phisics lecture note 3
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PHYSICS CHAPTER 1
1
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
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PHYSICS CHAPTER 1
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Table 1.6 shows written form (notation) of vectors.
Notation of magnitude of vectors.
1.2.1 Vectors
Vector ALength of an arrow – magnitude of vector A
displacement velocity acceleration
s
v
a
s av
vv
aa
s (bold) v (bold) a (bold)
Direction of arrow – direction of vector A
Table 1.6
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PHYSICS CHAPTER 1
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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
Ak
Ak
A
A
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PHYSICS CHAPTER 1
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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 man throws a stone with a velocity of 10 m s-1, 30 above
horizontal.
1.2.2 Direction of Vectors
30 v
x
y
0
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PHYSICS CHAPTER 1
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c) Cartesian coordinates
2-Dimension (2-D)
m)4m,2(),( y x s
s
y/m
x/m
4
20
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PHYSICS CHAPTER 1
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3-Dimension (3-D)
s
2
3
4
m2)3,4,(),,( z y x s
y/m
x/m
z /m
0
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PHYSICS CHAPTER 1
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d) Polar coordinates
e) Denotes with + or – signs.
N,12050 F
F
120
+
+-
-
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PHYSICS CHAPTER 1
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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
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PHYSICS CHAPTER 1
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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
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PHYSICS CHAPTER 1
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If there are more than 2 vectors therefore
Use vector polygon and associative rule. E.g. RQ P
RQ
P
R
Q
P
Q P
RQ P RQ P
Associative Rule
RQ P
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PHYSICS CHAPTER 1
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Distributive Rule :
a.
b.
For example :
Proof of case a: let = 2
B A B A
A A A
number realare,
B A B A
2
B
A
B A
O B A
2
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PHYSICS CHAPTER 1
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A
2O
B
2
B A
22
B A B A
222
B A B A
22
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PHYSICS CHAPTER 1
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Proof of case b: let = 2 and = 1
A
A A A
312
A
3
A A A A
12
A
2 A
A
3
A A A
1212
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PHYSICS CHAPTER 1
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For example :
1.2.4 Subtraction of Vectors
Parallelogram Triangle
D
C
O
DC
O
D
DC DC
C
D
DC
C
D
DC
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PHYSICS CHAPTER 1
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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.
1. Vector A has a magnitude of 8.00 units and 45 above the positive x
axis. Vector B also has a magnitude of 8.00 units and is directed alongthe negative x axis. Using graphical methods and suitable scale to
determine
a) b)
c) d)(Hint : use 1 cm = 2.00 units)
Exercise 1.2 :
B A
B A
B2 A
B A2