# Physical quantities and units of measurement

A physical quantity is any property of a natural phenomenon that can be measured. The measurement of a quantity occurs through the comparison with a homogeneous quantity (of the same type) that is taken as a reference, called the unit of measurement. The comparison operation must establish how many times the reference quantity is greater or less than the quantity to be measured. The measurement of the physical quantity is represented by a numerical value, followed by the symbol of the unit of measurement chosen to measure it.

For example, if you want to know the length of an object, you need to choose a sample length; generally we use the meter (defined below), whose symbol is m, and the measure consists in comparing the object to be measured with a sample of the meter. Once this is done, if the object is three times as long as the sample, it will be said that the object measures three meters and will write 3 m.

Since the physical quantities, and the consequent units that can be adopted by measurement, are innumerable, in 1960, through the IX International Conference of Weights and Measures, a system of homogeneous, absolute, invariant and decimal units of measurement was established: it is the International System of Units, generally indicated with the abbreviation SI, whose purpose is to make the exchange of knowledge between scientists of different nationalities easier. The SI represents the most recent version of the metric decimal system, introduced in France at the end of the 18th century. Anglo-Saxon peoples also use another non-decimal measurement system, still used today in the non-scientific field. The international system, now universally accepted, is based on seven fundamental quantities and their respective fundamental units of measure, arbitrarily chosen, from which all the others are derived. Table 1.1 shows the seven fundamental quantities with their respective units of measurement.

The unit of length is the meter (symbol m), defined in France in 1799 as the forty millionth part of a terrestrial meridian: to avoid confusion with this definition, starting from 1875 it has been kept at the Weights and Measures Office of Sèvres (near Paris) a platinum-iridium sample of the meter, which served as a reference. Recently the meter has been redefined as the distance traveled in the void by light in the time interval of 1 / 299.792.558 seconds. Of course this definition implies the definition of the unit of measurement of time, which in the International System is the second (symbol s). The second was initially defined as 1/86,400 of the average solar day duration, but since the Earth’s rotational speed is not constant, it was redefined in 1967 as the duration of 9,192,631.

The current trend in the definition of the units of measurement is to release them from any material sample and to base them on universal constants (the speed of light, the Avogadro number, etc.) and on the second, so as not to depend on samples that can alter with the time their characteristics.

The meaning of the other five fundamental quantities and the relative units of measurement will be introduced the first time they are referred to.

Dimensional analysis and derived quantities

The formulation of quantities derived through a combination of fundamental quantities is called dimensional analysis. Each derived physical quantity can be expressed, through a dimensional equation, in terms of quantities derived using a particular notation: each quantity is indicated with the initial in square brackets: the length with [ L ], the time with [ T ]. Thus, for example, a derived quantity such as speed, which is the ratio between the length traveled and the time taken to travel it, has a dimensional equation of the type:

Each physical law must verify the equality between the quantities present in the first member and those present in the second member. Dimensional analysis is used to verify the congruence of a physical law, since if it does not verify the dimensional analysis the law is certainly wrong. Of course, the verification of the dimensional analysis does not guarantee that a physical law is true, but can only demonstrate its falsity.

Exponential notation and order of magnitude

In physics, quantities expressed by very large numbers (for example, the distances between planets or stars) or by very small numbers (for example, the distances between elementary particles in an atomic nucleus) can be encountered and it is often inconvenient to write the number in full. For this purpose, exponential notation is used, which uses the powers of the number ten (powers of ten) replacing the zeros of a large number or the decimals of a small number. For example, writing 3,000,000 is equivalent to writing 3 · 10 6 , and the latter notation saves space and calculations. Similarly, the notation 5 · 10 −3 can be used to write 0.005 .

Furthermore, sometimes one is not interested in the exact result of an operation, but only in an estimate of it, to get an idea of ​​the dimensions involved in the phenomenon being studied. In this case, the order of magnitude of the number is used, which represents the power of 10 closest to the considered value. For example, it will be said that the order of magnitude of the mass of the Sun is 10 33 g.

The powers of ten are also used in the use of multiples and submultiples of the units of measurement: in many practical cases the fundamental and derived units of measurement are too small or too large to represent physical phenomena. Therefore multiples and submultiples of the units themselves are used, characterized by prefixes. Just as 1000 meters equals 1 kilometer, every time the unit of measurement is multiplied by 10 3 the prefix kilo will be preceded by the name of the unit itself. Similarly, 10 −3 corresponds to the prefix milli and so on. Table 1.2 lists the multiples and submultiples of the decimals in the International System.

Direct measures and indirect measures

The direct comparison of a quantity with its unit of measurement represents a direct measurement. In some cases it is impossible to measure a quantity directly to measure a quantity: for example, in the case of the mass of an elementary particle, too small for measuring instruments to determine it exist. In these cases, indirect measurement is used, i.e. the value is calculated by means of mathematical relationships between the measured quantity and quantities that can be measured directly. For example, if you need to know the number of objects in a warehouse, whose total weight P and the unit weight per object p are known , the relationship between total weight and unit weight P / p, gives the number of objects according to an indirect measure.