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Physical Quantities, Units and Measurement Cheat Sheet by

Physics Notes for Unit 1

Physical Quantities

Physical attributes that are measurable are known as Physical Quanti­ties. A physical quantity always consists of a numerical magn­itude and a unit.

Examples of Physical Quantities

200 km
12.3 dB
23 Hz
47.3 °C
300 kN

Accuracy of Measur­ement

Accu­racy refers to the closeness of a measured value to a standard or known value.

Precision

Prec­ision refers to the closeness of two
or more measur­ements to each other.

Random Errors

It occurs in all measur­ements.
It occurs whenever an observer estimates the last figure of a reading on an instru­ment.
Causes:
- human reaction time
- background noise
- mechanical vibrations
It cannot be predicted.
It can be reduced by taking large numbers of readings and averaging them.

Systematic Errors

It is not random but constant.
It may cause an observer to consis­tently undere­stimate or overes­timate a reading.
Causes:
- zero error of an instru­ment: any indication that a measuring system gives a false reading when the true value of a measured quantity is zero
It can be eliminated if we know the sources of the errors.

Taking Measur­ements

Different measuring instru­ments are used for measuring different quanti­ties. The choice of instrument will affect the precision of the measur­ement we obtain.
The precision of an instrument is usually equal to the smallest division of the instrument with a few exceptions such as the thermo­meter, ammeter and voltmeter.
 

SI Units and Base Quantities

The Inter­nat­ional System of Units is the modern form of the metric system, and is the most widely used system of measur­ement.
It is comprised of a system of units built on seven base units.

The Seven Base Units

Length
metre
m
Mass
kilogram
kg
Time
second
s
Electric Current
ampere
A
Temper­ature
kelvin
K
Amount of Substance
mole
mol
Luminous Intensity
candela
cd

Defini­tions of Base Units

second
The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ΔνCs, the unpert­urbed ground­-state hyperfine transition frequency of the caesiu­m-133 atom, to be 9,192,­631,770 when expressed in the unit Hz, which is equal to s−1.
metre
The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299,79­2,458 when expressed in the unit m⋅s−1, where the second is defined in terms of the caesium frequency ΔνCs.
kilogram
The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.6260­701­5×1­0−34 when expressed in the unit J⋅s, which is equal to kg⋅m⋅s­−1, where the metre and the second are defined in terms of c and ΔνCs.
ampere
The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.6021­766­34×­10−19 when expressed in the unit C, which is equal to A⋅s, where the second is defined in terms of ΔνCs.
kelvin
The kelvin, symbol K, is the SI unit of thermo­dynamic temper­ature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.3806­49×­10−23 when expressed in the unit J⋅K−1, which is equal to kg⋅m⋅s­−2­⋅K­−1, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.
mole
The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.0221­407­6×1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.
candela
The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monoch­romatic radiation of frequency 540×1012 Hz, Kcd, to be 683 when expressed in the unit lm⋅W−1, which is equal to cd⋅sr⋅­W−1, or cd⋅sr⋅­kg­−1­⋅m­−2­⋅s3, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.
Not necessary inform­ation
 

Prefixes and Orders of Magnitude

The SI system also establ­ishes a set of twenty prefixes to unit names and unit symbols
that may be used when specifying multiples and fractions of the units. This is useful for
expressing physical quantities that are either very big or very small.

Table of Prefixes

yotta
Y
1024
zetta
Z
1021
exa
E
1018
peta
P
1015
tera
T
1012
giga
G
109
mega
M
106
kilo
k
103
hecto
h
102
deka
da
101
deci
d
10-1
centi
c
10-2
milli
m
10-3
micro
μ
10-6
nano
n
10-9
pico
p
10-12
femto
f
10-15
atto
a
10-18
zepto
z
10-21
yocto
y
10-24
In O-Levels, the only prefixes that you need to know are nano, micro, milli, centi, deci, kilo, mega and giga.

Examples of Orders of Magnitudes

3,900 YHz
Highest energy gamma wave ray detected
30.86 Zm
One gigaparsec
30 Eg
Mass of the rings of Saturn
30 PHz
Frequency of an X-Ray
9.461 Tm
The distance light travels in a year
0.3 Gm/s
Speed of light in a vacuum
12.742 Mm
Diameter of the earth
16.5 kN
Bite force of a 5.2m Saltwater Crocodile
2.4 hg
Average mass of a grand piano
7 dag
Average mass of an adult human
1.1 dJ
Energy of an American half-d­ollar falling 1 metre
1.6667 cHz
1 rpm
2.75 mm/s
Fastest recorded speed of a snail
0.3 μm/s
Calculated speed of an amoeba (lower bound)
1.6 nN
Force required to break a typical covalent bond
50 pK
Lowest temper­ature produced
1 fg
Mass of a HIV-1 virus
1.65 ag
Mass of double­-st­randed DNA molecule consisting of 1,578 base pairs
3 zJ
Energy of a van der Waals intera­ction between atoms
0.0000­000­00016 ym
One Planck length

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