Chapter 1: Physical Quantities Unit, And Vectors

1. FOUNDATION AND MATRICS SCIENCE
STUDIES
PART 1

2. 1.PHYSICS PART 1
1.PHYSICS
1.1 INTRODUCTION TO PHYSICS
1.2 KINETIC MOTION
1.3 NEWTON LAW

3. 2.MATHEMATICS PART I
1.MATHEMATICS 1
1.1 NUMBER SYSTEMS
1.2 EQUATIONS,INEQUALITIES AND ABSOLUTE
1.3 POLYNOMINALS
1.4 SEQUENCES AND SERIES

4. PHYSICS CHAPTER 1
1
CHAPTER 1:
Physical quantities and
measurements
(3 Hours)
CHAPTER 1
PHYSI CAL
QUANTI TI ES,
u n i t
AND vect or s

5. 5
At the end of this chapter, students should be able to:
• State basic quantities and their respective SI units: length (m),
time (s), mass (kg), electrical current (A), temperature (K), amount
of substance (mol) and luminosity (cd).
State derived quantities and their respective units and symbols:
velocity (m s-1), acceleration (m s-2), work (J), force (N), pressure
(Pa), energy (J), power (W) and frequency (Hz).
Learning Outcome:
1.1 Physical Quantities and Units (1 hours)
2

6. 6
• Physical quantity is defined as a physical property that can be expressed in numbers
• It can be categorized into 2 types
– Basic (base) quantity
– Derived quantity
• Basic quantity is defined as a quantity that cannot be expressed in terms of other quantities.
• Table 1.1 shows all the basic (base) quantities.
1.1 Physical Quantities and Units

7. 7
• Derived quantity is defined as a quantity which can be expressed in term of
base quantity.
• Table 1.2 shows some examples of derived quantity.
Derived quantity Symbol Formulae Unit
Velocity v s/t m s-1
Volume …….. l  w  t m 3
Acceleration a v/t m s-2
Density  m/V …………….
Momentum p ………… kg m s-1
Force ……… m  a kg m s-2 @ N
Work W F  s ……….. @ J
Pressure P F/A N m-2 @ ……
Frequency f 1/T s-1 @ ……..

8. 8
 It is used for presenting larger and smaller values.
 Table 1.3 shows all the unit prefixes.
1.1.1 Unit Prefixes

9. 9
At the end of this chapter, students should be able to:
a)Define scalar and vector quantities,
b)Perform vector addition and subtraction operations
graphically.
c)Resolve vector into two perpendicular components (2-D)
– Components in the x and y axes.
– Components in the unit vectors in Cartesian coordinate.
Learning Outcome:
1.2 Scalars and Vectors

10. 10
At the end of this topic, students should be able to:
d) Define and use dot (scalar) product;
e) Define and use cross (vector) product;
Direction of cross product is determined by corkscrew
method or right hand rule.
Learning Outcome:
1.2 Scalars and Vectors
   
θ
A
B
θ
B
A
B
A cos
cos 




   
θ
A
B
θ
B
A
B
A sin
sin 





11. 11
• Scalar quantity is defined as a quantity
with magnitude only.
– e.g. mass, time, temperature, pressure, electric current, work,
energy and etc.
– Mathematics operational : ordinary algebra
• Vector quantity is defined as a quantity
with both magnitude & direction.
– e.g. displacement, velocity, acceleration, force, momentum,
electric field, magnetic field and etc.
– Mathematics operational : vector algebra
1.2 Scalars and Vectors

12. 12
• Table 1.4 shows written form (notation) of vectors.
• Notation of magnitude of vectors.
1.2.1 Vectors
s

Vector A
Length of an arrow– magnitude of vector A
displacement velocity acceleration
v

a

s a
v
v
v 

a
a 

s (bold) v (bold) a (bold)
Direction of arrow – direction of vector A

13. 13
• Two vectors equal if both magnitude and direction are the same. (shown in
figure 1.1)
• If vector A is multiplied by a scalar quantity k
– Then, vector A is
• if k = +ve, the vector is in the same direction as vector A.
• if k = -ve, the vector is in the opposite direction of vector A.
P
 Q

Q
P



Figure 1.1
A
k

A
k

A

A



14. 14
Can be represented by using:
a) Direction of compass, i.e east, west, north, south, north-east, north-west,
south-east and south-west
b)Angle with a reference line
e.g. A boy throws a stone at a velocity of 20 m s-1, 50 above horizontal.
1.2.2 Direction of Vectors
50
v

x
y
0

15. 15
c) Cartesian coordinates
• 2-Dimension (2-D)
m)
5
m,
1
(
)
,
( 
 y
x
s

s

y/m
x/m
5
1
0

16. 16
• 3-Dimension (3-D)
s

2
3
4
m
2)
3,
4,
(
)
,
,
( 
 z
y
x
s

y/m
x/m
z/m
0
...i +...j + ..k
s 

17. 17
d)Polar coordinates
e) Denotes with + or – signs.
 


N,150
30

F
F

150
+
+
-

18. 18
• There are two methods involved in addition of vectors graphically i.e.
– Parallelogram
– Triangle
• For example :
1.2.3 Addition of Vectors
Parallelogram Triangle
B

A

B

A

B
A



O
B
A



B

A

B
A



O

19. 19
• Triangle of vectors method:
a)Use a suitable scale to draw
vector A.
b)From the head of vector A draw a
line to represent the vector B.
c)Complete the triangle. Draw a line
from the tail of vector A to the
head of vector B to represent the
vector A + B.
A
B
B
A







Commutative Rule
B

A

A
B



O

20. 20
• For example :
1.2.4 Subtraction of Vectors
Parallelogram Triangle
D

C

O
D
C



O
......
 
D
C
D
C








C

D


D
C



C

D


D
C




21. 21
• notations –
• E.g. unit vector a – a vector with a magnitude of 1 unit in the direction of vector A.
• Unit vectors are dimensionless.
• Unit vector for 3 dimension axes :
1.2.5 Unit Vectors
A

â
c
b
a ˆ
,
ˆ
,
ˆ
1
ˆ 

A
A
a 

  1
ˆ 
a
)
(
@
ˆ
⇒
- bold
j
j
axis
y 1
ˆ
ˆ
ˆ 

 k
j
i
)
(
@
ˆ
⇒
- bold
i
i
axis
x
)
(
@
ˆ
⇒
- bold
k
k
axis
z

22. 22
• Vectors subtraction can be used
– to determine the velocity of one object relative to another object i.e. to
determine the relative velocity.
– to determine the change in velocity of a moving object.

23. 23
• Vector can be written in term of unit vectors as :
– Magnitude of vector,
x
z
y
k̂
ĵ
iˆ
k
r
j
r
i
r
r z
y
x
ˆ
ˆ
ˆ 



     2
z
2
y
2
x r
r
r
r 



24. 24
– E.g. :
 m
ˆ
2
ˆ
3
ˆ
4 k
j
i
s 



      m
5.39
2
3
4
2
2
2




s
ĵ
3
x/m
y/m
z/m
0
s

i
ˆ
4
k̂
2

25. 25
1.2.6 Resolving a Vector
R

y
R

x
R


0
x
y
θ
R
Rx
cos
 ..........
Rx 
 θ
R
Ry
sin
 θ
Rsin
.... 


26. 26
• The magnitude of vector R :
• Direction of vector R :
• Vector R in terms of unit vectors written as
......
..........
or 
R
R

x
y
R
R
θ 
tan or








 
x
y
R
R
θ 1
tan
.....
..........

R


27. 27
Scalar (dot) product
• The physical meaning of the scalar product can be explained by
considering two vectors and as shown in Figure 1.4a.
– Figure 1.4b shows the projection of vector onto the direction of
vector .
– Figure 1.4c shows the projection of vector onto the direction of
vector .
1.2.7 Multiplication of Vectors
A

B


A

B

A

B

Figure 1.4a

A

B

A

B

θ
B cos
Figure 1.4b

A

B

θ
Acos
Figure 1.4c
 
A
B
A
B
A




to
parallel
of
component


 
B
A
B
B
A




to
parallel
of
component



28. 28
• From the Figure 1.4b, the scalar product can be defined as
meanwhile from the Figure 1.4c,
where
• The scalar product is a scalar quantity.
• The angle  ranges from 0 to 180 .
– When
• The scalar product obeys the commutative law of multiplication i.e.
 
θ
B
A
B
A cos




vectors
o
between tw
angle
:
θ
 
θ
A
B
A
B cos






90
θ
0 
 scalar product is positive


180
θ
0
9 

scalar product is negative

90
θ  scalar product is zero
A
B
B
A








29. 29
• Example of scalar product is work done by a constant force where the
expression is given by
• The scalar product of the unit vectors are shown below :
    1
1
1
cos
ˆ
ˆ 2



 o
2
0
i
i
i
   
θ
F
s
θ
s
F
s
F
W cos
cos 





x
z
y
k̂
ĵ
iˆ
1
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ 




 k
k
j
j
i
i
    1
1
1
cos
ˆ
ˆ 2



 o
2
0
j
j
j
    1
1
1
cos
ˆ
ˆ 2



 o
2
0
k
k
k
   0
9
cos
ˆ
ˆ 

 o
0
1
1
j
i
0
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ 




 k
i
k
j
j
i
   0
9
cos
ˆ
ˆ 

 o
0
1
1
k
i
   0
9
cos
ˆ
ˆ 

 o
0
1
1
k
j

30. 30
Vector (cross) product
• Consider two vectors :
• In general, the vector product is defined as
and its magnitude is given by
where
• The angle  ranges from 0 to 180  so the vector product always positive value.
• Vector product is a vector quantity.
• The direction of vector is determined by
k
r
j
q
i
p
B ˆ
ˆ
ˆ 



k
z
j
y
i
x
A ˆ
ˆ
ˆ 



C
B
A





θ
AB
θ
B
A
C
B
A sin
sin 








vectors
o
between tw
angle
:
θ
RIGHT-HAND RULE
C


31. 31
For example:
– How to use right hand rule :
• Point the 4 fingers to the direction of the 1st vector.
• Swept the 4 fingers from the 1st vector towards the 2nd vector.
• The thumb shows the direction of the vector product.
– Direction of the vector product always perpendicular
to the plane containing the vectors and .
A

C

B
 A

B

C

C
B
A





C
A
B





A
B
B
A






 but  
A
B
B
A








B

)
(C

A


32. 32
THE END…
Next Chapter…
CHAPTER 2 :
Kinematics of Linear Motion