25/01/2014
Chapter 2: Vectors (components)
 We will learn in this chapter:
 Magnitude of a vector
King Saud University
College of Science
Physics & Astronomy Dept.
 Components of a vector
 Adding vectors
Phys 145 (General Physics)
Chapter 2: Vectors (Components)
Week n° 02
This presentation has been prepared by: Pr. Nabil BEN NESSIB
1
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
2
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
Magnitude and direction of a vector
Introduction: Scalar and vector quantities


A vector V (or V ) is defined by its direction  and magnitude V = |V|=| V |:
 In Physics quantities can be:
y
 Scalar quantities (Magnitude): ‫ﻛﻤﯿﺔ ﻗﯿﺎﺳﯿﺔ‬
Examples: mass, energy, time.
V
 Vector quantities (Magnitude and Direction): ‫ﻛﻤﯿﺔ ﻣﺘّﺠﮭﺔ‬

Examples: velocity, acceleration, Force.
O
 The magnitude (length of the vector) is a positive number.
x
 The direction is the angle between the vector and the positive
axis.
It is between 0° and 360° (between 0 and 2π radians).
Remark: The bold notation of a vector (V) is the printed notation.

3
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
The arrow notation of a vector ( V ) is the handwritten notation.
4
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
1
25/01/2014
Equality of vectors
Components of a vector
Two vectors are equal if they have the same magnitude and the same direction.

V1

V2

V3

y
Fy


V4
O

Fx
x
Fx
; so Fx  F cos  
F
F
sin    y ; so Fy  F sin  
F
We have only: V1  V2
All the other vectors are different.
cos   
5
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
Addition of two vectors
Fx and Fy are the components of the vector F.
6
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
Addition of two vectors
Analytic method (Using the components of each vector)
Geometric method (Parallelogram construction)
y
y
F1
Fy
F
F1y
F1
F
F2y
F2
O
F
O F
F2x Fx
1x
   

F  F1  F2 or F1  F1x xˆ  F1 y yˆ and F2  F2 x xˆ  F2 y yˆ
x
7
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
F2
x
So:

F   F1x  F2 x  xˆ   F1 y  F2 y  yˆ
8
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
2
25/01/2014
Video 01 of Chapter 02:
Adding vectors
Multiplication of a vector by a scalar
A unit vector is a vector having 1 as magnitude.

The negative of a vector (  V ) is defined as the vector that

when added to the original vector ( V ) gives zero.
When multiplying a vector by a positive scalar k , we obtain a
new vector having the same direction and the magnitude is
multiplied by k.
y
kF
F
O
9
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
x
10
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
Video 02 of Chapter 02:
Scalars and vectors
Summary of week 02
 Magnitude and direction of a vector are defined.
 Components of a vector are defined.
 How to add vectors is explained.
 How to multiply a vector by a scalar is explained.
11
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
12
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
3
25/01/2014
Quiz for week 02
End of Chapter 2
13
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
14
King Saud University, College of Science, Physics & Astronomy Dept. Phys 145(General Physics) © 2014
4