n))return'\\u2014';return n.toFixed(d==null?2:d).replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\n\n$('vc-shape').addEventListener('change',function(){var s=this.value;$('vc-fid').style.display=s==='hollow'?'flex':'none';$('vc-flen').style.display=s==='sphere'?'none':'flex';calc()});\n\nfunction calc(){\n  var shape=$('vc-shape').value,OD=parseFloat($('vc-od').value),ID=parseFloat($('vc-id').value)||0,L=parseFloat($('vc-len').value),rho=parseFloat($('vc-rho').value);\n  if(!OD||OD<=0||!rho||rho<=0){$('vc-results').classList.remove('vc-visible');return}\n  if(shape!=='sphere'&&(!L||L<=0)){$('vc-results').classList.remove('vc-visible');return}\n  var ODm=uS==='imperial'?OD*0.0254:OD\/1000,IDm=uS==='imperial'?ID*0.0254:ID\/1000,Lm=uS==='imperial'?L*0.0254:L\/1000;\n  var Ro=ODm\/2,Ri=IDm\/2,m,J;\n  if(shape==='solid'){m=rho*Math.PI*Ro*Ro*Lm;J=m*Ro*Ro\/2}\n  else if(shape==='hollow'){m=rho*Math.PI*(Ro*Ro-Ri*Ri)*Lm;J=m*(Ro*Ro+Ri*Ri)\/2}\n  else if(shape==='disc'){m=rho*Math.PI*Ro*Ro*Lm;J=m*Ro*Ro\/2}\n  else{m=rho*4\/3*Math.PI*Ro*Ro*Ro;J=2\/5*m*Ro*Ro}\n  var k=Math.sqrt(J\/m),w1k=2*Math.PI*1000\/60,KE=0.5*J*w1k*w1k;\n  if(uS==='imperial'){$('vc-r-J').innerHTML=fmt(J*23.7304,4)+' <span class=\"vc-rcard-unit\">lb\\u00B7ft\\u00B2<\/span>';$('vc-r-mass').innerHTML=fmt(m*2.20462,2)+' <span class=\"vc-rcard-unit\">lb<\/span>';$('vc-r-rog').innerHTML=fmt(k*39.3701,2)+' <span class=\"vc-rcard-unit\">in<\/span>'}\n  else{$('vc-r-J').innerHTML=(J<0.01?fmt(J*1e6,1)+' <span class=\"vc-rcard-unit\">g\\u00B7mm\\u00B2<\/span>':fmt(J,4)+' <span class=\"vc-rcard-unit\">kg\\u00B7m\\u00B2<\/span>');$('vc-r-mass').innerHTML=fmt(m,2)+' <span class=\"vc-rcard-unit\">kg<\/span>';$('vc-r-rog').innerHTML=fmt(k*1000,1)+' <span class=\"vc-rcard-unit\">mm<\/span>'}\n  $('vc-r-ke').innerHTML=fmt(KE\/1000,2)+' <span class=\"vc-rcard-unit\">kJ @1000RPM<\/span>';\n  $('vc-results').classList.add('vc-visible');\n  sH({shape:shape,OD:OD,rho:rho,_summary:shape+' OD='+OD+' J='+fmt(J,4)});\n}\n\nvar uB=document.querySelectorAll('.vc-unit-btn');uB.forEach(function(b){b.addEventListener('click',function(){uB.forEach(function(x){x.classList.remove('vc-active')});this.classList.add('vc-active');uS=this.getAttribute('data-system');$('vc-odu').textContent=uS==='imperial'?'(in)':'(mm)';$('vc-idu').textContent=uS==='imperial'?'(in)':'(mm)';$('vc-lenu').textContent=uS==='imperial'?'(in)':'(mm)';calc()})});\ndocument.querySelectorAll('.vc-preset-btn').forEach(function(b){b.addEventListener('click',function(e){e.preventDefault();$('vc-shape').value=this.getAttribute('data-s');$('vc-od').value=this.getAttribute('data-od');$('vc-id').value=this.getAttribute('data-id');$('vc-len').value=this.getAttribute('data-l');$('vc-rho').value=this.getAttribute('data-r');$('vc-fid').style.display=this.getAttribute('data-s')==='hollow'?'flex':'none';$('vc-flen').style.display=this.getAttribute('data-s')==='sphere'?'none':'flex';calc()})});\n$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);\n$('vc-copy-btn').addEventListener('click',function(){var t='Rotor Moment of Inertia\\nJ: '+$('vc-r-J').textContent+'\\nMass: '+$('vc-r-mass').textContent+'\\nk: '+$('vc-r-rog').textContent;if(navigator.clipboard){navigator.clipboard.writeText(t).then(function(){var b=$('vc-copy-btn');b.classList.add('vc-copied');b.textContent='Copied!';setTimeout(function(){b.classList.remove('vc-copied');b.textContent='Copy'},2000)})}});\ndocument.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});\n\nvar fD=[{q:'What is mass moment of inertia?',a:'<p>J (kg\\u00B7m\\u00B2) is rotational analog of mass. T=J\\u03B1.<\/p>'},{q:'How to find J for complex rotors?',a:'<p>Break into shapes, use parallel axis theorem: J=J<sub>cm<\/sub>+md\\u00B2.<\/p>'},{q:'What is radius of gyration?',a:'<p>k=\\u221A(J\/m). Equivalent concentrated mass distance.<\/p>'},{q:'Does length affect J?',a:'<p>Yes, J proportional to length via mass for cylinders.<\/p>'},{q:'How is J related to energy?',a:'<p>KE=\\u00BDJ\\u03C9\\u00B2. Used in flywheel and acceleration calcs.<\/p>'}];\nvar fL=$('vc-faq-list');fD.forEach(function(f){fL.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>'+f.q+'<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">'+f.a+'<\/div><\/div><\/div>'});\nfL.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open')});\n\nfunction sH(e){var k='vc_history_'+SLUG,a=[];try{a=JSON.parse(localStorage.getItem(k))||[]}catch(x){}e._ts=new Date().toISOString();a.unshift(e);if(a.length>10)a=a.slice(0,10);try{localStorage.setItem(k,JSON.stringify(a))}catch(x){}}\n\nfunction rF(){try{\nkatex.render('J_{solid}=\\\\frac{1}{2}mR^2=\\\\frac{\\\\pi\\\\rho R^4 L}{2}',$('vc-katex-1'),{displayMode:true,throwOnError:false});\nkatex.render('J_{hollow}=\\\\frac{1}{2}m(R_o^2+R_i^2)',$('vc-katex-2'),{displayMode:true,throwOnError:false});\nkatex.render('J_{sphere}=\\\\frac{2}{5}mR^2',$('vc-katex-3'),{displayMode:true,throwOnError:false});\n}catch(e){}}\n$('vc-fid').style.display='none';rF();calc();\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Calcule o momento de in\u00e9rcia para um cilindro maci\u00e7o, um cilindro oco, um disco e uma esfera. Insira as dimens\u00f5es e a densidade do material para encontrar J, a massa e o raio de gira\u00e7\u00e3o.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100212","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/calculator\/100212","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":1,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/calculator\/100212\/revisions"}],"predecessor-version":[{"id":100527,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/calculator\/100212\/revisions\/100527"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/media?parent=100212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/categories?post=100212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/tags?post=100212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}