This document provides an overview of key topics in physics and physical measurements. It discusses: - The goals and scope of physics as the study of natural phenomena and how nature works. - The importance of measurements in physics for making quantitative comparisons between laws and the natural world, and the International System of Units (SI) for measurements. - Common physical quantities like length, mass, time, temperature and their typical orders of magnitude.

1. Topic 1
Physics and Physical
Measurements
Contents:
1.1 The realm of physics
1.2 Measurement and
uncertainties
1.3 Mathematical and graphical
techniques
1.4 Vectors and scalars (next PPT)
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2. Introduction
WHAT IS PHYSICS?
• Physics (from a Greek term meaning nature)
is historically the term to designate the study
of natural phenomena (also natural
philosophy till early in the 19th century)
• Goal of physics: to understand and predict
how nature works
• Everything in nature obeys the laws of
physics
• Everything we build also obeys the laws of
physics
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3. PHYSICS & MATHS
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4. MEASUREMENTS
• Allow us to make quantitative comparisons
between the laws of physics and the natural
world
• Common measured quantities: length, mass,
time, temperature…
• A measurement requires a system of units
Measurement = number x unit
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5. THE INTERNATIONAL SYSTEM OF UNITS
(SI)*
• The 11th Conférence Générale des Poids et Mesures
(CGPM) (1960) adopted the name Système
International d'Unités (International System of Units,
SI), for the recommended practical system of units
of measurement.
• The 11th CGPM laid down rules for the base units,
the derived units, prefixes and other matters.
• The SI is not static but evolves to match the world's
increasingly demanding requirements for
measurement
* Also mks(meter-kilogram-second)
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6. SI BASE UNITS
• A choice of seven well-defined units which by convention
are regarded as dimensionally independent:
Physical quantity
unit
symbol
LENGTH
meter
m
MASS
kilogram
kg
TIME
second
s
ELECTRIC CURRENT
ampere
A
THERMODYNAMIC TEMPERATURE kelvin
K
AMOUNT OF SUBSTANCE
mole
mol
LUMINOUS INTENSITY
candela
cd
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7. SI BASE UNIT OF LENGTH
• Previously: 1 meter (from the Greek metron=measure)=
one ten-millionth of the distance from the North Pole to
the equator; standard meter (platinum-iridium alloy rod
with two marks one meter apart) produced in 1799
the new definition of the meter is:
• The meter is the length of the path travelled by light in
vacuum during a time interval of 1/299,792,458 of a
second
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8. TYPICAL DISTANCES
• Diameter of the Milky Way
• One light year
• Distance from Earth to Sun
• Radius of Earth
• Length of a football field
• Height of a person
• Diameter of a CD
• Diameter of the aorta
• Diameter of a red blood cell
• Diameter of the hydrogen atom
• Diameter of the proton
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2x1020 m
4x1016 m
1.5x1011 m
6.37x106 m
102 m
2x100 m
1.2x10-1 m
1.8x10-2 m
8x10-6 m
10-10 m
2x10-15m
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9. SI BASE UNIT OF MASS
The kilogram is equal to the mass of the international
prototype of the kilogram.
Cylinder of platinum and
iridium 0.039 m in height
and diameter
The mass is not the weight (=measure of the gravitational force)
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10. TYPICAL MASSES
• Galaxy (Milky Way)
• Sun
• Earth
• Elephant
• Automobile
• Human
• Honeybee
• Red blood cell
• Bacterium
• Hydrogen atom
• Electron
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4x1041 kg
2x1030 kg
5.97x1024 kg
5400 kg
1200 kg
70 kg
1.5x10-4 kg
10-13 kg
10-15 kg
1.67x10-27 kg
9.11x10-31 kg
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11. SI BASE UNIT OF TIME
•
Previously: the revolving Earth was considered a fairly accurate
timekeeper.
Mean solar day = 24 h = 24 x 60 min = 24x60x60 s = 84,400 s
Today the most accurate timekeepers are the atomic clocks
(accuracy 1 second in 300,000 years)
• The second is the duration of 9,192,631,770 periods of
the radiation corresponding to the transition between
the two hyperfine levels of the ground state of the
caesium 133 atom.
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12. TYPICAL TIMES
• Age of the universe
• Age of the Earth
• Existence of human species
• Human lifetime
• One year
• One day
• Time between heartbeat
• Human reaction time
• One cycle of a high-pitched sound
wave
• One cycle of an AM radio wave
• One cycle of a visible light(IC NL)
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5 x 1017 s
1.3 x 1017 s
6 x 1013 s
2 x 109 s
3 x 107 s
8.6 x 104 s
0.8 s
0.1 s
5 x 10-5 s
10-6 s
2 x 10-15 s
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13. SI BASE UNIT OF TEMPERATURE
• The kelvin, unit of thermodynamic
temperature, is the fraction 1/273.16 of the
thermodynamic temperature of the triple
point of water.
The triple point of any substance is a state
of temperature and pressure at which the
material can coexist in all three phases
(solid, liquid and gas) at equilibrium.
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14. SI DERIVED UNITS
Formed by combining base units according to the
Algebraic relations linking the corresponding
Quantities. (Any derived unit could be written in basic units form)
Physical quantity
FREQUENCY
unit
Hertz
equivalent
Hz = 1/s=s-1
FORCE
Newton
N = kg.m.s-2
PRESSURE
Pascal
Pa = N.m-2 = kg. m-1s-2
ENERGY, WORK
Joule
J = N.m = kg.m2.s-2
POWER
Watt
W = J.s-1 = kg.m2.s-3
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15. COMMON SI PREFIXES
Power
1015
1012
109
106
103
102
101
10–1
10–2
10–3
10–6
10–9
10–12
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10–15
Prefix
peta
tera
Abbreviation
P
T
giga
mega
kilo
hecto
deka
deci
centi
milli
micro
nano
G
M
k
h
da
d
c
m
μ
n
pico
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femto
p
f
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16. CGS SYSTEM
Sometimes we might express the unit in
another more realistic form like the unit used for
the density of water.
Most students know 1 g/cm 3 more than
1000kg/m3
• centimeter
cm
1 cm= 10-2 m
• gram
g
1 g = 10-3 kg
• second
s
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17. SIGNIFICANT FIGURES
Scientific notation
This is the way to express any number in
physics.
a.b x 10p
where 1 ≤ a ≤ 9 and p belongs to Z
Example
3.50 x 10-3
power of ten
number of
order unity
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18. SIGNIFICANT FIGURES
• The result of a measurement is known only
within a certain accuracy
• Significant figures are the number of digits
reliably known (excluding digits that
indicate the decimal place)
• 3.72 and 0.0000372 have both 3 significant
figures
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19. Rules for SF
1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are
ALWAYS significant.
2) ALL zeroes between non-zero numbers are ALWAYS
significant.
Example: 700023 (Six significant figures)
3) ALL zeroes which are SIMULTANEOUSLY to the
right of the decimal point AND at the end of the
number are ALWAYS significant.
Example: 7.200 and 6.50100
4) ALL zeroes which are to the left of a written decimal
point and are in a number >= 10 are ALWAYS
significant.
Example: 1.0001 (All significant)
0.001 (Only the digit 1 is significant)
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20. Rules for SF
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21. SIGNIFICANT FIGURES
d=21.2 m
t=8.5 s
v=?
v=d/t=2.4941176 m.s-1?
• Rule of thumb (multiplication and division):
The number of significant figures after
multiplication or division is equal to the
number of significant figures in the least
accurate known quantity
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v=d/t=2.5 m.s-1
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22. Examples:
• Simplify the following expressions using the correct
number of significant digits:
a) 3.40cm x 7.125cm = ????
b) 54m / 6.5s = ????
c) 3.2145km x 4.23km = ????
Answers:
a) 24.2cm2
b) 8.3ms-1
c) 13.6km2
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23. SIGNIFICANT FIGURES
t1=16.74s
t2=5.1 s
t1+t2=?
t1+t2=21.84 s?
• Rule of thumb (addition and subtraction):
The number of decimal places after addition
or subtraction is equal to the smallest
number of decimal places of any of the
individual terms.
t1+tIB=21.8 NL)
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2 Physics (IC s

24. Examples:
• Simplify the following expressions using the correct
number of significant digits:
a) 5.012km + 3.4km + 2.33km = ???
b) 45g – 8.3g = ????
c) 6.201cm + 7.4cm + 0.68cm + 12.0cm = ????
Answers:
a) 10.7km
b) 37g
c) 26.3cm
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25. SIGNIFICANT FIGURES
How many significant figures are in
• 35.00
4
• 35
2
• 3.5x10-2
2
• 3.50x10-3
3
• 60.0
3
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26. CONVERTING UNITS
• You will need to be able to convert from one unit
to another for the same quantity.
Example:
Convert 72 km.h-1 to m.s-1
72km .h
−1
km 1000m
1h
= 72
×
×
h
1km
3600s
72
=
m .s −1 = 20m .s −1
3.6
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27. Conversions
• You will need to be able to convert from
one unit to another for the same quantity
– J to kWh
– J to eV
– Years to seconds
– And between other systems and SI
• Example: convert 1g/cm3 into kg/m3
Answer: 1000 kg/m3
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28. KWh to J and J to eV
• 1 kWh = 1kW x 1 h
= 1000W x 60 x 60 s
= 1000 Js-1 x 3600 s
= 3600000 J
= 3.6 x 106 J
• 1 eV = 1.6 x 10-19 J
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29. SI Format
The accepted SI format is
– m.s-1 not m/s
– m.s-2 not m/s/s
• i.e. we use the suffix not dashes
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30. ORDER OF MAGNITUDES
• An order of magnitude calculation is a
rough estimate designed to be accurate
to within a factor of about 10
• To get ideas and feeling for what size
of numbers are involved in situation
where a precise count is not possible
or important
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31. ORDER OF MAGNITUDE
TYPICAL DISTANCES
• Diameter of the Milky Way
• One light year
• Distance from Earth to Sun
• Radius of Earth
• Length of a football field
• Height of a person
• Diameter of a CD
• Diameter of the aorta
• Diameter of a red blood cell
• Diameter of the hydrogen atom
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• Diameter of the protonPhysics (IC NL)
2x1020 m
4x1016 m
1.5x1011m
6.37x106m
102m
2x100 m
1.2x10-1m
1.8x10-2 m
8x10-6 m
10-10 m
31
2x10-15 m

32. ORDER OF MAGNITUDE
EXAMPLE
Estimate the number of seconds in a human
"lifetime."
You can choose the definition of "lifetime."
Do all reasonable choices of "lifetime" give
answers that have the same order of magnitude?
The order of magnitude estimate: 109 seconds
• 70 yr = 2.2 x 109 s
• 100 yr = 3.1 x 109 s
• 50 yr = 1.6 x 109 s
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33. Summary for Range of Magnitudes
•
•
•
•
•
You will need to be able to state (express) quantities to the nearest order of
magnitude, that is to say to the nearest 10x
Range of magnitudes of quantities in our universe
Sizes
– From 10-15 m
(subnuclear particles)
– To 10+25 m (extent of the visible universe)
masses
– From 10-30 kg
(electron mass)
– To 10+50 kg (mass of the universe)
Times
– From 10-23 s
(passage of light across a nucleus)
– To 10+18 s
(age of the universe)
You will also be required to state (express) ratios of quantities as differences of order
of magnitude.
Example:
– the hydrogen atom has a diameter of 10-10 m
– whereas the nucleus is 10-15 m
– The difference is 105
– A difference of 5 orders of magnitude
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34. Errors and Uncertainties
Errors
Errors can be divided into 2 main classes
• Random errors
• Systematic errors
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35. Mistakes
• Mistakes on the part of an individual such
as
– misreading scales
– poor arithmetic and computational skills
– wrongly transferring raw data to the final
report
– using the wrong theory and equations
• These are a source of error but are not
considered as an experimental error
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36. Systematic Errors
• Cause a random set of measurements to
be spread about a value rather than being
spread about the accepted value
• It is a system or instrument value
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37. Systematic Errors result from
• Badly made instruments
• Poorly calibrated instruments
• An instrument having a zero error (off-set
error), a form of calibration
• Poorly timed actions
• Note that systematic errors are not
reduced by multiple readings
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38. Random Errors
• Are due to variations in performance of the
instrument and the operator.
• Even when systematic errors have been
allowed for, there exists error.
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39. Random Errors result from
• Vibrations and air convection
• Misreading
• Variation in thickness of surface being
measured
• Using less sensitive instrument when a
more sensitive instrument is available
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40. Reducing Random Errors
• Random errors can be reduced by
• taking multiple readings, and eliminating
obviously erroneous result
• or by averaging the range of results.
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41. Accuracy
• Accuracy is an indication of how close a
measurement is to the accepted value
indicated by the relative or percentage
error in the measurement
• An accurate experiment has a low
systematic error
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42. Precision
• Precision is an indication of the agreement
among a number of measurements made
in the same way indicated by the absolute
error
• A precise experiment has a low random
error
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43. uncertainties
• In any experimental measurement there is
always an estimated last digit for the measured
quantity.
• You are not certain about the last digit.
• The last digit varies between two extremes
expressed as ±∆A
• Example: a length on a 20cm ruler is expressed
as
3.25 ± 0.05cm
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44. Expression of physical
measurements and uncertainties
Any experimental measure is expressed in the form
A = Ao ± ∆A
Real value or
final value
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Approximate value or
measured value
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Uncertainty
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45. Example:
• Uncertainty in a single measurement:
Bob weighs himself on his bathroom scale.
The smallest divisions on the scale are 1-kg marks. So the least
count (limit of reading) of the instrument is 1kg.
Bob reads his weight as closest to the 76-kg mark.
He knows his weight should be greater than 75.5kg, otherwise the
reading will be closer to the 75th mark.
He also knows that his weight should be smaller than 76.5kg,
otherwise the reading should be closer to the 77th mark.
So, Bob’s weight must be:
Weight = (76.0 ± 0.5)kg
Note: In general, the uncertainty in a single measurement from a single
instrument is half the least count of the instrument.
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46. Types of uncertainties.
1. Absolute uncertainty
2. Relative uncertainty
∆A
written as
±∆A
∆A
∆A
or
Ao
A
3. Percentage uncertainty
∆A
%
A
Remark: the absolute uncertainty is always positive
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47. Working with uncertainties.
• Uncertainty on a sum or a difference.
Rule: in addition or subtraction uncertainties just add
S = A + B ⇒ ∆S = ∆A + ∆B
D = A − B ⇒ ∆D = ∆A + ∆B
• Uncertainty on a product or a quotient.
Rule: in a product or a quotient relative or percentage
uncertainties add.
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∆P ∆A ∆B
P = A ×B ⇒
=
+
P
A
B
A
∆Q ∆A ∆B
Q = ⇒
=
+
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B IB Q
A
B
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48. Example:
• Uncertainty on a sum or a difference.
Mick and Jane are Acrobats:
Mick is (186 ± 2)cm tall, while Jane is (147 ± 3)cm tall.
If Jane stands on top of Mick’s head, how far is her head
above the ground?
Solution:
Combined height = 186cm + 147cm = 333cm
Uncertainty on combined height = 2cm + 3cm = 5cm
Implies, Combined Height = (333 ± 5)cm
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49. Example:
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50. Working with uncertainties cont.
Or
Also for
∆P
∆A
∆B
P = A ×B ⇒
%=
%+
%
P
A
B
A
∆Q
∆A
∆B
Q = ⇒
%=
%+
%
B
Q
A
B
∆P
∆A
∆P
∆A
P =A ⇒
=n
or
%=n
%
P
A
P
A
n
An
∆Q
∆A
∆B
Q =
⇒
=n
+m
m
Q
A
B
B
∆Q
∆A
∆B
or
%=n
%+m
%
Q
A
B
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51. Practicing uncertainties
The length of each side of a sugar cube is measured as
10 mm with an uncertainty of ± 2 mm.
Which of the following is the absolute uncertainty in the
volume of the sugar cube?
A.± 6 mm3
B.± 8 mm3
C.± 400 mm3
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52. • The volume V of a cylinder of height h and radius r is given
by the expression
V=πr2h.
In a particular experiment, r is to be determined from
measurements of V and h. The uncertainties in V and in h are
as shown below.
The approximate uncertainty in r is
• A. 10 %.
• B. 5 %.
• C. 4 %.
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D. 2
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53. Limit of Reading and Uncertainty
• The Limit of Reading of a measurement
is equal to the smallest graduation of the
scale of an instrument
• The Degree of Uncertainty of a
measurement is equal to half the limit of
reading
• e.g. If the limit of reading is 0.1cm then the
absolute uncertainty range is ±0.05cm
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54. Reducing the Effects of Random
Uncertainties
• Take multiple readings
• When a series of readings are taken for a
measurement, then the arithmetic mean of
the reading is taken as the most probable
answer
• The greatest deviation or residual from the
mean is taken as the absolute error
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55. Diagramming Accuracy and
Precision
•
Accurate
•Accurate and precise
precise
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56. Diagramming Accuracy and Precision in
relation to error and uncertainty
figure 1
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57. Figure 2
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