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Definition
Measuring a quantity means determining the value by the use of another one, fixed, of the same species
for definition taken as a unit. For each certain quantity, the choice of measurement's unit
is arbitrary and that is demonstrated by the myriad of existing units used by countries around the world,
still today.
A little bit of hystory
Not all the various sizes that appear on our observations are independent, but most of them are connected
by well-defined relationships. Substantially, these relations allow to express the various quantities as
derived from a limited number of other quantities defined as independent variables. For example, areas and
volumes, can be expressed as a function of linear dimensions. Thus, it is proved the necessity to choose units
of various sizes serving as fundamental units from which to derive the other, according to these. In particular,
mechanical phenomena in all sizes are defined on the basis of only three units taken as fundamental, because
independent among them, and then defined as derived from that. The set of fundamental 3 units and all derived
constitute the absolute system of measure's units for Mechanical's phenomena.
Wanting to study electromagnetic's phenomena need to add a fourth fundamental unit crucially on an electrical field.
Therefore, we can say that, the measurement units of all physical quantity can be framed in a set of 4 fundamental
units. In the past it have had importance, for the mechanical field, the so called "absolute system C.G.S.",
having as fundamental units the Centimeter, Gram and Second, while the electrical parameter used was either the
dielectric constant, or magnet permeability both considered in a vacuum condition.
The Hague (Netherlands' Capital) International Congress of 1935 has officially endorsed the adoption of a single
unit system, called the Giorgi's definitive system, by the name of the Professor Giovanni Giorgi, who have
already proposed it in 1901.
The final Giorgi's system assumes, for mechanical measures, the following fundamental units (also known as a M.K.S. system):
- Length Unit Meter, represented by the meter specimen made of Platinum-Iridium, when
at a zero degree C° temperature. The meter specimen is kept in the International Museeum of
Weights and Measures of Sevres, France
- Mass-Weigth Unit Kilogram-mass, represented by the Kilogram specimen made of Platinum-Iridium,
in the same conditions of the previous conserved in the same place, and equal the mass of a dm3
of distilled water when at a zero degree C° temperature.
- Time Unit Second, represented by the 86400th part of an average solar day.
On the base of these three fundamental units, derivative units are deduced, major of which are:
- Force Unit: it is the power that make a variation (acceleration) of 1 meter at square second
to a mass of 1 Kilogram-mass. This Unit was called Newton.
- Work Unit> or energy: it is the quantity of work generated by the "Force" unit when
moving for a meter a Kilogram-mass in the same direction of the Force itself. It is called Joule. 1J = 1N * 1m
- Power Unit: it is the power that generate the work of 1 di 1 Joule per second. Denominated Watt. 1W = 1J/1s.
After the second world war, in 1946, the International Committee of Weights and Measures decided to use
the Ampere (A) as a unit of electrical measurement to be added to the Giorgi's system. The amp was defined as
the intensity of the constant current which, maintained in two straight conductors, parallel, of infinite length
and of negligible circular cross section, and placed at a distance of one meter apart in vacuum,
would produce between these conductors a force equal to 2 * 10
-7 units M.K.S.
of force per square meter in length, in other words 2 * 10-7 Newton.
The four basic units of the Giorgi's system internationally adopted are well specified as:
Meter, Kilogram-mass, Second and Ampere (also called MKSA's system). Based on these we define all the other
derived quantities.
At the General Conferences on Weights and Measures in the period between 1954-1971, has be defined and adopted
the International System (I.S.), it contemplates the addition of three new sample units:
- Kelvin: is the unit of thermodynamic temperature and is equal to the fraction of 1/273.16 of the temperature of the triple point of water.
- Candle: the candle is the unit of measurement of intensity light and it is the intensity light, in a given direction, of a source that emits
Monochrome radiation 540 * 1012 hertz in frequency and that has a radiant intensity, in that direction, of 1/683 watt per steradian.
- Mole: is a substance quantity of a given system that contains a number of elementary entities equal to the atoms contained in 0.012 kilogram
of the carbon isotope 12 C.
In the same period of time, to meet the growing need for more precision, the meter and the second samples have been redefined.
Currently, the I.S. is adopted in almost all countries of the world. In our country, in particular, the same was received and
legalized with the Presidential's Decree enactment No. 802 of 12 August 1982, transposing the EEC directive No. 80/181 of 20 December 1979.
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Quantity Table
In the following table, main machanics and electrics measure units are reassumed
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| Quantity |
Definition Formula |
Unit Name |
Abbreviations |
Fundamentals
lenght ( l )
mass
time ( t )
electric current ( I )
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Specimen |
meter
kilogram-mass
second
ampere
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m
Kg
sec
A
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Geometrics
Area
Volume
Angle
Number of Spire
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S = l2
V = l3
α (number)
N (number)
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meter square
meter cube
radiant
spire
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m2
m3
r
sp
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General Physics
Energy and Work
Power
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W * t
P = W / t
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Joule
Watt
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J
W
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Mechanics
Linear Speed
Linear Acceleration
Angular Speed
Force (weight)
Mechanics Couple
Pressure
Specific Gravity
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V = l / t
a = v / t = l / t2
ω = α / t
f = W / l
C = W / α
p = f / S
γ = f / l2
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meter per second
meter per second square
radiant per second
newton
joule per radiant
newton per meter square
newton per metro cube
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m/sec
m/sec2
r/sec
N
J/r
N/m2
N/m3
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Electrical
Quantity of electricity
Electric Voltage
Electric Field
Electric Resistance
Capacity
Inductance
Dielectric Constant
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Q = I * t
V = P / I
F = V / l
R = V / I
C = Q / V
L = V*t / I
ε = C*l / S
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Coulomb (A per sec)
Volt
Volt per meter
Ohm
Farad
Henry
Farad per meter
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C
V
V/m
Ω
F
H
F/m
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Magnetics
Magnetico Flow
Magnetic Voltage
Magnetic Field
Reluctance
Magnetic Induction
Magnetic Permeability
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Φ = V*t / N
F = N * I
H = F / l
R = N*I / Φ
B = Φ / S
μ = B / H
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Weber
Amperspire
Amperspire per meter
Henry-1
Weber per meter square
Henry per meter square
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Vb
Asp
Asp/m
H-1
Vb/m2
H/m
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International System's Multiples and Submultiples
Very often it is necessary to express a value using a multiple or a submultiple of a measures' units
to avoid writing a number with too many digits. The following table lists the prefixes of these multiples
and submultiples that are used in the I.S., symbol and multiplicative factor are shown, as well.
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| Italian |
Symbol |
English |
Moltiplication Factor |
Full numeric digits |
| yotta | Y | yotta | 1024 | 1 000 000 000 000 000 000 000 000 |
| zetta | Z | zetta | 1021 | 1 000 000 000 000 000 000 000 |
| exa | E | exa | 1018 | 1 000 000 000 000 000 000 |
| peta | P | peta | 1015 | 1 000 000 000 000 000 |
| tera | T | tera | 1012 | 1 000 000 000 000 |
| giga | G | giga | 109 | 1 000 000 000 |
| mega | M | mega | 106 | 1 000 000 |
| chilo | K | kilo | 103 | 1 000 |
| etto | h | hecto | 102 | 100 |
| deca | da | deka | 101 | 10 |
| submultiples |
| dieci | d | dieci | 10-1 | 0.1 |
| centi | c | centi | 10-2 | 0.01 |
| milli | m | milli | 10-3 | 0.001 |
| micro | µ | micro | 10-6 | 0.000 001 |
| nano | n | nano | 10-9 | 0.000 000 001 |
| pico | p | pico | 10-12 | 0.000 000 000 001 |
| femto | f | femto | 10-15 | 0.000 000 000 000 001 |
| atto | a | atto | 10-18 | 0.000 000 000 000 000 001 |
| zepto | z | zepto | 10-21 | 0.000 000 000 000 000 000 001 |
| yocto | y | yocto | 10-24 | 0.000 000 000 000 000 000 000 001 |
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