Physical quantities , vector representation and rectangular coordinate system

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