{"id":199328,"date":"2025-03-11T15:16:36","date_gmt":"2025-03-11T15:16:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199328"},"modified":"2025-03-11T15:16:48","modified_gmt":"2025-03-11T15:16:48","slug":"write-down-the-equation-to-calculate-the-torque-if-the-magnitude-of-a-force-and-the-lever-arm-are-given","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/11\/write-down-the-equation-to-calculate-the-torque-if-the-magnitude-of-a-force-and-the-lever-arm-are-given\/","title":{"rendered":"Write down the equation to calculate the torque if the magnitude of a force and the lever arm are given"},"content":{"rendered":"\n<p>Write down the equation to calculate the torque if the magnitude of a force and the lever arm are given.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Torque Equation<\/strong><\/h3>\n\n\n\n<p>The equation to calculate torque ((\\tau)) when the magnitude of the force ((F)) and the lever arm ((r)) are given is:<\/p>\n\n\n\n<p>[<br>\\tau = r \\times F \\times \\sin(\\theta)<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(\\tau) = Torque (measured in Newton-meters, Nm)<\/li>\n\n\n\n<li>(r) = Lever arm (distance from the pivot point to the point where the force is applied, measured in meters)<\/li>\n\n\n\n<li>(F) = Force applied (measured in Newtons, N)<\/li>\n\n\n\n<li>(\\theta) = Angle between the force vector and the lever arm<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 words)<\/strong><\/h3>\n\n\n\n<p>Torque is a measure of the rotational force applied to an object around a pivot point. It determines how effectively a force can cause an object to rotate. The greater the torque, the greater the tendency of an object to rotate.<\/p>\n\n\n\n<p>The equation (\\tau = r \\times F \\times \\sin(\\theta)) incorporates three key factors:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Lever Arm ((r))<\/strong> \u2013 The distance from the pivot point to the point where force is applied. A longer lever arm increases torque, making it easier to rotate an object.<\/li>\n\n\n\n<li><strong>Force ((F))<\/strong> \u2013 The magnitude of the applied force. A larger force generates a greater torque.<\/li>\n\n\n\n<li><strong>Angle ((\\theta))<\/strong> \u2013 The effectiveness of the force depends on its direction. The torque is maximum when the force is applied perpendicular to the lever arm ((\\theta = 90^\\circ), where (\\sin(90^\\circ) = 1)). If the force is applied parallel ((\\theta = 0^\\circ)), no torque is produced ((\\sin(0^\\circ) = 0)).<\/li>\n<\/ol>\n\n\n\n<p>In practical applications, torque is crucial in machines, engines, and tools like wrenches. For example, when using a wrench to tighten a bolt, increasing the length of the wrench handle (lever arm) or applying more force increases the torque, making it easier to turn the bolt.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Write down the equation to calculate the torque if the magnitude of a force and the lever arm are given. The correct answer and explanation is : Torque Equation The equation to calculate torque ((\\tau)) when the magnitude of the force ((F)) and the lever arm ((r)) are given is: [\\tau = r \\times F [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-199328","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199328","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=199328"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199328\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199328"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199328"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}