{"id":65867,"date":"2026-09-30T13:56:46","date_gmt":"2026-09-30T10:56:46","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65867"},"modified":"2026-09-30T13:56:46","modified_gmt":"2026-09-30T10:56:46","slug":"angular-momentum-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/angular-momentum-calculator\/","title":{"rendered":"Angular Momentum Calculator"},"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\">Angular Momentum from Inertia and Angular Velocity or Point-Mass Data<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65867\" data-favorite-title=\"Angular Momentum\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/angular-momentum-calculator\/\" data-favorite-excerpt=\"Calculate angular momentum L from moment of inertia and angular velocity, or from point-mass data (mass, velocity, radius). Enter your values in any unit and get L in kg\u00b7m\u00b2\/s (J\u00b7s).\" aria-label=\"Add to Favorites\" 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\/en\/physics\/angular-momentum-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65867\" data-post=\"65867\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Object type<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"object_type\"><option value=\"rigid\" selected>Rotating body (moment of inertia)<\/option><option value=\"point\">Point mass (mass, velocity, radius)<\/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 has-term\" id=\"input-2\"><label for=\"field-2\">Moment of inertia (I)<\/label><div class=\"term\">I<\/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=\"moment_of_inertia_i\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 2\" min=\"0\" value=\"2\"\/><div class=\"unit\" id=\"calc-unit-2\">kg\u00b7m\u00b2<\/div><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unit\" aria-label=\"Unit\"><option value=\"kgm2\" selected>kg\u00b7m\u00b2<\/option><option value=\"gcm2\">g\u00b7cm\u00b2<\/option><option value=\"lbft2\">lb\u00b7ft\u00b2<\/option><option value=\"lbin2\">lb\u00b7in\u00b2<\/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><small id=\"calc-info-2\">Resistance of the body to changes in rotation. A solid disk is \u00bdMR\u00b2, a thin hoop MR\u00b2, a solid sphere \u2156MR\u00b2.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-3\"><label for=\"field-4\">Angular velocity (\u03c9)<\/label><div class=\"term\">\u03c9<\/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=\"angular_velocity_\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 60\" min=\"0\" value=\"60\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"unit\" aria-label=\"Unit\"><option value=\"rads\">rad\/s<\/option><option value=\"rpm\" selected>rpm<\/option><option value=\"degs\">\u00b0\/s<\/option><option value=\"hz\">rev\/s (Hz)<\/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><small id=\"calc-info-4\">How fast the body spins. 60 rpm = 1 revolution per second.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-4\" hidden><label for=\"field-6\">Mass (m)<\/label><div class=\"term\">m<\/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=\"mass_m\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1\" min=\"0\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"unit\" aria-label=\"Unit\"><option value=\"kg\" selected>kg<\/option><option value=\"g\">g<\/option><option value=\"lb\">lb<\/option><option value=\"oz\">oz<\/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><small id=\"calc-info-6\">Mass of the object treated as a point mass.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-5\" hidden><label for=\"field-8\">Tangential velocity (v)<\/label><div class=\"term\">v<\/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=\"tangential_velocity_v\" id=\"field-8\" aria-describedby=\"calc-info-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 5\" min=\"0\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-9\" name=\"unit\" aria-label=\"Unit\"><option value=\"ms\" selected>m\/s<\/option><option value=\"kmh\">km\/h<\/option><option value=\"fts\">ft\/s<\/option><option value=\"mph\">mph<\/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><small id=\"calc-info-8\">Speed of the point mass along its circular path (perpendicular to the radius).<\/small><\/div><div class=\"field is-single has-term\" id=\"input-6\" hidden><label for=\"field-10\">Radius (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=\"radius_r\" id=\"field-10\" aria-describedby=\"calc-info-10\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.8\" min=\"0\" value=\"0.8\"\/><div class=\"grid grid-cols-1\"><select id=\"field-11\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\" selected>m<\/option><option value=\"cm\">cm<\/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><small id=\"calc-info-10\">Distance from the rotation axis to the point mass.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65867\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/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> Angular Momentum Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Angular momentum<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Formulas used<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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\">Copy link to this calculation<\/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>Leave a Comment<\/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=\"65867\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/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\">Like <\/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\">Helpful <\/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\">Confused <\/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\">Disappointed <\/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\">Inaccurate <\/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>Angular Momentum Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ L = I \\omega \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(L\\) \u2014 angular momentum (kg\u00b7m\u00b2\/s, equal to J\u00b7s)<\/li>\n<li>\\(I\\) \u2014 moment of inertia about the rotation axis (kg\u00b7m\u00b2)<\/li>\n<li>\\(\\omega\\) \u2014 angular velocity (rad\/s)<\/li>\n<\/ul>\n<p>For a point mass moving in a circle of radius \\(r\\) with tangential speed \\(v\\), the same quantity is written as \\(L = m v r\\), because the moment of inertia of a point mass is \\(I = mr^2\\) and \\(\\omega = v\/r\\).<\/p>\n<\/p>\n<p><em>Note: the backslash-free closing tag below belongs to the shortcode.<\/em><\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.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>Angular Momentum \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a flywheel with a moment of inertia of 2 kg\u00b7m\u00b2 spins at 60 rpm. First convert the angular velocity to radians per second:<\/p>\n<p>\\[ \\omega = 60 \\,\\text{rpm} \\times \\frac{2\\pi}{60} = 2\\pi \\approx 6.283 \\,\\text{rad\/s} \\]<\/p>\n<p>\\[ L = I\\omega = 2 \\times 6.283 = 12.566 \\,\\text{kg\u00b7m}^2\/\\text{s} \\]<\/p>\n<p><strong>Result:<\/strong> the angular momentum is approximately <strong>12.57 kg\u00b7m\u00b2\/s<\/strong> (equivalently 12.57 J\u00b7s). This matches the calculator's default values, so you can reproduce it directly.<\/p>\n<p>For comparison, in point-mass mode a 1 kg object moving at 5 m\/s on a circle of radius 0.8 m carries \\(L = mvr = 1 \\times 5 \\times 0.8 = 4\\) kg\u00b7m\u00b2\/s.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Angular Momentum Calculator<\/h2>\n<ol>\n<li><strong>Choose the Object type.<\/strong> Select <em>\"Rotating body (moment of inertia)\"<\/em> if you know \\(I\\) and \\(\\omega\\), or <em>\"Point mass (mass, velocity, radius)\"<\/em> if you know \\(m\\), \\(v\\) and \\(r\\). The input fields switch automatically.<\/li>\n<li><strong>Rigid-body mode:<\/strong> enter the <strong>Moment of inertia (I)<\/strong> and pick its unit (kg\u00b7m\u00b2, g\u00b7cm\u00b2, lb\u00b7ft\u00b2, lb\u00b7in\u00b2), then enter the <strong>Angular velocity (\u03c9)<\/strong> in rad\/s, rpm, \u00b0\/s, or rev\/s (Hz).<\/li>\n<li><strong>Point-mass mode:<\/strong> enter the <strong>Mass (m)<\/strong>, the <strong>Tangential velocity (v)<\/strong>, and the <strong>Radius (r)<\/strong> from the rotation axis, each with its own unit selector.<\/li>\n<li>Read the <strong>Angular momentum<\/strong> result in kg\u00b7m\u00b2\/s (J\u00b7s), together with a table showing all quantities converted to SI and other common units, and the exact formulas applied to your values.<\/li>\n<\/ol>\n<h2>What Is Angular Momentum?<\/h2>\n<p>Angular momentum is the rotational analogue of linear momentum. While linear momentum \\(p = mv\\) describes how much straight-line motion a body carries, angular momentum \\(L\\) describes how much rotational motion it carries about an axis. It depends on both how massive the object is and how its mass is distributed: a spinning flywheel with most of its mass far from the axis stores much more angular momentum than a compact object spinning at the same rate.<\/p>\n<p>The two input modes of this calculator are physically equivalent. A rigid body is treated as a collection of mass elements, and its resistance to spinning is summarized by the moment of inertia \\(I\\). A point mass on a circular path is the simplest special case, where \\(I = mr^2\\) and \\(\\omega = v\/r\\), so \\(L = I\\omega = mvr\\). If you need \\(I\\) for a common shape, remember: a solid disk is \\(\\tfrac{1}{2}MR^2\\), a thin hoop is \\(MR^2\\), and a solid sphere is \\(\\tfrac{2}{5}MR^2\\).<\/p>\n<p>The SI unit of angular momentum is kg\u00b7m\u00b2\/s, which is identical to the joule-second (J\u00b7s) \u2014 the same unit used for Planck's constant. The calculator also compares your result with the reduced Planck constant \\(\\hbar = 1.055 \\times 10^{-34}\\) J\u00b7s, the natural quantum unit of angular momentum. Everyday rotating objects have angular momenta that are astronomically larger than \\(\\hbar\\), which is why quantum effects are invisible at macroscopic scales.<\/p>\n<p>Interpreting the result: a larger \\(L\\) means more stored rotational motion, so more effort (a bigger torque acting over a longer time) is needed to stop or reverse the rotation. This is directly related to the <a href=\"https:\/\/wpcalc.com\/en\/physics\/impulse-calculator\/\">angular analogue of impulse<\/a> \u2014 torque times time equals the change in angular momentum.<\/p>\n<h2>Conservation of Angular Momentum<\/h2>\n<p>The most important property of angular momentum is that, in the absence of an external torque, it is conserved. A spinning skater who pulls in her arms decreases her moment of inertia, so her angular velocity must increase to keep \\(L = I\\omega\\) constant \u2014 the classic demonstration of this principle. The same physics governs collapsing stellar cores spinning up into neutron stars, gyroscopes, and satellites reorienting with reaction wheels.<\/p>\n<p>Conservation of angular momentum is the rotational counterpart of the conservation of linear momentum, which you can explore with the <a href=\"https:\/\/wpcalc.com\/en\/physics\/momentum-calculator\/\">linear momentum calculator<\/a>, and it complements the <a href=\"https:\/\/wpcalc.com\/en\/physics\/conservation-of-energy-calculator\/\">conservation of energy principle<\/a> in analyzing rotational collisions and spinning systems. For the circular motion underlying the point-mass mode, the <a href=\"https:\/\/wpcalc.com\/en\/physics\/centripetal-force-calculator\/\">centripetal force calculator<\/a> is a useful companion.<\/p>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li><strong>Fixed rotation axis:<\/strong> the calculator assumes rotation about a single, fixed axis. For tumbling objects or rotation about a free axis (like a thrown wrench), angular momentum is a vector and \\(I\\) may change with orientation, which requires vector treatment.<\/li>\n<li><strong>Tangential velocity:<\/strong> in point-mass mode, the velocity must be perpendicular to the radius. The general vector formula is \\(L = mvr\\sin\\theta\\); the calculator uses \\(\\sin\\theta = 1\\), the case of pure circular motion.<\/li>\n<li><strong>Nonnegative inputs:<\/strong> magnitudes only. If you need to distinguish spin directions (clockwise vs counterclockwise), assign the sign yourself: reversing the spin direction flips the sign of \\(L\\) but not its magnitude.<\/li>\n<li><strong>Unit conversions:<\/strong> standard factors are applied automatically \u2014 1 rpm = 0.10472 rad\/s, 1 lb\u00b7ft\u00b2 = 0.04214 kg\u00b7m\u00b2, 1 mph = 0.44704 m\/s \u2014 so you can mix unit systems freely, but results are always reported in SI.<\/li>\n<li><strong>Axis choice matters:<\/strong> the moment of inertia must be the one about the actual rotation axis. Using \\(I\\) about the wrong axis (e.g., about the center vs. about a pivot point) gives a wrong answer.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate angular momentum L from moment of inertia and angular velocity, or from point-mass data (mass, velocity, radius). Enter your values in any unit and get L in kg\u00b7m\u00b2\/s (J\u00b7s).<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[62],"tags":[86],"class_list":["post-65867","post","type-post","status-publish","format-standard","hentry","category-physics","tag-rotational-motion"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65867","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=65867"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65867\/revisions"}],"predecessor-version":[{"id":65932,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65867\/revisions\/65932"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65867"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65867"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}