A Guide to Physical Quantities, Part 1 — Introduction

Physics is an experimental science. We make and break laws by doing experiments — and that means we measure things. So before any formula, any problem, any exam, you need one idea straight: what can we actually measure, and what can we not?

This is Part 1 of a short series on physical quantities. Get this foundation right and the rest of physics has something solid to stand on.

Quantity vs quality

Take beauty. Can you measure it? No. You can say one person is more beautiful than another, but you can't hand them a number. There's no unit for beauty.

Now take mass. You can say 1 kg, or 2 kg. A number, with a unit attached.

So the world splits in two:

• Things we can measure. Call them quantities.
• Things beyond measurement. Call them qualities — beauty, love, the feeling at the end of a good day.

From here on, we care about the first kind: physical quantities, the things physics can measure.

The seven base quantities

There's a lot we can measure. But measurement needs a starting point.

Think about matter for a second. Everything around you is built from atoms, and atoms are built from a few fundamental particles — electrons, protons, neutrons. A handful of basic pieces, and everything else follows.

Physical quantities work the same way. A few base quantities sit underneath, and everything else is built from them. There are seven:

1. Length
2. Mass
3. Time
4. Electric Current
5. Temperature
6. Amount of Substance
7. Luminous Intensity

Only seven — that's a list you can memorise tonight. And here's the kind part: for most of your course, you'll lean on just the first five.

One honest note. Scientists chose these seven. There was no message from the sky saying "these are the basic ones." They're convenient, agreed-upon starting points — nothing more sacred than that.

Derived quantities

Every other quantity is built from the base seven. We call those derived quantities.

Charge is a clean example. You don't measure charge directly from a fresh base unit — you build it:

$\text{Charge} = \text{Current} \times \text{Time}$

Speed, force, energy, pressure — all derived. Each one is a recipe written in base quantities.

Dimensions — the recipe, written down

A dimension is just that recipe in shorthand. We write the base quantities with letters and read off how a derived quantity is built:

• Length → $L$
• Mass → $M$
• Time → $T$

Force, for instance, is mass times acceleration. Acceleration is length over time squared, so:

$[\text{Force}] = [M\,L\,T^{-2}]$

Read it out loud: mass to the first power, length to the first, time to the power minus two. That bracket is the dimensional formula of force. Velocity, in the same shorthand, is $[L\,T^{-1}]$ — length per time. We'll use these brackets all the time, so get friendly with them now.

The one rule for adding quantities

Physical quantities aren't bare numbers. They carry meaning. That meaning hands you a rule, and it's the rule beginners break most:

You can add or subtract only quantities of the same type.

Mass plus mass gives mass. Time plus time gives time. But mass plus time? Meaningless. You can't grow time by piling on kilograms.

$\text{Mass} + \text{Mass} = \text{Mass}$ $\text{Time} + \text{Time} = \text{Time}$

Notice what didn't change: adding or subtracting never changes the type of a quantity. Mass in, mass out.

Your turn. Two of these operations make sense and one is nonsense. Which is the nonsense, and why? (a) 5 m + 3 m (b) 10 s − 4 s (c) 2 kg + 7 s

Check: (c) is nonsense. You can add length to length and time to time, but mass and time are different types — there's no meaning in their sum.

How we get new quantities

If adding never changes the type, where do new quantities come from? From the other operation:

You can multiply or divide different quantities, and the result is something genuinely new.

$\text{Velocity} = \frac{\text{Displacement}}{\text{Time}}$ $\text{Force} = \text{Mass} \times \text{Acceleration}$

Divide displacement by time and you don't get a length or a time — you get velocity, a brand-new quantity with its own dimensions. That's the engine that builds all those derived quantities from the base seven.

(One caution for later: this works cleanly for ordinary numbers-with-units. Once vectors enter, multiplication gets its own rules. Hold that thought — it's coming.)

Quick recap

• We measure quantities; qualities like beauty stay unmeasured.
• Seven base quantities underpin everything: length, mass, time, current, temperature, amount of substance, luminous intensity.
• Everything else is a derived quantity, built by multiplying and dividing the base ones.
• A dimension writes that recipe in shorthand — force is $[M\,L\,T^{-2}]$.
• Add/subtract only same-type quantities; it never changes the type. Multiply/divide to make new quantities.

There's more than one way to sort physical quantities, though. Ever heard the words scalar and vector? That's Part 2 — see you there.