What is a physical quantity

A physical quantity is anything that can be measured: a length, a time interval, a mass, a temperature. What distinguishes a physical quantity from a mere quality is precisely the possibility of associating it with a number through a repeatable measurement procedure.

Every physical quantity is made up of two inseparable parts: a numerical value and a unit of measurement. The value alone says nothing — saying “the room is 5 long” is meaningless until we specify whether it is 5 metres, 5 paces or 5 kilometres. No measurement makes sense without specifying the unit: the unit is what fixes the “yardstick” against which the number acquires meaning.

Principle — The seven base quantities of the SI

The International System of Units (SI) is based on seven base quantities. All other quantities are derived from these.

Quantity	Symbol	SI unit	Unit symbol
Length	$\ell$	metre	m
Mass	$m$	kilogramme	kg
Time	$t$	second	s
Electric current	$i$	ampere	A
Temperature	$T$	kelvin	K
Amount of substance	$n$	mole	mol
Luminous intensity	$I_v$	candela	cd

All the other quantities we shall meet in physics are derived units, obtained by combining the seven base ones. Some of the most common:

• velocity: $[\,\text{m/s}\,]$
• acceleration: $[\,\text{m/s}^2\,]$
• force: $[\,\text{N}\,] = [\,\text{kg}\cdot\text{m/s}^2\,]$
• energy: $[\,\text{J}\,] = [\,\text{N}\cdot\text{m}\,]$
• power: $[\,\text{W}\,] = [\,\text{J/s}\,]$

The fact that every derived unit can be expressed as a product of powers of the base units is the foundation of dimensional analysis, a powerful tool for checking the consistency of formulae.

The SI after 2019

In 2019 the SI was redefined in terms of fundamental constants of nature — such as the speed of light $c$, the Planck constant $h$, the Boltzmann constant $k_B$, the elementary charge $e$ and the Avogadro number $N_A$ — rather than material prototypes (such as the old platinum-iridium cylinder that defined the kilogramme). The units are thus anchored to unchanging quantities, reproducible anywhere in the universe.

Collegamenti

Argomenti: Grandezze fisiche e misura

Esercizi collegati: Esercizio svolto — Il rubinetto che perde · Esercizio svolto — Area di un rettangolo misurato · Problema — Volume di un parallelepipedo