Tiêu đề 2. VECTOR_SYN _ W.S-1 TO 4 _VOL-1_(8 TO 60).pdf ✅

Olympiad Class Work Book VIII – Physics (Vol – I) CONCEPT FLOW CHART Physical Quanitites Scalars With units Parallelogram Law Scalar Product Without units Types of Vectors Triangle Law Lami’s Theorem Polygon Law Vector Product Addition Multiplication Operations Vectors Oliver Heaviside Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, Vector Analysis.
VIII – Physics (Vol – I) Olympiad Class Work Book VECTORS Introduction to scalars and vectors: Based on the mathematical behaviour of all the physical quantities are classi- fied into various types. Among them, we are going to discuss two categories based on their importance in dealing with physical quantities. They are 1) Scalar physical quantities 2) Vector physical quantities Scalar Physical quantities. 1. It can be also defined as the physical quantities which have only magnitude but no direction are called scalar quantities Examples: Length, Mass, Time, Temperature, Area, Volume, Distance covered etc. 2. The physical quantity that follows simple algebra is called scalar physical quantity or simply “scalar”. 3. For the case of 2 kg sugar, tells about the magnitude of its mass but has no direction. 4. The scalars can be added, subtracted, multiplied and divided by ordinary laws of algebra 5. A scalar is specified by a number and unit, where number represents its magnitude 6. A scalar may be positive or negative. A scalar can be represented by a single letter. Vector physical quantities: 1. A physical quantity which follows the vector law of addition and with specified direction is called vector physical quantity or simply “vector”. 2. It can also be defined as the physical quantities which are expressed in mag- nitude as well as direction are called vector quantities are simply called as vectors. They should also obey law of vector addition 3. Vectors has both magnitude and direction 4. Displacement, velocity, acceleration, force, magnetic field induction are a few examples of vectors 5. Vectors cannot be added, subtracted and multiplied by ordinary laws of algebra 6. A vector in writing, can be represented by either by a single letter in bold face or by a single letter with an arrow head on it. Example: Displacement = S or S  Note: 1) If a vector is displaced parallel to itself it does not change. (magnitude and direction remains same) 2) If a vector is rotated through an angle other than multiple of 2 or 0 360 it changes. (magnitude remains same but direction changes)
Olympiad Class Work Book VIII – Physics (Vol – I) 3) If the frame of reference is translated or rotated the vector does not change (through its component may change.) x y Translation of a vector parallel to itself A B C A B C Rotation of a vector x y B A A B O x y Vector O ' y ' x ' Representation of a vector: 1. Geometrically or graphically a vector is represented by a straight line with an arrow head i.e. arrowed line (). 2. Here, the length of the arrowed line drawn on a suitable scale represents the magnitude and the arrow head represents the direction of the given vector. 3. For example, when an object goes on the path ABC, then the displacement of the object is AC . The arrow head at ‘C’ show that the object is displaced from A to C. 4. The magnitude of a vector is denoted as a or a 5. The magnitude of a vector is scalar Distance Displacement B A C Note: Properties of a vector: 1) In addition to magnitude and unit a) It has a specified direction b) It obeys parallelogram law of vector addition c) Their addition is Commutative A B B A        2) Graphical representation of vectors: Graphically a vector is represented by a line with an arrow head. Length of line shows the magnitude and arrow shows the direction. Tail Head base
VIII – Physics (Vol – I) Olympiad Class Work Book SOME IMPORTANT POINTS REGARDING VECTORS: a) If a vector is displaced parallel to itself it does not change. A B C A B C b) If a vector is rotated through an angle other than multiple of 2 or 0 360 it changes Cartesian co-ordinate system: 1) In order to describe the motion of an object we must specify its position relative to observer. 2) One of the most convenient co-ordinate system is Cartesian co-ordinate sys- tem. It consists of three mutually perpendicular axes designated as X-axis, Y- axis and Z-axis 3) Location of any X, Y and Z as shown in the figure. y P x z X Y Z Types of vectors: 1. Equal vectors: If two vectors have same magnitude and direction they are said to be equal vectors. A B A B