# chapter01 ```Chapter 1
Introduction
Measurement and
unit
Physical quantity

Its any quantity that can be measured
e.g length
Unit

A physical quantity is expressed as a
number with units e.g length: L=2m,
time; t=1s.
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S.I Units
S.I stands for systeme
internationale in French, meaning
“international system”.
SI units are agreed international
standard units.
Base quantities are measured in SI
units
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Basic physical quantities are
quantities which are not expressed
in terms of other quantities.
They are also called fundamental
physical quantities.
The SI units of base quantities are
called basic units or fundamental
units.
Table 1: Base Physical
Quantities
Quantity
SI Unit Name
Unit Symbol
Mass
kilogram
kg
Length
meter
m
Time
second
s
Electric current
Ampere
A
Temperature
Kelvin
K
Amount of substance
mole
mol
Luminous intensity
candela
cd
Derived quantities
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are expressed in terms of basic
quantities by multiplication or
division.
Table 2 shows some examples of
derived quantities.
Table 2: Derived Quantities
Derived Quantity
Unit Name
Unit Symbol
Force
Newton
N
Acceleration
Meter per second
square
Pressure
Pascal
Work
Joule
Power
Watt
Density
Mass per volume
m/s
2
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Unit Prefixes
For larger and smaller units, we
write them in a short hand by
multiply by powers of 10 as in
Figure 3.
Table 3:Unit Prefixes
Prefix
Symbol
Peta
P
Tera
Factor
Prefix
Symbol
1015
deci
d
10 1
T
1012
centi
c
10 2
Giga
G
10 9
milli
m
10 3
Mega
M
10 6
micro
&micro;
10 6
Kilo
k
10 3
nano
n
10 9
Hector
h
10 2
pico
p
10 12
Deca
da
fento
f
10 15
10
Factor
Changing units
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Replace the unit you are given
with the equivalent quantity in the
unit you want
Example : Write 72km/hr in m/s
72km  72000m
1hr  60 X 60 s  3600s
72000m
therefore,72km / hr 
 20m / s
3600 s
Dimensional analysis
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It deals with the physical quantity
in question regardless of its unit
It describes any quantity in terms
of fundamental quantities.
Dimensions of a physical quantity
are the powers to which the
fundamental quantities must be
raised
This is the way of dealing with
Table 4: Some Physical
quantities with their dimensions
Quantity
Dimension
Mass
M
Length
L
Time
T
Acceleration
LT 2
Force
ML/T2
work
We write [X] meaning ‘‘dimension of quantity X’’
Application of
Dimensional analysis
1.
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Checking if a given equation is
consistent/valid
Dimensionally consistent equation
has both sides the same
dimensions/same SI units
Let us consider the following
equation:
1 2
s  ut  at
2
Where S is the displacement, u is the initial
velocity, a is the acceleration and t is the time
taken. Show that this equation is dimensionally
consistent/correct/valid.
We rewrite the equation, all quantities replaced by
their dimensions, we get:
s = ut +
1
at 2
2
→ L = LT−1 &times; T + LT−2 &times; T 2
L=L+L
L = 2L
We finally get the same dimension of length both sides
of the equation. Therefore, the equation is
dimensionally correct.
2. We also use dimensional
analysis to derive an equation
If we know that a quantity is
related in same way to other
quantities, then it is possible to
derive an equation expressing the
relationship
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Example: Suppose we are told
that the acceleration a of a particle
moving with uniform speed v in a
circle of radius r is proportional to
some power of r, say r n, and some
power of v, say v m. Determine the
values of n and m and write the
simplest form of an equation for
the acceleration
We write the relation as
:a ∝ r n v m
a = kr n v m
where k is the proportionality constant
Writing the equation dimensionally, we get
LT−2 = k[L]n [LT −1 ]m
k is dimensionless, so we can take it out of the equation
LT−2 = [L]n LT −1
LT−2 = Ln Lm T −m
m
equating the powers, we get
1 = n + m and − 2 = −m
from which, we get m = 2 and n = −1
Therefore, the derived equation is
v2
a=k
r
Decimal point, scientific notation,
precision, accuracy and order of
magnitude
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Decimal point: the number 7.32
has two decimal places and 1500
has no decimal point.
Scientific notation: this is writing
numbers in powers of 10. For
example, 6342147.14 can be
written in scientific notation as
6.34214714 X 10 6
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When counting decimal places
from right to left, the exponent is
positive
When counting decimal places
from left to right, the exponent is
negative
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Significant figures (s.f) are the
number of digits in scientific
notation e.g 4.71 has 3 s.f.
Uncertainty in measurement:
in any measurement there is
always an error, and this is called
uncertainty
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Accuracy refers to closeness of a
measured value to a standard or
known value. For example, if in a
lab you obtain a weight
measurement of 3.2 kg for a given
substance, but the actual or the
known weight is 10 kg, then your
measurement is not accurate.
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Precision refers to the closeness
of two or more measurements to
each other. For example, if you
weigh a given substance five times
and get 3.2 kg each time, then
Order of magnitude: it is a rough approximation of a
quantity to the closest power of 10 e.g 8~10 this reds 8
is of the order of 10
Examples
123~100, and 0.07~0.1
To find order of magnitude, round up or down to
nearest power of 10 e.g 7.62 &times; 104 ~105 , 3.2 &times; 102 ~103 ,
8.417 &times; 10−6 ~10−5 , 1.5 &times; 10−8 ~10−8
Coordinate Systems
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Used to describe the position of a
point in space
Coordinate system consists of
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a fixed reference point called the
origin
specific axes with scales and labels
instructions on how to label a point
relative to the origin and the axes
Types of Coordinate
Systems
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Cartesian
Plane polar
Cartesian coordinate
system
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Also called
rectangular
coordinate
system
x- and y- axes
Points are labeled
(x,y)
Plane polar coordinate
system
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Origin and
reference line are
noted
Point is distance r
from the origin in
the direction of
angle , ccw from
reference line
Points are labeled
(r,)
Trigonometry Review
opposite side
sin  
hypotenuse
cos  
hypotenuse
opposite side
tan  
More Trigonometry
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Pythagorean Theorem
2
2
2
r  x y
To find an angle, you need the
inverse trig function
1
0.707  45
 for example,   sin
Be sure your calculator is set
appropriately for degrees or