CSEC Focus: Understanding SI units is fundamental to physics and is examined in both Paper 1 (multiple choice) and Paper 2 (structured questions). You must be able to identify base and derived units, use them correctly in calculations, and convert between units using prefixes.
What Are SI Units?
The International System of Units (Système International d’Unités) is the globally accepted system of measurement used in science, industry, and technology. It was established in 1960 to provide a consistent, coherent system for measuring physical quantities.
SI units provide a standard “language” for physics that ensures a measurement in one country means exactly the same thing in another country. For CSEC Physics, you need to understand two main categories: base units and derived units.
Why Standard Units Matter
Imagine if every country used a different “meter” or “second” – scientific communication would be impossible! SI units ensure that when you say “the wire is 2.5 meters long,” everyone understands exactly what that means, regardless of where they are in the world.
The 5 Fundamental (Base) Units for CSEC
While there are 7 base units in the complete SI system, your CSEC Physics course focuses on five fundamental quantities and their corresponding base units:
| Fundamental Quantity | Symbol for Quantity | SI Base Unit | Symbol for Unit |
|---|---|---|---|
| Mass | m | kilogram | kg |
| Length | l | metre | m |
| Time | t | second | s |
| Temperature | T | kelvin | K |
| Electric Current | I | ampere | A |
Exam Alert: You must know these 5 base units and their symbols. In the exam, quantity symbols are written in italics (like m for mass), while unit symbols are written in normal type (like kg for kilogram).
How Base Units Are Defined
- Kilogram (kg): Originally defined as the mass of a specific platinum-iridium cylinder kept in France. It’s the only base unit still defined by a physical object.
- Metre (m): Defined as the distance light travels in a vacuum in 1/299,792,458 of a second.
- Second (s): Defined using atomic clocks: the duration of 9,192,631,770 periods of radiation corresponding to the transition between two energy levels of the caesium-133 atom.
- Kelvin (K): 1/273.16 of the thermodynamic temperature of the triple point of water.
- Ampere (A): The constant current that, if maintained in two straight parallel conductors of infinite length placed 1 metre apart in a vacuum, would produce a force of 2 × 10⁻⁷ newton per metre of length.
💡 Remember: Base units are the building blocks. All other units in physics are derived from these five.
Derived Units: Combinations of Base Units
Derived quantities are obtained by multiplying or dividing fundamental quantities. Their units are called derived units.
What is a Derived Quantity?
A derived quantity is formed by combining two or more fundamental quantities using mathematical operations. For example:
- Speed = Distance ÷ Time (length/time)
- Area = Length × Width (length × length = length²)
- Density = Mass ÷ Volume (mass/length³)
Common Derived Units in CSEC Physics
| Derived Quantity | Unit Name | Unit Symbol | Derivation (in Base Units) |
|---|---|---|---|
| Speed/Velocity | metre per second | m/s or m s⁻¹ | m ÷ s = m s⁻¹ |
| Acceleration | metre per second squared | m/s² or m s⁻² | m ÷ s² = m s⁻² |
| Force | newton | N | kg m s⁻² |
| Energy/Work | joule | J | kg m² s⁻² |
| Power | watt | W | kg m² s⁻³ |
| Pressure | pascal | Pa | kg m⁻¹ s⁻² |
| Electric Charge | coulomb | C | A s |
| Potential Difference | volt | V | kg m² s⁻³ A⁻¹ |
| Resistance | ohm | Ω | kg m² s⁻³ A⁻² |
Important Formatting Rule: When writing derived units, do NOT use dots or dashes between unit symbols. Write m s⁻¹ NOT m.s⁻¹ or m-s⁻¹. Also, leave a space between the number and the unit: 5 m s⁻¹ NOT 5ms⁻¹.
Units Named After Scientists
Many derived units are named after famous scientists who made significant contributions to physics. Here’s the important rule for writing them:
RULE: When the unit name is written in full, use lowercase (e.g., “10 newtons”). When using the symbol, use uppercase (e.g., “10 N”).
- Newton (N) – after Isaac Newton (force)
- Joule (J) – after James Prescott Joule (energy)
- Watt (W) – after James Watt (power)
- Pascal (Pa) – after Blaise Pascal (pressure)
- Kelvin (K) – after Lord Kelvin (temperature) – Note: This is a base unit!
- Ampere (A) – after André-Marie Ampère (electric current) – Note: This is a base unit!
- Volt (V) – after Alessandro Volta (potential difference)
- Ohm (Ω) – after Georg Ohm (resistance)
SI Prefixes: Handling Very Large and Very Small Numbers
SI prefixes are used to express multiples or fractions of units, making numbers easier to work with.
Practical Tip: It’s easier to say “the wire diameter is 0.5 mm” than “0.0005 m”. Using appropriate prefixes makes measurements more intuitive.
Common Prefixes You Must Know
| Prefix | Symbol | Power of 10 | Example |
|---|---|---|---|
| tera | T | 10¹² | 1 Tm = 1,000,000,000,000 m |
| giga | G | 10⁹ | 1 GHz = 1,000,000,000 Hz |
| mega | M | 10⁶ | 1 MW = 1,000,000 W |
| kilo | k | 10³ | 1 kg = 1,000 g |
| centi | c | 10⁻² | 1 cm = 0.01 m |
| milli | m | 10⁻³ | 1 mm = 0.001 m |
| micro | μ | 10⁻⁶ | 1 μm = 0.000001 m |
| nano | n | 10⁻⁹ | 1 nm = 0.000000001 m |
| pico | p | 10⁻¹² | 1 ps = 0.000000000001 s |
Special Notes:
• “Micro” uses the Greek letter mu (μ)
• 1 decimeter³ (dm³) = 1 liter (L) = 0.001 m³
• Be careful with millimeter (mm) vs millisecond (ms) – the space matters!
Standard Form (Scientific Notation)
Standard form is used to express very large or very small numbers conveniently. A number is in standard form when it’s written as:
A × 10n
where A is a number between 1 and 10, and n is an integer (positive or negative).
Examples of Standard Form
- Speed of light: 300,000,000 m/s = 3.00 × 10⁸ m/s
- Charge of electron: 0.00000000000000000016 C = 1.6 × 10⁻¹⁹ C
- Diameter of a hair: 0.0001 m = 1 × 10⁻⁴ m
Common Mistakes to Avoid
- Using unit symbols incorrectly: Writing “kgs” instead of “kg” (unit symbols are never plural)
- Confusing quantity and unit symbols: Writing “m” for metre (unit) and m for mass (quantity)
- Incorrect capitalization: Writing “Newton” for the unit (should be “newton” when written out, “N” as symbol)
- Missing spaces: Writing “5m” instead of “5 m”
- Wrong prefix conversions: Thinking 1 cm² = 0.01 m² (actually 1 cm² = 0.0001 m² because area conversions involve squaring the conversion factor)
CSEC Exam Practice
A) Newton
B) Joule
C) Kelvin
D) Watt
Explanation: Kelvin (K) is the base unit for temperature. Newton, joule, and watt are all derived units.
Explanation:
250 mg = 250 × 10⁻³ g (since milli = 10⁻³)
250 × 10⁻³ g = 0.250 g
0.250 g = 0.250 × 10⁻³ kg = 2.50 × 10⁻⁴ kg
Explanation:
Pressure = Force/Area
Force = mass × acceleration = kg × m s⁻² = kg m s⁻²
Area = m²
Pressure = (kg m s⁻²)/(m²) = kg m⁻¹ s⁻²
🎯 Final CSEC Tip: Always include units in your final answers in the exam. A numerical answer without units will lose marks. When doing calculations, carry units through the entire process – this helps catch mistakes and ensures your final answer has the correct units.
Quick Reference Summary
- 5 Base Units: kg, m, s, K, A (know these perfectly)
- Derived Units: Formed from base units (e.g., N = kg m s⁻²)
- Prefixes: Use for convenient expression (kilo=10³, milli=10⁻³, micro=10⁻⁶)
- Standard Form: A × 10ⁿ where 1 ≤ A < 10
- Writing Rules: No plurals for symbols, lowercase for written names, uppercase for symbols of units named after people