1.1 Uses of SI Units and Their Prefixes

SI Units - Fundamental Units

SI units form the basis for all physical measurements and are fundamental for scientific calculations. They include:

Mass (m): kg (kilogram)
Length (l): m (metre)
Time (t): s (second)
Amount of substance (n): mol (mole)
Temperature (T): K (kelvin)
Electric current (I): A (ampere)

Each of these base quantities has a defined unit in the International System of Units (SI), and other physical quantities are derived from these fundamental units.

Derived Units

Derived units are combinations of base units, calculated through their physical relationships. For example, force is described by Newton's second law $F = ma$ (force equals mass times acceleration). To find the units for force:

Mass = $\text{kg}$
Acceleration = $\text{ms}^{-2}$ Thus, the unit for force becomes: $F = \text{kg} \cdot \text{ms}^{-2} = \text{N}$ (Newton)

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Example: SI Units of Voltage

Voltage $V$ can be derived by starting with the relationship:

$V = \frac{E}{Q}$

Where $E$ is energy (Joules, J) and $Q$ is charge (Coulombs, C).

Energy $E = \frac{1}{2}mv^2$ has SI units: $\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2}$ .
Charge $Q$ is current $I$ multiplied by time, with SI units As (Ampere-seconds). Therefore, voltage $V$ becomes:

V = \frac{\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2}}{\text{A} \cdot \text{s}} = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-3} \cdot \text{A}^{-1}

This is the derived unit for voltage.

SI Unit Prefixes

Prefixes allow us to express very large or small quantities more easily by using multiples of 10. Here are the most commonly used prefixes in physics:

Prefix	Symbol	Multiplier
Tera	T	$10^{12}$
Giga	G	$10^9$
Mega	M	$10^6$
Kilo	k	$10^3$
Centi	c	$10^{-2}$
Milli	m	$10^{-3}$
Micro	$\mu$	$10^{-6}$
Nano	n	$10^{-9}$
Pico	p	$10^{-12}$
Femto	f	$10^{-15}$

These prefixes can be used to adjust the scale of measurements. For instance:

6pF (picofarads) is $6 \times 10^{-12} \text{F}$
9GΩ (gigaohms) is $9 \times 10^9 \text{Ω}$
10µm (micrometres) is $10 \times 10^{-6} \text{m}$

Energy Conversion Examples

MeV to Joules (J):

$1 \text{eV} = :highlight[1.6 \times 10^{-19}] \text{J}$
To convert $:highlight[76] \text{MeV}$ to Joules, first convert MeV to eV: $76 \text{MeV} = 76 \times 10^6 \text{eV}$ Then convert eV to J: $76 \times 10^6 \times 1.6 \times 10^{-19} \text{J} = :highlight[1.216 \times 10^{-11}] \text{J}$

kWh to Joules (J):

$1 \text{kWh} = 1000 \times 3600 \text{J} = :highlight[3.6 \times 10^6] \text{J}$
Therefore, $1 \text{kWh} = :highlight[3.6] \text{MJ}$ (megajoules).

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Key Takeaways for Exam Preparation:

Understand how to derive units for various quantities based on their physical relationships (e.g., force, voltage, etc.).
Be familiar with SI prefixes and how to convert between different scales.
Practice conversions between units, such as energy units from eV to Joules and kWh to Joules. By mastering these concepts, you will be able to handle questions on SI units, derived units, and prefixes confidently.

Uses of SI Units and Their Prefixes Simplified Revision Notes for A-Level AQA Physics