Introduction

1.1 Introduction

Physics rests on measurement. Every law, every experiment, and every observation in physics ultimately comes down to measuring something — a length, a time interval, a mass. But what does "measuring a physical quantity" actually mean?

Measurement is fundamentally an act of comparison. When you say a rod is 2 metres long, you are comparing its length against a certain basic, arbitrarily chosen, internationally accepted reference standard. That standard is called a unit.

The result of any measurement of a physical quantity is always expressed as a number (or numerical measure) accompanied by a unit. Write the length of the rod as $2\ \text{m}$: the number $2$ tells you how many times the unit fits into the quantity measured; the unit tells you what standard it was measured against. Without the unit, the number alone is meaningless — $2$ could mean $2$ metres, $2$ kilometres, or $2$ light-years.

Why We Need Only a Limited Number of Units

At first glance, the number of physical quantities we might want to measure seems very large — length, mass, time, velocity, force, energy, pressure, and hundreds more. If every single quantity needed its own independent unit, the task of measurement would be unmanageable.

But physical quantities are not independent of one another — they are inter-related. Because of these relationships, we do not need a separate unit for every physical quantity; only a limited number of units are actually needed to express all of them.

Base (Fundamental) Units and Derived Units

The units chosen for the fundamental or base quantities are called fundamental units or base units. The units of all other physical quantities can then be expressed as combinations of these base units. Such units, obtained for the derived quantities, are called derived units.