SI System of Units
There are units for all physical quantities that we can measure. If the mass m of a body is to be determined with a balance, we compare the mass with the unit kilogram (kg). Our ancestors already took care of defining the units. However, with the revision of the SI (decided in 2018, in force since 2019), the definition of the units was fundamentally revised: since then, all units have been based on fixed natural constants. The values of the units did not change as a result.
The SI system of units is a convention used worldwide. In the English-speaking world, other units such as feet and inches are used in everyday life, but SI units are widespread there too in a professional context. The SI system has 7 base units from which all other units are derived. The base units are:
| Quantity and name | Symbol | Unit | Unit symbol |
|---|---|---|---|
| Length | \(l\) | metre | m |
| Mass | \(m\) | kilogram | kg |
| Time | \(t\) | second | s |
| Electric current | \(I\) | ampere | A |
| Thermodynamic temperature | \(T\) | kelvin | K |
| Amount of substance | \(n\) | mole | mol |
| Luminous intensity | \(I_v\) | candela | cd |
It is sufficient to be able to determine these 7 units with high precision. From combinations of these units, we can define all other units.
For example, to determine the derived unit of velocity v, we use the formula for calculating velocity from distance and time, v = s/t. The unit of the distance s is the metre m, and the unit of time is the second s. To determine the unit of velocity, we can use the same formula as for calculating the value of the velocity. We set [v] = [s] / [t] = m / s. Here we use the notation [v] for the unit of velocity v.
Velocity is given directly as a combination of the two SI units metre and second. There is no separate name for it. The unit of force F, on the other hand, has its own name, “newton”. The unit newton can be determined as a combination of SI units, for example via the formula for force from mass and acceleration:
So we compare a measured force with a combination of the units metre, kilogram and second.
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