Introduction: Why Units Matter in Physics (9630)
Welcome to the foundational chapter of your Physics course! Measurements are the absolute heart of physics, and to communicate those measurements clearly—whether you’re designing a satellite or calculating the speed of light—we need a universal language. That language is the SI unit system.
In this section, we will learn about the building blocks of all physical quantities (the base units), how they combine to form derived units, and how to use prefixes (like 'kilo' or 'nano') to handle incredibly huge or tiny numbers easily. Don't worry if you find conversions tricky; we’ll break them down step-by-step!
1. The Foundation: SI Base (Fundamental) Units
The International System of Units (SI, from the French Système International d'Unités) provides seven core units. These are known as Fundamental or Base Units. Every other unit in physics is built from combinations of these seven.
You need to know the following six base quantities and their corresponding SI units:
Quick Review: The Essential Six Base Units
- Length: metre (\(m\))
- Mass: kilogram (\(kg\))
- Time: second (\(s\))
- Electric Current: ampere (\(A\))
- Temperature (Thermodynamic): kelvin (\(K\))
- Amount of Substance: mole (\(mol\))
(Note: Although there is a seventh base unit, the candela, the OxfordAQA syllabus confirms that knowledge of the candela (light intensity) is not required for this course.)
Key Takeaway:
The base units are the essential, independent units from which all other scientific measurements are derived. Remember the strange one: mass is the only base quantity defined by a prefix (\(kg\)).
Always use the correct form of the unit name. For example, Temperature must be given in kelvin (\(K\)) in most formulas, not degrees Celsius (\(^{\circ}C\)).
2. SI Derived Units
When you combine two or more base units, you get a Derived Unit. These are used to measure derived physical quantities, such as force, energy, power, and speed.
For example:
- Speed is measured in length divided by time: \(\text{metres per second}\) (\(m/s\) or \(m s^{-1}\)).
- Volume is length multiplied by length multiplied by length: \(\text{metres cubed}\) (\(m^3\)).
Some derived units are so frequently used that they are given their own special names and symbols. You should be comfortable recognizing these and knowing their base unit equivalents:
Examples of Special Derived Units
- Force: newton (\(N\)). Defined as \(kg \ m \ s^{-2}\). (This comes from \(F = ma\), where \(m\) is in \(kg\) and \(a\) is in \(m s^{-2}\).)
- Energy/Work: joule (\(J\)). Defined as \(N \ m\) or \(kg \ m^2 \ s^{-2}\).
- Power: watt (\(W\)). Defined as \(J/s\) or \(kg \ m^2 \ s^{-3}\).
- Potential Difference (Voltage): volt (\(V\)). Defined as \(J/C\) or \(kg \ m^2 \ A^{-1} \ s^{-3}\).
Key Takeaway:
Derived units are simply mathematical combinations of the base units. Being able to write a derived unit in terms of its base units is essential for checking equations (though dimensional analysis is not required, understanding unit composition is).
3. Using SI Prefixes and Standard Form
Physics deals with extremes. Sometimes we measure distances in millions of metres (astronomy), and sometimes in billionths of a metre (atomic physics). To manage these very large or very small numbers without writing out endless zeros, we use SI Prefixes and Standard Form.
a) Standard Form (Scientific Notation)
Standard form expresses a number as \(A \times 10^n\), where \(A\) is a number between 1 and 10, and \(n\) is an integer. This is crucial because all SI prefixes represent specific powers of ten.
Example: The speed of light is \(300,000,000 \ m/s\). In standard form, this is \(3.0 \times 10^8 \ m/s\).
b) The Essential SI Prefixes
You must know the symbol, value, and standard form for the following prefixes:
| Prefix | Symbol | Value | Standard Form (\(10^n\)) |
|---|---|---|---|
| Tera | T | 1,000,000,000,000 | \(10^{12}\) |
| Giga | G | 1,000,000,000 | \(10^{9}\) |
| Mega | M | 1,000,000 | \(10^{6}\) |
| kilo | k | 1,000 | \(10^{3}\) |
| centi | c | 0.01 | \(10^{-2}\) |
| milli | m | 0.001 | \(10^{-3}\) |
| micro | \(\mu\) (mu) | 0.000001 | \(10^{-6}\) |
| nano | n | 0.000000001 | \(10^{-9}\) |
| pico | p | 0.000000000001 | \(10^{-12}\) |
| femto | f | 0.000000000000001 | \(10^{-15}\) |
Did you know? The prefix ‘micro’ uses the Greek letter mu (\(\mu\)) because 'm' was already taken by 'milli'!
c) Using Prefixes for Conversion
When performing calculations, you must convert all prefixed quantities back into their base SI units (often called "the standard form").
Step-by-step Process:
1. Identify the prefix.
2. Replace the prefix symbol with its corresponding power of ten.
Example 1: Convert \(500 \ mA\) to \(A\).
The prefix 'milli' (\(m\)) means \(\times 10^{-3}\).
$$500 \ mA = 500 \times 10^{-3} \ A = 0.5 \ A$$
Example 2: Convert \(5.2 \ GJ\) to \(J\).
The prefix 'Giga' (\(G\)) means \(\times 10^{9}\).
$$5.2 \ GJ = 5.2 \times 10^{9} \ J$$
Memory Aid for Powers of Ten
Notice that most required prefixes move in steps of \(10^3\) (or \(10^{-3}\)). The exceptions are kilo (\(10^3\)), centi (\(10^{-2}\)), and deci (\(10^{-1}\), though deci is less commonly tested at AS level than the others).
Key Takeaway:
SI prefixes are a shortcut for standard form. To use any quantity in a calculation, always substitute the prefix with its specific power of ten.
4. Crucial Unit Conversions (Non-Prefix Conversions)
Sometimes you need to convert between units that measure the same quantity but are defined differently, or units that use different combinations of base units. The syllabus specifically requires you to handle conversions involving Energy units: the Joule (\(J\)), the Electronvolt (\(eV\)), and the Kilowatt-hour (\(kW h\)).
a) Electronvolt (eV) to Joule (J)
The electronvolt is a unit of energy commonly used in particle physics and atomic scales. It is defined as the amount of kinetic energy gained by a single electron when it is accelerated through an electric potential difference of one volt.
The conversion is directly related to the magnitude of the elementary charge, \(e\).
$$1 \text{ eV} = e \times 1 \text{ V}$$ $$1 \text{ eV} = 1.60 \times 10^{-19} \text{ C} \times 1 \text{ V}$$ $$\mathbf{1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}}$$ (Since \(1 \text{ C} \times 1 \text{ V} = 1 \text{ J}\))
Step-by-step Conversion:
1. To convert eV to J: Multiply the eV value by \(1.60 \times 10^{-19}\).
2. To convert J to eV: Divide the J value by \(1.60 \times 10^{-19}\).
b) Kilowatt-hour (kW h) to Joule (J)
The kilowatt-hour is a commercial unit of energy (it's what your home electricity meter measures). Although it looks complicated, it's just the definition of power multiplied by time.
We know:
$$Power (P) = \frac{Energy (E)}{Time (t)}$$
$$Energy (E) = P \times t$$
To find the value of \(1 \text{ kW h}\) in Joules (the SI unit for energy), we convert the power and time components to SI units:
1. Convert kilowatts (\(kW\)) to Watts (\(W\)): $$1 \text{ kW} = 1 \times 10^3 \text{ W}$$
2. Convert hours (\(h\)) to seconds (\(s\)): $$1 \text{ h} = 60 \text{ minutes} \times 60 \text{ seconds} = 3600 \text{ s}$$
3. Multiply the SI components: $$1 \text{ kW h} = (1 \times 10^3 \text{ W}) \times (3600 \text{ s})$$ $$\mathbf{1 \text{ kW h} = 3.6 \times 10^6 \text{ J}}$$
Key Takeaway:
Be prepared to perform conversions between non-SI energy units (eV and kW h) and the SI unit (Joule). Always use standard form and the correct conversion factor provided on your data sheet (or memorized, if necessary, such as the elementary charge).
✅ Quick Review: Use of SI Units and Prefixes
What You Must Know:
- Base Units: Length (m), Mass (kg), Time (s), Current (A), Temp (K), Amount of Substance (mol).
- Derived Units: Recognise derived units (like J, N, W) and know that they are combinations of base units.
- Prefixes: Be able to convert using T, G, M, k, c, m, \(\mu\), n, p, f, by replacing the prefix with the correct power of 10.
- Standard Conversions: Be able to convert between J and eV (\(1.60 \times 10^{-19} \text{ J}\)) and J and kW h (\(3.6 \times 10^6 \text{ J}\)).
The purpose of this entire system is consistency. By always converting everything to its base SI unit before calculation, physicists worldwide can trust each other's results!