{"id":1088,"date":"2024-08-07T09:43:10","date_gmt":"2024-08-07T09:43:10","guid":{"rendered":"https:\/\/www.meniit.com\/study-material\/?p=1088"},"modified":"2024-08-07T09:44:10","modified_gmt":"2024-08-07T09:44:10","slug":"motion-in-plane","status":"publish","type":"post","link":"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/motion-in-plane","title":{"rendered":"Motion in a Plane"},"content":{"rendered":"<h2 style=\"text-align: justify;\">Motion In Two Dimension<\/h2>\n<p style=\"text-align: justify;\">The motion of an object is called two dimensional, if two of the three co-ordinates are required to specify the position of the object in space changes w.r.t time.<\/p>\n<p style=\"text-align: justify;\">In such a motion, the object moves in a plane. For example, a billiard ball moving over the billiard table, an insect crawling over the floor of a room, earth revolving around the sun etc.<\/p>\n<p style=\"text-align: justify;\">Two special cases of motion in two dimension are (i) Projectile motion, (ii) 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\/motion-in-plane\/#Motion-in-a-Plane\" title=\"Motion in a Plane\">Motion in a Plane<\/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\/motion-in-plane\/#PROJECTILE-MOTION\" title=\"PROJECTILE MOTION\">PROJECTILE MOTION<\/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\/motion-in-plane\/#Relative-Motion-In-Two-Dimensions\" title=\"Relative Motion In Two Dimensions\">Relative Motion In Two Dimensions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/motion-in-plane\/#Rain-Main-Problems\" title=\"Rain Main Problems\">Rain Main Problems<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/motion-in-plane\/#Circular-Motion\" title=\"Circular Motion\">Circular Motion<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Motion-in-a-Plane\"><\/span>Motion in a Plane<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">For the simplicity let\u2019s consider two mutually perpendicular directions to study the planar motion as <em>x<\/em>-axis and y-axis.<\/p>\n<p style=\"text-align: justify;\">At any time t particle is at (<em>x<\/em>, y) and after an infinitesimally small interval of time dt particle reaches to (<em>x<\/em> + d<em>x<\/em>, y + dy) coordinates.<\/p>\n<p style=\"text-align: justify;\">d<em>x<\/em> and dy are the horizontal (<em>x<\/em>-axis) and vertical (y-axis) components of the displacement.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1089 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-in-a-plane.png\" alt=\"motion-in-a-plane\" width=\"352\" height=\"288\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-in-a-plane.png 352w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-in-a-plane-300x245.png 300w\" sizes=\"auto, (max-width: 352px) 100vw, 352px\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1090 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-in-a-plane-a.png\" alt=\"motion-in-a-plane-a\" width=\"815\" height=\"778\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-in-a-plane-a.png 815w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-in-a-plane-a-300x286.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-in-a-plane-a-768x733.png 768w\" sizes=\"auto, (max-width: 815px) 100vw, 815px\" \/><\/p>\n<p style=\"text-align: justify;\">As we have learnt in vectors that two mutually perpendicular directions are independent of each other. None of them will have any impact on each other. So we can study the motion in a plane as superposition of two separate motions one along <em>x<\/em>-axis and another along y-axis. For solving problems in motion in a plane we apply equations of motion separately along <em>x-axis<\/em> and y-axis.<\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"PROJECTILE-MOTION\"><\/span>PROJECTILE MOTION<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1091 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/projectile-motion.png\" alt=\"projectile-motion\" width=\"681\" height=\"324\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/projectile-motion.png 681w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/projectile-motion-300x143.png 300w\" sizes=\"auto, (max-width: 681px) 100vw, 681px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Types of Projectile Motion<\/strong><\/p>\n<ol style=\"text-align: justify;\">\n<li>Oblique projectile motion.<\/li>\n<li>Horizontal projectile motion.<\/li>\n<\/ol>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1092 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/type-projectile-motion.png\" alt=\"type-projectile-motion\" width=\"685\" height=\"208\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/type-projectile-motion.png 685w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/type-projectile-motion-300x91.png 300w\" sizes=\"auto, (max-width: 685px) 100vw, 685px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Oblique Projectile<\/strong><\/p>\n<p style=\"text-align: justify;\">When a body is thrown at an angle from horizontal then motion under gravity is known as oblique projectile motion.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1093 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/oblique-projectile.png\" alt=\"oblique-projectile\" width=\"967\" height=\"457\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/oblique-projectile.png 967w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/oblique-projectile-300x142.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/oblique-projectile-768x363.png 768w\" sizes=\"auto, (max-width: 967px) 100vw, 967px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Equation of trajectory<\/strong> : A projectile thrown with velocity u at an angle \u03b8 with the horizontal. The velocity u can be resolved into two rectangular components.<\/p>\n<p style=\"text-align: justify;\">u cos\u03b8 component along X-axis and u sin \u03b8 component along Y-axis.<\/p>\n<p style=\"text-align: justify;\">For horizontal motion,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1095 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/equation-of-trajectory.png\" alt=\"equation-of-trajectory\" width=\"876\" height=\"408\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/equation-of-trajectory.png 876w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/equation-of-trajectory-300x140.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/equation-of-trajectory-768x358.png 768w\" sizes=\"auto, (max-width: 876px) 100vw, 876px\" \/><\/p>\n<p style=\"text-align: justify;\">This equation shows that the trajectory of projectile is parabolic because it is similar to equation of parabola<\/p>\n<p style=\"text-align: center;\">y=ax \u2013 b<em>x<\/em><sup>2<\/sup><\/p>\n<p style=\"text-align: justify;\"><strong>Horizontal Projectile<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Trajectory of horizontal projectile: <\/strong>The horizontal displacement <em>x<\/em> is governed by the equation<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1097 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/horizontal-projectile.png\" alt=\"horizontal-projectile\" width=\"912\" height=\"234\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/horizontal-projectile.png 912w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/horizontal-projectile-300x77.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/horizontal-projectile-768x197.png 768w\" sizes=\"auto, (max-width: 912px) 100vw, 912px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Relative-Motion-In-Two-Dimensions\"><\/span>Relative Motion In Two Dimensions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1098 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/relative-motion-in-two-dimensions.png\" alt=\"relative-motion-in-two-dimensions\" width=\"906\" height=\"484\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/relative-motion-in-two-dimensions.png 906w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/relative-motion-in-two-dimensions-300x160.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/relative-motion-in-two-dimensions-768x410.png 768w\" sizes=\"auto, (max-width: 906px) 100vw, 906px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Motion of Man while Crossing a River<\/strong><\/p>\n<p style=\"text-align: justify;\">Consider a man swimming in a river with a velocity of <i><span style=\"font-style: italic;\">V<\/span><\/i><i><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>MR<\/sub> relative to river at an angle of \u03b8 with the river flow. The velocity of river is <i><span style=\"font-style: italic;\">V<\/span><\/i><i><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>R<\/sub>. Let there be two observers I and II.<\/p>\n<p style=\"text-align: justify;\"><strong>Observer I<\/strong> is on ground.<\/p>\n<p style=\"text-align: justify;\"><strong>Observer II\u00a0<\/strong>is on a raft floating along with the river and hence moving with the same velocity as that of river.<\/p>\n<p style=\"text-align: justify;\">Hence motion w.r.t. observer II is same as motion w.r.t. river. i.e., the man will appear to swim at an angle \u03b8 with the river flow for observer II.<\/p>\n<p style=\"text-align: justify;\">For observer I the velocity of swimmer will be <i><span style=\"font-style: italic;\">V<\/span><\/i><i><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>M<\/sub> = <i><span style=\"font-style: italic;\">V<\/span><\/i><i><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>MR<\/sub> + <i><span style=\"font-style: italic;\">V<\/span><\/i><i><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>R<\/sub><\/p>\n<p style=\"text-align: justify;\">Hence the swimmer will appear to move at an angle \u03b8\u2032 with the river flow.<\/p>\n<ol style=\"text-align: justify;\">\n<li>Motion of swimmer for observer I<\/li>\n<li>Motion of swimmer for observer II<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">The motion observed by the observer I is same as the motion with respect to the ground frame of reference.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1102 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-of-swimmer.png\" alt=\"motion-of-swimmer\" width=\"789\" height=\"90\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-of-swimmer.png 789w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-of-swimmer-300x34.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-of-swimmer-768x88.png 768w\" sizes=\"auto, (max-width: 789px) 100vw, 789px\" \/><\/p>\n<p style=\"text-align: justify;\">Here v<sub>MR<\/sub> sin\u03b8 is the component of velocity of man in the direction perpendicular to the river flow. This component of velocity is responsible for the man crossing the river. Hence if the time to cross the river is t,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1104 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-of-swimmer-a.png\" alt=\"motion-of-swimmer-a\" width=\"256\" height=\"76\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Drift<\/strong><\/p>\n<p style=\"text-align: justify;\">It is defined as the displacement of man in the direction of river flow. It is simply the displacement along x-axis, during the period the man crosses the river.<\/p>\n<p style=\"text-align: justify;\">(v<sub>MR<\/sub> cos \u03b8 + v<sub>R<\/sub>) is the component of velocity of man in the direction of river flow and this component of velocity is responsible for drift along the river flow. If drift is x then,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1105 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-of-swimmer-b.png\" alt=\"motion-of-swimmer-b\" width=\"364\" height=\"124\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-of-swimmer-b.png 364w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/motion-of-swimmer-b-300x102.png 300w\" sizes=\"auto, (max-width: 364px) 100vw, 364px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Crossing the River in Shortest Time<\/strong><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1108 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/cross-the-river.png\" alt=\" cross-the-river\" width=\"993\" height=\"130\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/cross-the-river.png 993w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/cross-the-river-300x39.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/cross-the-river-768x101.png 768w\" sizes=\"auto, (max-width: 993px) 100vw, 993px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>NOTE:<\/strong> In the case of crossing the river in shortest time there will be drift along x direction.<\/p>\n<p style=\"text-align: justify;\"><strong>Crossing the River in Shortest Path, Minimum Drift<\/strong><\/p>\n<p style=\"text-align: justify;\">The minimum possible drift is zero. In this case the man swims in the direction perpendicular to the river flow as seen from the ground. This path is known as <strong>Shortest Path.<\/strong><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1110 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/minimum-drift-1.png\" alt=\"minimum-drift\" width=\"928\" height=\"529\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/minimum-drift-1.png 928w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/minimum-drift-1-300x171.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/minimum-drift-1-768x438.png 768w\" sizes=\"auto, (max-width: 928px) 100vw, 928px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Rain-Main-Problems\"><\/span>Rain Main Problems<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">If rain is falling vertically with a velocity <i><span style=\"font-style: italic;\">V<\/span><\/i><i><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>R<\/sub> and an observer is moving horizontally with velocity <i><span style=\"font-style: italic;\">V<\/span><\/i><i><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>M<\/sub>, the velocity of rain to relative observer will be:<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1113 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/rain-main-problems.png\" alt=\"rain-main-problems\" width=\"792\" height=\"453\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/rain-main-problems.png 792w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/rain-main-problems-300x172.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/rain-main-problems-768x439.png 768w\" sizes=\"auto, (max-width: 792px) 100vw, 792px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Circular-Motion\"><\/span>Circular Motion<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Angular Displacement (d\u03b8 or \u03b8)<\/strong><\/p>\n<p style=\"text-align: justify;\">The angle described by radius vector is called angular displacement. Infinitesimal angular displacement is a vector quantity. However, finite angular displacement is<\/p>\n<p style=\"text-align: justify;\"><strong>S.I. Unit :<\/strong> Radian<\/p>\n<p style=\"text-align: justify;\"><strong>Dimension<\/strong> : M\u00b0L\u00b0T\u00b0<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1134 size-full alignnone\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-displacement-1.png\" alt=\"angular displacement\" width=\"891\" height=\"364\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-displacement-1.png 891w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-displacement-1-300x123.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-displacement-1-768x314.png 768w\" sizes=\"auto, (max-width: 891px) 100vw, 891px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Angular Velocity (\u03c9)<\/strong><\/p>\n<p style=\"text-align: justify;\">The rate of change of angular displacement with time is called angular velocity. It is a vector quantity. The angle traced per unit time by the radius vector is called angular speed.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1117 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-velocity.png\" alt=\"angular-velocity\" width=\"842\" height=\"426\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-velocity.png 842w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-velocity-300x152.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-velocity-768x389.png 768w\" sizes=\"auto, (max-width: 842px) 100vw, 842px\" \/><\/p>\n<ul style=\"text-align: justify;\">\n<li><strong>Direction<\/strong> : Infinitesimal angular displacement, angular velocity and angular acceleration are vector quantities whose direction is given by right hand rule.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>Relation Between Angular Velocity and Linear Velocity<\/strong><\/p>\n<p style=\"text-align: justify;\">Suppose the particle moves along a circular path from point A to point B in infinitesimally time dt.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1118\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-velocity-and-linear-velocity.png\" alt=\"angular-velocity-and-linear-velocity\" width=\"922\" height=\"427\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-velocity-and-linear-velocity.png 922w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-velocity-and-linear-velocity-300x139.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-velocity-and-linear-velocity-768x356.png 768w\" sizes=\"auto, (max-width: 922px) 100vw, 922px\" \/><\/p>\n<p style=\"text-align: justify;\">Linear velocity of a particle performing circular motion is the vector product of its angular velocity and radius vector.<\/p>\n<p style=\"text-align: justify;\"><strong>Angular Acceleration (\u03b1)<\/strong><\/p>\n<p style=\"text-align: justify;\">The rate of change of angular velocity with time is called angular acceleration.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1119 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-acceleration.png\" alt=\"angular acceleration\" width=\"690\" height=\"312\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-acceleration.png 690w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-acceleration-300x136.png 300w\" sizes=\"auto, (max-width: 690px) 100vw, 690px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Relation Between Angular Acceleration and Linear Acceleration<\/strong><\/p>\n<p style=\"text-align: justify;\">For perfect circular motion we know\u00a0 \u00a0v = \u03c9r<\/p>\n<p style=\"text-align: justify;\">On differentiating with respect to time<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1122 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-acceleration-a.png\" alt=\"angular acceleration a\" width=\"919\" height=\"177\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-acceleration-a.png 919w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-acceleration-a-300x58.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-acceleration-a-768x148.png 768w\" sizes=\"auto, (max-width: 919px) 100vw, 919px\" \/><\/p>\n<p style=\"text-align: justify;\">It is, therefore not equal to the net acceleration.<\/p>\n<p style=\"text-align: justify;\">Infact it is the component of acceleration along the tangent and hence suffix t is used for tangential acceleration.<\/p>\n<p style=\"text-align: justify;\"><strong>a<sub>t<\/sub> is known as the tangential acceleration.<\/strong><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1123 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-acceleration-b.png\" alt=\"angular acceleration b\" width=\"707\" height=\"42\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-acceleration-b.png 707w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/angular-acceleration-b-300x18.png 300w\" sizes=\"auto, (max-width: 707px) 100vw, 707px\" \/><\/p>\n<p style=\"text-align: justify;\">\n<div class=\"newspaper-x-tags\"><strong>TAGS: <\/strong><span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/angular-displacement\" rel=\"tag\">Angular Displacement<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/angular-velocity\" rel=\"tag\">Angular Velocity<\/a><\/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\/equation-of-trajectory\" rel=\"tag\">Equation of trajectory<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/horizontal-projectile\" rel=\"tag\">Horizontal Projectile<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/linear-velocity\" rel=\"tag\">Linear Velocity<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/motion-in-a-plane\" rel=\"tag\">Motion in a Plane<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/motion-in-two-dimension\" rel=\"tag\">Motion In Two Dimension<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/oblique-projectile\" rel=\"tag\">Oblique Projectile<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/projectile-motion\" rel=\"tag\">Projectile Motion<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/relative-motion-in-two-dimensions\" rel=\"tag\">Relative Motion In Two Dimensions<\/a> <\/div>\n","protected":false},"excerpt":{"rendered":"<p>Motion In Two Dimension The motion of an object is called two dimensional, if two of the three co-ordinates are&nbsp;&nbsp;&#8230;.<a class=\"read_more\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/motion-in-plane\" rel=\"nofollow\">Read More >><\/a><\/p>\n","protected":false},"author":6,"featured_media":1279,"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":[255,254,240],"tags":[386,387,341,383,384,388,380,379,382,381,385],"class_list":["post-1088","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11th-physics","category-class-xith","category-neet","tag-angular-displacement","tag-angular-velocity","tag-circular-motion","tag-equation-of-trajectory","tag-horizontal-projectile","tag-linear-velocity","tag-motion-in-a-plane","tag-motion-in-two-dimension","tag-oblique-projectile","tag-projectile-motion","tag-relative-motion-in-two-dimensions"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/1088","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\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/comments?post=1088"}],"version-history":[{"count":5,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/1088\/revisions"}],"predecessor-version":[{"id":1135,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/1088\/revisions\/1135"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/media\/1279"}],"wp:attachment":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/media?parent=1088"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/categories?post=1088"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/tags?post=1088"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}