{"id":836,"date":"2024-07-17T10:00:18","date_gmt":"2024-07-17T10:00:18","guid":{"rendered":"https:\/\/www.meniit.com\/study-material\/?p=836"},"modified":"2024-10-04T05:12:01","modified_gmt":"2024-10-04T05:12:01","slug":"circular-motion","status":"publish","type":"post","link":"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/circular-motion","title":{"rendered":"Circular Motion"},"content":{"rendered":"<p style=\"text-align: justify;\">For a body moving in a circle of radius R with uniform speed v centripetal acceleration,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-837 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-1-1.png\" alt=\"formula\" width=\"638\" height=\"142\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-1-1.png 638w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-1-1-300x67.png 300w\" sizes=\"auto, (max-width: 638px) 100vw, 638px\" \/><\/p>\n<p style=\"text-align: justify;\">This force acts along the radius and towards the centre of the circle.<\/p>\n<p style=\"text-align: justify;\">For a stone moving in circular path, the centripetal force is provided by tension in the string.<\/p>\n<p style=\"text-align: justify;\">For planets moving around the sun, gravitational force provides the necessary centripetal force.<\/p>\n<p style=\"text-align: justify;\">For a car taking a circular turn on a horizontal road, frictional force provides the centripetal force.<\/p>\n<p style=\"text-align: justify;\">Let us study applications of the laws of motion on the horizontal circular motion.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_69_1 counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/circular-motion\/#Motion-of-a-Car-on-a-Level-Road\" title=\"Motion of a Car on a Level Road\">Motion of a Car on a Level Road<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/circular-motion\/#Motion-of-a-car-on-a-banked-road\" title=\"Motion of a car on a banked road\">Motion of a car on a banked road<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/circular-motion\/#Non-Uniform-Circular-Motion\" title=\"Non Uniform Circular Motion\">Non Uniform Circular Motion<\/a><\/li><\/ul><\/nav><\/div>\n<h3><span class=\"ez-toc-section\" id=\"Motion-of-a-Car-on-a-Level-Road\"><\/span>Motion of a Car on a Level Road<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-839 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-of-a-car.png\" alt=\"Motion of a Car on a Level Road\" width=\"393\" height=\"211\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-of-a-car.png 393w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-of-a-car-300x161.png 300w\" sizes=\"auto, (max-width: 393px) 100vw, 393px\" \/><\/p>\n<p style=\"text-align: justify;\">When a car is moving on a level road, forces acting on the car are :<\/p>\n<ul>\n<li style=\"text-align: justify;\">Its weight, <em>mg<\/em><\/li>\n<li style=\"text-align: justify;\">Normal reaction, N<\/li>\n<li style=\"text-align: justify;\">Frictional force, <em>f<\/em>(along the surface of the road, towards the centre of the turn)<\/li>\n<\/ul>\n<p>N \u2013 mg = 0<br \/>\nN = mg\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8230;(I)<\/p>\n<p style=\"text-align: justify;\">Frictional force, or the component of the contact force between road and the tyres along the surface provides the necessary centripetal force. It is the static friction that provides the centripetal acceleration. It opposes the impending motion of the car moving away from the circle.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-840 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-2.png\" alt=\"formula \" width=\"762\" height=\"156\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-2.png 762w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-2-300x61.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-2-760x156.png 760w\" sizes=\"auto, (max-width: 762px) 100vw, 762px\" \/><\/p>\n<p style=\"text-align: justify;\">Note that this expression is independent of the mass of the car.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-842 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-3.png\" alt=\"formula \" width=\"678\" height=\"80\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-3.png 678w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-3-300x35.png 300w\" sizes=\"auto, (max-width: 678px) 100vw, 678px\" \/><\/p>\n<p>&nbsp;<\/p>\n<div style=\"margin: 5px; padding: 10px; background-color: #fbdfed;\">\n<h4 id=\"example-solution\" style=\"color: #cc1d74;\"><strong>Example : <\/strong><\/h4>\n<p style=\"text-align: justify;\">Find the maximum speed with which a car can turn on a bend without skidding, if radius of bend is 20 m and coefficient of friction between the road and the tyres is 0.4.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-550 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/solution-3.png\" alt=\"solution\" width=\"923\" height=\"372\" \/><\/p>\n<\/div>\n<div style=\"margin: 5px; padding: 10px; background-color: #fbdfed;\">\n<h4 id=\"example-solution\" style=\"color: #cc1d74;\"><strong>Example :\u00a0<\/strong><\/h4>\n<p style=\"text-align: justify;\">A cyclist speeding at 4.5 km\/h on a level road takes a sharp circular turn of radius 3 m without reducing the speed. The coefficient of static friction between the road and the tyres is 0.1.<\/p>\n<p style=\"text-align: justify;\">(i) Will he slip while taking the turn?<\/p>\n<p style=\"text-align: justify;\">(ii) Will he slip if his speed is 9 km\/h?<\/p>\n<p style=\"text-align: justify; color: #cc1d74;\"><strong>SOLUTION:\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\">Frictional force provides the necessary centripetal force. He will slip if his speed is large, than the safe speed of turning. Maximum speed for not slipping is<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-550 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/solution-4-1.png\" alt=\"example 3\" width=\"923\" height=\"372\" \/><\/p>\n<\/div>\n<h3><span class=\"ez-toc-section\" id=\"Motion-of-a-car-on-a-banked-road\"><\/span>Motion of a car on a banked road<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Motion of a car on a rough banked road<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-845 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/Motion-of-a-car-on-a-banked-road.png\" alt=\"Motion of a car on a banked road\" width=\"633\" height=\"281\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/Motion-of-a-car-on-a-banked-road.png 633w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/Motion-of-a-car-on-a-banked-road-300x133.png 300w\" sizes=\"auto, (max-width: 633px) 100vw, 633px\" \/><\/p>\n<p style=\"text-align: justify;\">If we want to increase the maximum possible speed then the road should be banked as shown in the figure (this is the phenomenon of raising outer edge of the curved road above the inner edge) by this we can reduce the contribution of friction to the circular motion of the car.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-846 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-4.png\" alt=\"formula\" width=\"740\" height=\"465\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-4.png 740w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-4-300x189.png 300w\" sizes=\"auto, (max-width: 740px) 100vw, 740px\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-847 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-5.png\" alt=\"formula \" width=\"720\" height=\"201\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-5.png 720w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-5-300x84.png 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/>This speed is known as optimum speed.<\/p>\n<p style=\"text-align: justify;\">At this speed, frictional force is not required at all to provide centripetal force. Driving at this speed causes little wear and tear of the tyres. If speed of car is less than this, frictional force will be up the slope.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-848 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-6-1.png\" alt=\"formula\" width=\"722\" height=\"150\" \/><\/p>\n<div style=\"margin: 5px; padding: 10px; background-color: #fbdfed;\">\n<h4 id=\"example-solution\" style=\"color: #cc1d74;\"><strong>Example :\u00a0<\/strong><\/h4>\n<p style=\"text-align: justify;\">A circular racetrack of radius 100 m is banked at an angle of 45\u00b0. What is the<\/p>\n<p style=\"text-align: justify;\">(i) Optimum speed of race car to avoid wear and tear of its tyres?<\/p>\n<p style=\"text-align: justify;\">(ii) Maximum permissible speed to avoid slipping if the coefficient of friction is 0.2?<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-550 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/solution-5.png\" alt=\"solution\" width=\"923\" height=\"372\" \/><\/p>\n<\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Non-Uniform-Circular-Motion\"><\/span>Non Uniform Circular Motion<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">When a particle is moving in a circle with changing speed (v), in addition to the centripetal acceleration v<sup>2<\/sup>\/r, a tangential acceleration a<sub>t<\/sub> = dv\/dt is also a component of the acceleration \u201ca\u201d of the particle. That is<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-850 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-7.png\" alt=\"formula\" width=\"735\" height=\"304\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-7.png 735w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-7-300x124.png 300w\" sizes=\"auto, (max-width: 735px) 100vw, 735px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-937 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/uniform-circular-motion-e1721471930611.png\" alt=\"uniform-circular-motion\" width=\"792\" height=\"211\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/uniform-circular-motion-e1721471930611.png 792w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/uniform-circular-motion-e1721471930611-300x80.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/uniform-circular-motion-e1721471930611-768x205.png 768w\" sizes=\"auto, (max-width: 792px) 100vw, 792px\" \/><\/p>\n<div style=\"padding: 10px; background-color: #d4effc;\">\n<p style=\"text-align: justify;\"><strong>Consider the statement :<\/strong> \u201cThe force acting on a particle moving on a circular path is centripetal\u201d. This statement is true only when the speed of the particle is constant. The correct statement should be like this,<\/p>\n<p style=\"text-align: justify;\">\u201cThere must be a centripetal component of the force acting on the particle moving on a circular path\u201d.<\/p>\n<p style=\"text-align: justify;\">The tangential component of the force acting on the particle moving on a circular path is nonzero only when the speed is changing otherwise it is zero.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div style=\"margin: 5px; padding: 10px; background-color: #fbdfed;\">\n<p id=\"example-solution\" style=\"color: #cc1d74;\"><strong>Example : <\/strong><\/p>\n<p style=\"text-align: justify;\">A car starts from rest on a horizontal circular road of radius 190 m and gains speed at a uniform rate of 1.2 m\/s<sup>2<\/sup>, The coefficient of static friction between the road and the tyres is 0.37. Calculate the distance travelled by the car before it begins to skid.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-550 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/solution-6.png\" alt=\"solution\" width=\"923\" height=\"372\" \/><\/p>\n<\/div>\n<div class=\"newspaper-x-tags\"><strong>TAGS: <\/strong><span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/circular-motion\" rel=\"tag\">Circular Motion<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/motion-of-a-car-on-a-banked-road\" rel=\"tag\">Motion of a car on a banked road<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/motion-of-a-car-on-a-level-road\" rel=\"tag\">Motion of a Car on a Level Road<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/non-uniform-circular-motion\" rel=\"tag\">Non Uniform Circular Motion<\/a> <\/div>\n","protected":false},"excerpt":{"rendered":"<p>For a body moving in a circle of radius R with uniform speed v centripetal acceleration, This force acts along&nbsp;&nbsp;&#8230;.<a class=\"read_more\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/circular-motion\" rel=\"nofollow\">Read More >><\/a><\/p>\n","protected":false},"author":5,"featured_media":1230,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"om_disable_all_campaigns":false,"rank_math_lock_modified_date":false,"footnotes":""},"categories":[255,254,253],"tags":[341,343,342,344],"class_list":["post-836","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11th-physics","category-class-xith","category-jee","tag-circular-motion","tag-motion-of-a-car-on-a-banked-road","tag-motion-of-a-car-on-a-level-road","tag-non-uniform-circular-motion"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/836","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/comments?post=836"}],"version-history":[{"count":20,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/836\/revisions"}],"predecessor-version":[{"id":1602,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/836\/revisions\/1602"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/media\/1230"}],"wp:attachment":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/media?parent=836"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/categories?post=836"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/tags?post=836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}