Use of SI units and their prefixes

Welcome to the World of Measurement!

Welcome to the very beginning of your AQA AS Physics journey! Before we can calculate the speed of a galaxy or the energy of an electron, we need to agree on how to measure things. Think of SI units as the "universal language" of science. Whether you are a physicist in London, Tokyo, or New York, these units ensure everyone is talking about the same thing.

In this chapter, we are going to look at the building blocks of all physics measurements: the fundamental units, how we combine them, and the prefixes we use to handle everything from the massive to the microscopic. Don't worry if this seems like a lot of facts at first—once you get the hang of the patterns, it becomes second nature!

1. The "Magnificent Six": Fundamental SI Units

In the AQA syllabus, there are six base units (also called fundamental units) that you need to know. Everything else in physics is built from these six!

The Base Quantities and Units:
1. Mass: measured in kilograms (kg)
2. Length: measured in metres (m)
3. Time: measured in seconds (s)
4. Electric Current: measured in amperes (A)
5. Temperature: measured in kelvin (K)
6. Amount of Substance: measured in moles (mol)

Note: You might remember "candela" for light intensity from elsewhere, but for this syllabus, it is excluded. Also, you don't need to memorize the complex scientific definitions of these units!

Why Kelvin instead of Celsius?

In everyday life, we use Celsius. But in Physics, we use Kelvin because it starts at "Absolute Zero" (the point where particles stop moving).
Quick Tip: To turn Celsius into Kelvin, just add 273.15. So, \(0^\circ C = 273.15 K\).

Quick Review Box:
- There are 6 base units you need to know.
- Mass is the only base unit that already has a prefix (the 'kilo' in kilogram)!
- Always use lowercase 's' for seconds and 'm' for metres.

2. Derived Units: The Lego Bricks of Physics

If the base units are the individual Lego bricks, derived units are the cool models you build with them. A derived unit is just a combination of base units.

For example, let's look at Speed:
The formula for speed is \(v = \frac{d}{t}\).
Since distance (\(d\)) is measured in metres (m) and time (\(t\)) is in seconds (s), the unit for speed is \(m/s\) (or \(m \cdot s^{-1}\)).

Common Derived Units:
- Force (Newton, N): Derived from \(F = ma\), so \(1 N = 1 kg \cdot m \cdot s^{-2}\).
- Energy (Joule, J): Derived from \(Work = Force \times distance\), so \(1 J = 1 kg \cdot m^2 \cdot s^{-2}\).
- Power (Watt, W): Energy per second, so \(1 W = 1 J / s = 1 kg \cdot m^2 \cdot s^{-3}\).

Key Takeaway: Whenever you see a unit named after a scientist (Newton, Joule, Watt), it is a derived unit that can be broken back down into the "Magnificent Six" base units.

3. SI Prefixes: Handling the Big and the Small

Physics deals with the size of the entire universe and the size of an atom. Writing all those zeros would be exhausting! That’s where prefixes come in. They are essentially a shorthand for Standard Form (powers of 10).

The Prefixes You Must Know:

From biggest to smallest:
- Tera (T): \(10^{12}\) (A trillion)
- Giga (G): \(10^9\) (A billion)
- Mega (M): \(10^6\) (A million)
- kilo (k): \(10^3\) (A thousand)
- centi (c): \(10^{-2}\) (A hundredth - Used mostly for cm)
- milli (m): \(10^{-3}\) (A thousandth)
- micro (\(\mu\)): \(10^{-6}\) (A millionth)
- nano (n): \(10^{-9}\) (A billionth)
- pico (p): \(10^{-12}\)
- femto (f): \(10^{-15}\)

Memory Aid: The Mnemonic

To remember the "big" ones: Terrible Giant Monsters killed...
To remember the "small" ones: ...many micro nasty peaky flies.
(T, G, M, k ... m, \(\mu\), n, p, f)

Common Mistake Alert: Watch out for 'm' and 'M'!
- Lowercase 'm' means milli (\(10^{-3}\)).
- Uppercase 'M' means Mega (\(10^{6}\)).
Using the wrong one could make your answer a billion times too big or small!

4. Converting Between Units

Sometimes you need to convert between different units of the same quantity. This is very common in energy calculations.

Energy: Joules (J) vs Electronvolts (eV)

In particle physics, Joules are way too big. We use the electronvolt (eV) instead.
- To go from eV to J: Multiply by \(1.6 \times 10^{-19}\).
- To go from J to eV: Divide by \(1.6 \times 10^{-19}\).

Analogy: Think of Joules as 'Kilometres' and eV as 'Millimetres'. They both measure length, but one is for huge things and the other is for tiny things!

Energy: Joules (J) vs Kilowatt-hours (kWh)

Your electricity bill uses kilowatt-hours. This is a unit of energy, not power!
\(1 kWh = 1000 W \times 3600 s = 3,600,000 J\) (or \(3.6 MJ\)).

Step-by-Step Conversion (J to kWh):
1. Start with your energy in Joules.
2. Divide by 1,000 to get kJ.
3. Divide by 3,600 to get kWh.

Did you know? A kilowatt-hour is the amount of energy a 1000-watt heater uses in one hour. It’s a lot of Joules, which is why we use kWh for homes!

5. Final "Quick Check" for Success

Before you move on to the next chapter, ask yourself:
- Can I name the 6 base SI units? (kg, m, s, A, K, mol)
- Do I know what \(10^{-6}\) is? (micro, \(\mu\))
- Do I know what \(10^{9}\) is? (Giga, G)
- Can I convert \(1 kWh\) into Joules? (\(3.6 \times 10^6 J\))

Don't worry if this seems tricky at first! You will use these units every single day in Physics. The more you use them, the more they will feel like a second language. Keep practicing your standard form, and you'll be an expert in no time!