Physical quantities and vector representation
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This document discusses vectors and the rectangular coordinate system. It defines vectors as physical quantities that require both magnitude and direction, while scalars only require magnitude. Vectors can be represented symbolically with bold letters or graphically with arrows. The rectangular coordinate system uses two perpendicular axes, usually labeled x and y, that intersect at the origin point. Vectors in 2D space are defined by their coordinates on the x and y axes, while vectors in 3D space additionally use a z axis and are defined by their coordinates on all three axes.
Physical quantities and vector representation
- 2. Lecture No : 1 Chapter 2 VECTORS AND EQUILIBRIUM Topic BASIC CONCEPTS OF VECTORS2.1 LECTURER: ZEESHAN QASIM
- 3. Outline Physical Quantities Vector Representation Rectangular Coordinate System
- 4. Physical Quantities Definition Those quantities which can be observed ,measured and have some physical significance are called physical quantities. Those quantities in terms of which all the laws of physics can be expressed are called physical quantities Types of Physical Quantities Scalars Vectors Scalars Physical quantiles which are completely describe by magnitude with suitable or specific units are called scalar quantities Examples Time , Distance , Mass , Temperature, speed, volume , Area etc.
- 5. Vectors Physical quantities which require both magnitude and direction for complete description are called vector quantities Three Keys Magnitude Suitable or specific unit Direction Example Force , velocity ,displacement ,torque momentum Acceleration, weight etc
- 6. Vector Representation Symbolic Representation Graphically Representation Arrow Head Representation e.g. A Bold face Representation e.g. A Y P O X
- 7. Vectors are represented in two ways. (1) Symbolic Representation (2) Graphical representation Symbolic Representation In this type, vector is represented by a Bold face latter such as A , d, r and v etc .it can be represented by a letter that have an arrow above the letter as A . Graphical Representation In this type, vector is represented by a straight line with an arrow head at its one end .The length line is selected according to a suit able scale .This length representation of magnitude of vector . Arrow head placed at one end represented by direction of vector. Representation of magnitude of vector . The magnitude of any vector is represented by light face letter such as A, d , r and v or by the modulus of a vector such as A and V
- 8. Rectangular Coordinate System Second Name: Cartesian Co-ordinate System Coordinate axes and Origen Two references lines drawn at right angles to each other are known as coordinate axes And their point of intersection is known as Origin. This system of coordinate axes is called Cartesian or rectangular coordinate system. Cartesian Co-ordinate System The coordinate system of two Mutually perpendicular lines is called Cartesian Co-ordinate System One of the lines is names as x-axis and y-axes. Usually the x-axes is taken as horizontal axis ,positive direction to right side. The other line called y-axis and is taken as a vertical axis ,positive direction to upward.
- 9. Two –dimensional co-ordinate System The coordinate system of two Mutually perpendicular lines is called Cartesian Co-ordinate System Y X` X O Y` Fig (a) Y P(a,b) d b 𝐗` 𝜽 X O a y` Fig(b) The point p shown in fig(b) has coordinates (a,b). This notation means that if we start at the origin , we can reach P by moving a unit along the positive x-axis and then b unit along the positive y-axis. Direction of a vector is represented by the angle 𝛉 𝐰𝐡𝐢𝐜𝐡 𝐭𝐡𝐞 𝐯𝐞𝐜𝐭𝐨𝐫 𝐦𝐚𝐤𝐞𝐬 𝐰𝐢𝐭𝐡 𝐩𝐨𝐬𝐢𝐭𝐢𝐯𝐞 𝐱 − 𝐚𝐱𝐢𝐬 𝐢𝐧 𝐚𝐧𝐭𝐢 − 𝐜𝐥𝐨𝐜𝐤 𝐰𝐢𝐬𝐞 𝐝𝐢𝐫𝐞𝐜𝐭𝐢𝐨𝐧
- 10. Three –dimensional co-ordinate System The coordinate system of Three Mutually perpendicular lines is called Cartesian Co-ordinate System z o y x Fig(a) z P(a,b,c) 𝜸 o 𝜷 y 𝜶 x Fig (b) The direction of a vector in space requires another axis which is at right angle to both X and Y axis as shown in fig (a) . The third axis is called Z –axis The direction of a vector in space is specified by the three angles which the representative line of the vector makes with x,y and z axis in shown fig(b) The point p of a vector A is denoted by three co-ordinates (a,b,c) . It is represented by three angles 𝜶, 𝜷, 𝜸 which the vector makes with x,y and z –axis