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rule 1, we should include only one doubtful digit; thus the result should
be expressed as 106
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*Note:

1
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Scientific Notation

Scientific Notation is a method of writing numbers in the following form:
n 10m, where n is any number between 1 and 10 (1 n 10) while m is any positive or
negative integer
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234 105
0
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010 10− 4
This method is used in expressing very large or very small numbers and in
indicating whether the zeros at the end of a number are significant or not
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0 103
5,000 = 5
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3

only the first zero is significant
all zeros are significant

Measurement of Physical Quantities

Physical quantity is a quantity, which actually exist and is therefore directly or
indirectly measurable in the laboratory
...
A unit is a measure of a quantity that is equal to 1
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*Note: Units and standards can be defined freely
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Two kinds of physical quantities according to units:
✓

Fundamental quantities — quantities that are relatively easy to define and
choose a suitable standard
...


In practice, the smallest possible number of fundamental quantities are chosen
and the rest of the other quantities are merely defined in terms of them
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4

Three Widely Used Systems of Units

1
...
1

The International System of Units (SI)
SI System — abbreviation of the French equivalent of the English term
International System of Units
— metric system or the MKS system
— internationally accepted system of units
SI Fundamental Units
Quantity
time
length
mass
amount of substance
temperature
electric current
luminous intensity

Name

Symbol

second
meter
kilogram
mole
kelvin
ampere
candela

s
m
kg
mol
k
A
cd

7

✓

mass — resistance to force, which causes objects to move (the more
massive the object, the more force is needed to move the object
from rest)

✓

amount of substance — amount of material contained in an object in terms
of the number of atoms or molecules

✓

temperature — hotness or coldness of a substance

✓

electric current — amount of negative charges flowing

✓

luminous intensity — brightness of light

✓

MKS — stands for the first letters of the three base units of length (meter),
mass (kilogram), and time (seconds)

✓

standard of time in the SI system — second (s)
— the time required for a cesium – 133
atom to undergo 9,192,631,770
vibrations

Two advantages of the SI system:
1
...
conveniently relates different units of measure using the SI prefixes added to
the unit
...
4
...
It is also known
as the CGS syste
The normal rules of algebraic addition, subtraction, multiplication and division are used
with scalars, while special mathematical rules are needed to manipulate vectors
...
2

Addition of Vectors

Vector addition is the process of finding a single vector which will produce the same
effect produced by the given vectors
...
The vector,
which is opposite to the resultant but of the same magnitude is called the equilibriant
...

2
...
1

The Graphical Method

In this method, a directed line segment is used to represent vector quantities
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An appropriate scale is used in drawing the length of the arrow
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2
...
Vector A is 2
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5 cm long represents a 15
km displacement 300 north of east
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2
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Parallelogram Method — this method is applicable to two vectors at a time
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With these two
vectors as adjacent sides of a parallelogram, construct the
parallelogram
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For the
direction of R , measure the angle

with side of the parallelogram
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Using
the second resultant and the fourth vector, apply the parallelogram
method again to get the third resultant vector
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The last resultant vector
obtained is the total resultant vector of all the given vectors
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14

2
...
This is done by
drawing the vectors head–to–tail one at a time (as illustrated in Fig
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3a)
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The resultant vector R goes from the tail of
the first vector to the head of the last vector
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2
...
2
...
2
...
The vectors need
not be drawn to scale, but a working diagram must be drawn
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The Pythagorean Theorem — this method is limited to two vectors that are
perpendicular with each other as shown in Fig
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4
...
2
...
Cosine Law and Sine Law — this is used when the two vectors are not
perpendicular with each other as illustrated in Fig
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5
...
Cosine law is used for
solving the magnitude of the resultant R
15

R2 = A2 + B2 – 2ABcos

R2 = A2 + B2 + 2ABcosφ

or

and sine law for the direction
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2
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Component Method — a more accurate, faster and more convenient method for
solving variety of interesting problems involving vectors is the
component method because it is applicable to all types of vectors
...
2
...
The
sign of Fx and Fy depends on the direction of the projection of F on the
x and y axes respectively
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Fiy = F1y + F2y + F3y +
...
The quadrant in which R points is determined from
a rough drawing of R based on its components values
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Calculate the magnitude and direction of the resultant of the following two
displacement vectors:
a
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50 km E
40 km W
70 km 60° N of E
Solutions:
N
a)
Fig
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7

R 2 = 302 + 402
R = 50 km
30
= tan -1
40
= 36
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2
...
4km
70km sin1200
sin =
104
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50

R

70 km
0

60

R = 104
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5° N of E

E
50 km

2
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2
...

Solutions:

Fx = 200 cos30 0 − 100 cos450 − 150 cos0 0 + 200 cos37 0
= 173
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7 − 150 + 159
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2 N
17

Fy = 200 sin 30 0 + 100 sin 450 + 150 sin 0 0 − 200 sin 37 0
= 100 + 70
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36
= 50
...
2) + (50
...
9N
50
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2
θ R = 24
...
There are several types of motion like motion along a straight line, circular
motion and rotational motion
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To understand motion fully, it is a must to know distance and displacement, speed
and velocity, and acceleration
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1

Distance and Displacement

Distance is a scalar quantity that measures the position of a moving object from a
reference point, while displacement refers to the change in position
...

3
...
The
significant difference is that velocity is a vector quantity while speed is a scalar quantity, which
means that velocity specifies both how fast and in what direction an object moves, whereas
speed specifies only how fast an object moves
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Velocity is the time rate of change of displacement
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v=

s
t

(3
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2
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2
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2)

Instantaneous Speed and Instantaneous Velocity

Instantaneous speed, or velocity, is the speed or velocity at any given instant
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3)
v=
t
Sample Problems with Solutions:
1
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4 s
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24m
=
32
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0 m s

v1 =

s2
t
224 m
=
33
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7 m s

v2 =

At t = 32 s, the distance traveled by the slower runner is

d 2 = (v 2 )(32s )

= (6

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