In this article, I shall write about the physics syllabus on the topic of measurement. The writings in this and following articles on physics syllabus cover the A level (H2) physics, which also includes materials for O level physics.

My hope is to give a fairly complete idea on the kind of things students learn in physics, in a way that people with little or no physics knowledge can understand. So the style would be informal.

"Syllabus" is a decription on what we learn in a course. For this article, I shall start off with the topic of "Measurement", usually the first topic in a school physics course. So, lets go!

In the topic of Measurement, we learn what are the kind of things that people often measure. The basic ones in physics include mass, length, time, temperature, etc. Each of these has a unit. Kilogram, metre, and second (for time) are familiar examples.

Less familiar units may include Ampere for electric current, Kelvin for temperature, and mole for amount of substance.

The last one - mole - has nothing to do with the lump that can grow on our skin, nor the small mammal that lives underground. It is actually about a certain (very huge) number - used as a unit to tell us the number of atoms or molecules in a particular substance.

If you really want to know huge a number 1 mole is, it is roughly 6 followed by 23 zeros. Or 600,000,000,000,000,000,000,000. To see how we use this in physics, take a look at my blog on ideal gases.

Even if we have not studied physics, we can imagine that there are lots and lots of different types of things in the world we can measure. So there must be lots and lots of units.

But guess what, all units in the world - maybe even the universe - can be made up from just 7 basic units. These are the units for

- mass,
- length,
- time,
- temperature,
- electric current,
- amount of substance, and
- brightness of light.

What does "made up from just 7 basic units" mean? As a simple example, we can think of velocity. If we say that a car is moving at 60 km/h (kilometres per hour), then we have a unit that is made up of 2 basic units - kilometer (for length) and hour (for time).

Units made up from base units, like km/h (kilometres power hour) or m/s (metres per second) are called "derived units"

We also learn a simple way to check if a physics equation is wrong. The way is to compare the units on left side and right side of an equation. If the units are different, that the equation is definitely wrong. (But if the units are the same, then we cannot be sure. Then we have to find another way to check.)

For each unit, we also learn how to modify it for measurements that are very big or very small. For example, we use the unit of metre to measure length. But metre is a bit long compare to things we use everyday, like books, coins, pen, laptop, ...

So instead of say 0.01 metre (0.01 m) for the size of a coin, we say 1 centimetre (1 cm), which is the length of 1 m divided by 100. The "c" added in front of the "m" to make "cm" saves us from having to learn a completely different name for long and short units.

The "c" in "cm" is called a prefix. We need to learn 10 of these. The smallest is "pico", which is the fraction of 1 part in 1 trillion. The largest is "tera", which is 1 trillion. In case you do not know, 1 trillion is 1 followed by 12 zeros, like this : 1,000,000,000,000.

On the other side of the scale learn the prefix "pico", which means a fraction of 1 part in 1 trillion.

What is the use of such huge numbers and such small numbers ??

Answer: For distances of stars and sizes of atoms.

Physics is very much about making numbers useful - by adding meanings to to them. One way is by adding units like what I have described above, like 1 metre for distance, or 5 metres per second for speed. Another way is by combining this quantity with another, like direction.

We can talk about walking 1 m to the east, or running at a speed of 2 m/s to the south. It turns out to be convenient to combine say a distance and a direction into one single idea - called a vector.

And there are a few rules that are invented to add or subtract vectors. For example, a force is a vector because we can think of its magnitude (how strong it is) and its direction. But if 2 forces pull on a heavy box in difference directions, what is the resulting effect?

Turns out that there is a simple way in physics to find the resulting effect of these 2 forces - that is, a way to "add" forces pulling in different directions so as to find out which way the box moves.

The quantities described so far - distances, temperature, time, ... are numbers that we can measure. E.g. using a ruler, a thermometer, a stop watch, ...

But how accurate are these instruments really? If we look at our ruler, we see markings - usually for centimetres and millimetres. We can use this to say measure the length of a book. But what if one end of the book falls between two millimetre markings on the ruler?

Usually, we just take the nearer marking as the reading. But this also means that there is a small error. Is this error important?

That - is an important question !

The answer is - it depends on what we want to use the measured number for. If we are just curious, then it does not matter. Just take the nearer marking as the value.

If it is to choose a book cover, then we have think a bit harder. What if the nearer value is 0.1 or 0.2 mm shorter than the length of the book. Then we may end up with a book cover with a very tight fit, which may even cause slight tearing on the cover or the book.

You can learn these concepts and more at Dr Hock's maths and physics tuition.