{"id":22171,"date":"2022-01-13T18:32:22","date_gmt":"2022-01-13T13:02:22","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=22171"},"modified":"2025-02-28T16:14:24","modified_gmt":"2025-02-28T10:44:24","slug":"motion-in-a-plane-class-11-notes-physics-chapter-4","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/motion-in-a-plane\/class-11\/notes-physics\/chapter-4\/","title":{"rendered":"Motion in a Plane Class 11 Notes Physics Chapter 4"},"content":{"rendered":"<h2>Motion in a Plane Class 11 Notes Physics Chapter 4<\/h2>\n<p><strong>\u2022 Motion<\/strong> in a plane is called as motion in two dimensions e.g., projectile motion, circular motion etc. For the analysis of such motion our reference will be made of an origin and two co-ordinate axes X and Y.<\/p>\n<p><strong>\u2022 Scalar and Vector Quantities<\/strong><br \/>\nScalar Quantities. The physical quantities which are completely specified by their magnitude or size alone are called scalar quantities.<br \/>\nExamples. Length, mass, density, speed, work, etc.<\/p>\n<p>Vector Quantities. Vector quantities are those physical quantities which are characterised by both magnitude and direction.<br \/>\nExamples. Velocity, displacement, acceleration, force, momentum, torque etc.<\/p>\n<p><strong>\u2022 Characteristics of Vectors<\/strong><br \/>\nFollowing are the characteristics of vectors:<br \/>\n(i) These possess both magnitude and direction.<br \/>\n(ii) These do not obey the ordinary laws of Algebra.<br \/>\n(iii) These change if either magnitude or direction or both change.<br \/>\n(iv) These are represented by bold-faced letters or letters having arrow over them.<\/p>\n<p><strong>\u2022 Unit Vector<\/strong><br \/>\nA unit vector is a vector of unit magnitude and points in a particular direction. It is used to specify the direction only. Unit vector is represented by putting a cap (^) over the quantity.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32585853312_72c0d763f8_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-1\" width=\"641\" height=\"115\" \/><\/p>\n<p><strong>\u2022 Equal Vectors<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32585853252_e27f3152fa_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-2\" width=\"815\" height=\"42\" \/><\/p>\n<p><strong>\u2022 Zero Vector<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32585853192_1407089d49_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-3\" width=\"859\" height=\"58\" \/><\/p>\n<p><strong>\u2022 Negative of a Vector<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32585853122_82f7acbe16_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-4\" width=\"861\" height=\"122\" \/><\/p>\n<p><strong>\u2022 Parallel Vectors<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32359440550_13ba57ba6e_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-5\" width=\"877\" height=\"63\" \/><\/p>\n<p><strong>\u2022 Coplanar Vectors<\/strong><br \/>\nVectors are said to be coplanar if they lie in the same plane or they are parallel to the same plane, otherwise they are said to be non-coplanar vectors.<\/p>\n<p><strong>\u2022 Displacement Vector<\/strong><br \/>\nThe displacement vector is a vector which gives the position of a point with reference to a point other than the origin of the co-ordinate system.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32585852882_9c9e6cf1b6_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-6\" width=\"312\" height=\"42\" \/><\/p>\n<p><strong>\u2022 Parallelogram Law of Vector Addition<\/strong><br \/>\nIf two vectors, acting simultaneously at a point, can be represented both in magnitude and direction by the two adjacent sides of a parallelogram drawn from a point, then the resultant is represented completely both in magnitude and direction by the diagonal of the parallelogram passing through that point.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32359440450_e2c7f87cbf_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-7\" width=\"892\" height=\"341\" \/><br \/>\n<strong>\u2022 Triangle Law of Vector Addition<\/strong><br \/>\nIf two vectors are represented both in magnitude and direction by the two sides of a triangle taken in the same order, then the resultant of these vectors is represented both in magnitude and direction by the third side of the triangle taken in the opposite order.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/31896122194_0552fdeda1_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-8\" width=\"854\" height=\"61\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32359440360_f18cfb3257_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-9\" width=\"859\" height=\"683\" \/><\/p>\n<p><strong>\u2022 Polygon Law of Vector Addition<\/strong><br \/>\nIf a number of vectors are represented both in magnitude and direction by the sides of a polygon taken in the same order, then the resultant vector is represented both in magnitude and direction by the closing side of the polygon taken in the opposite order.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/31896122044_9de84470ef_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-10\" width=\"442\" height=\"362\" \/><\/p>\n<p><strong>\u2022 Properties of Vector Addition<\/strong><br \/>\nVector addition has following properties:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32615800231_d630ec7876_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-11\" width=\"410\" height=\"213\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32585852702_8060bbaef4_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-12\" width=\"874\" height=\"521\" \/><\/p>\n<p><strong>\u2022 Resolution of Vectors<\/strong><br \/>\nIt is a process of splitting a single vector into two or more vectors in different directions which together produce the same effect as is produced by the single vector alone.<br \/>\nThe vectors into which the given single vector is splitted are called component of vectors. In fact, the resolution of a vector is just opposite to composition of vectors.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32359440230_4e6099e40f_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-13\" width=\"804\" height=\"384\" \/><br \/>\nIf the components of a given vector are perpendicular to each other, then they are called rectangular components.<br \/>\n<strong>\u2022 Position Vector<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32615800051_21727cb8cb_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-14\" width=\"859\" height=\"304\" \/><\/p>\n<p><strong>\u2022 Multiplication of Vectors<\/strong><br \/>\n(i) Scalar product (Dot product). Scalar product of two vectors is defined as the product of the magnitude of two vectors with cosine of smaller angle between them.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32585852362_f648e78058_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-15\" width=\"886\" height=\"368\" \/><br \/>\n<strong>\u2022 Properties of Scalar Product<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32698847606_41759cbc62_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-16\" width=\"821\" height=\"327\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32585852032_be215e58ab_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-17\" width=\"775\" height=\"322\" \/><\/p>\n<p><strong>\u2022 Properties of Cross Product<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32698847306_b68aaa75b7_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-18\" width=\"703\" height=\"690\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32615799831_b08fd3a27c_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-19\" width=\"662\" height=\"567\" \/><br \/>\n<strong>\u2022 Lami\u2019s Theorem<\/strong><br \/>\nLami\u2019s theorem states, \u201cIf a particle under the simultaneous action of three forces is in equilibrium, then each force has a constant ratio with the sine of the angle between the other two forces.\u201d<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32585851822_8743b07eec_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-20\" width=\"278\" height=\"237\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/31896120884_8c1ce8d969_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-21\" width=\"474\" height=\"136\" \/><br \/>\n<strong>\u2022 Projectile Motion<\/strong><br \/>\nThe projectile is a general name given to an object that is given an initial inclined velocity and which subsequently follows a path determined by the gravitational force acting on it and by the frictional resistance of the air. The path followed by a projectile is called its trajectory.<br \/>\nEquation of projectile motion. The general case of projectile motion corresponds to that of an object that has been given an initial velocity u at some angle 8 above (or below) the horizontal. The horizontal and vertical displacements x and y are given by<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32615799691_6a3cfe2b2d_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-22\" width=\"732\" height=\"565\" \/><\/p>\n<p><strong>\u2022 Angular Displacement<\/strong><br \/>\nAngular displacement of the object moving around a circular path is defined as the angle traced out by the radius vector at the centre of the circular path in a given time.<br \/>\n\u03b8 (angle) = arc\/radius<br \/>\n\u03b8 \u2014&gt; the magnitude of angular displacement. It is expressed in radians (rad).<\/p>\n<p><strong>\u2022 Angular Velocity<\/strong><br \/>\nAngular velocity of an object in circular motion is defined as the time rate of change of its angular displacement.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/31896120584_386d7f3499_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-24\" width=\"519\" height=\"83\" \/><\/p>\n<p><strong>\u2022 Angular Acceleration<\/strong><br \/>\nAngular acceleration of an object in circular motion is defined as the time rate of change of its angular velocity.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/31896120414_259ccf7709_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-25\" width=\"637\" height=\"210\" \/><br \/>\n<strong>\u2022 Uniform Circular Motion<\/strong><br \/>\nWhen a body moves in a circular path with a constant speed, then the motion of the body is known as uniform circular motion.<br \/>\nThe time taken by the object to complete one revolution on its circular path is called time period. For circular motion, the number of revolutions completed per unit time is known as the frequency (v). Unit of frequency is 1 Hertz (1 Hz). It is found that<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32615799441_01a5fed906_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-26\" width=\"620\" height=\"120\" \/><br \/>\n<strong>\u2022 Centripetal Acceleration<\/strong><br \/>\nTo maintain a particle in its uniform circular motion a radially inward acceleration should be continuously maintained. It is known as the centripetal acceleration.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/31896120234_f5ecd4bbf9_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-27\" width=\"301\" height=\"50\" \/><br \/>\n<strong>\u2022 IMPORTANT TABLES<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/31896120284_73dfd77991_o.png\" alt=\"motion-in-a-plane-cbse-notes-for-class-11-physics-28\" width=\"754\" height=\"702\" \/><\/p>\n<h4><\/h4>\n","protected":false},"excerpt":{"rendered":"<p>Motion in a Plane Class 11 Notes Physics Chapter 4 \u2022 Motion in a plane is called as motion in [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"Notes for Class 11 Physics Chapter 4 Motion in a 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