Physical Quantities and Units

What Makes a Good Unit?

The standard reference we measure against is called a unit. While we could invent our own units (like measuring length in 'arm-spans'), for science to be universal, a unit should have several key properties. It should be:

• Well-defined: Everyone agrees on exactly what it means.
• Accessible & Reproducible: It should be possible for scientists anywhere to create and use the standard.
• Invariant: It must not change over time or with location.

The Two Types of Quantities

To create a logical and organized system of measurement, we divide all physical quantities into two categories:

1. Fundamental (or Base) Quantities

These are a small set of quantities chosen to be the independent building blocks of our measurement system. The units for these quantities are called fundamental units. Think of them as the primary colors of physics.

2. Derived Quantities

These are all other quantities, which are 'derived' by combining the fundamental quantities through mathematical equations. Their units, called derived units, are combinations of the fundamental units.

Examples of Derived Quantities

• Area: Defined as length × width, its unit is meter × meter = m².
• Speed: Defined as distance / time, its unit is meter / second = m/s.
• Density: Defined as mass / volume, its unit is kilogram / cubic meter = kg/m³.

This system allows us to define and measure any physical quantity, no matter how complex, using just a small, agreed-upon set of fundamental building blocks.

Why We Measure

Physics is not only about observing the world; it is about describing it with precision. To transform our observations into scientific laws, we need a way to quantify what we see. This process of quantification is called measurement. Answering questions like 'How far?', 'How heavy?', or 'How fast?' is the first step towards a deep understanding of natural phenomena.

Physical Quantities

Any property of a system that can be measured is called a physical quantity. Examples are all around us: the length of a track, the mass of a planet, the time it takes for a process to occur, the force of gravity, and the temperature of a star are all physical quantities.

The Two Parts of a Measurement

The act of measurement is a comparison. We compare the quantity we want to measure with an internationally accepted, standard reference of that same quantity. This means every measurement has two essential parts:

• A numerical value (n): This tells us 'how many'.
• A unit (u): This tells us 'of what standard'.

$$\text{Physical Quantity } (Q) = \text{Numerical Value } (n) \times \text{Unit } (u)$$

For example, a measurement of length $L = 5$ meters means our length is 5 times the standard reference length called a 'meter'.

The Inverse Relationship

An important consequence of this relationship is that for a given physical quantity, the numerical value is inversely proportional to the size of the unit: $n \propto 1/u$. If we choose a smaller unit, we will need more of them to measure the same quantity, so the numerical value will be larger. For example:

$$5 \text{ meters} = 500 \text{ centimeters}$$

The centimeter is a smaller unit than the meter, so the numerical value is larger.

A Common Language for Science

In the past, scientists in different parts of the world used different systems of units. Some common ones were:

• CGS system: Based on the centimeter, gram, and second.
• FPS system: Based on the foot, pound, and second.
• MKS system: Based on the meter, kilogram, and second.

This created a 'Tower of Babel' situation in science, making it difficult to compare results and collaborate. To solve this, the scientific community agreed on a single, global standard: the International System of Units, or SI (from the French Système International d'Unités).

The 7 SI Base Units

The SI system is built on a foundation of seven fundamental quantities. Every other quantity in physics can be derived from these seven. Think of them as the unshakeable pillars of measurement.

Handling the Immense Scales of the Universe

Physical quantities can be incredibly large or incredibly small. The mass of the sun is about $2 \times 10^{30}$ kg, while the mass of an electron is about $9 \times 10^{-31}$ kg. Writing out all these zeros is inconvenient. The SI system solves this with a simple system of prefixes, which represent powers of 10.