Introduction: The Language of Physics
Physics has its own language—a system of physical quantities and units that allow us to describe and measure the world around us. Before you can solve problems about motion, energy, or electricity, you must first speak this language fluently. This guide will walk you through everything you need to know about physical quantities and units for your CSEC Physics exam.
1. What Are Physical Quantities?
A physical quantity is anything that can be measured and expressed with a numerical value and a unit. For example:
- The length of your desk:
1.2 metres - The time for a pendulum swing:
2.0 seconds - The mass of your textbook:
1.5 kilograms
Key Concept: Without a unit, a number has no physical meaning in science. Saying “the temperature is 25” is meaningless unless you specify whether it’s 25°C, 25 K, or 25°F.
2. Fundamental (Base) Quantities
These are the basic building blocks of physics—quantities that cannot be defined in terms of other quantities. In CSEC Physics, you focus on five fundamental quantities:
| Fundamental Quantity | Symbol | SI Base Unit | Unit Symbol |
|---|---|---|---|
| Mass | m | kilogram | kg |
| Length | l | metre | m |
| Time | t | second | s |
| Temperature | T | kelvin | K |
| Electric Current | I | ampere | A |
Important Formatting Rules:
- Symbols for quantities are written in italics: m, t, T
- Symbols for units are not italicized: kg, m, s
- Units are never written in plural form: 10 kg (not 10 kgs)
3. SI Units: The International Standard
The International System of Units (SI) provides precise, universal definitions for measurement.
The Kilogram (kg)
- The base unit of mass
- Defined as the mass of the International Prototype Kilogram, a platinum-iridium cylinder kept in Sèvres, France
- All other masses are compared to this standard
The Metre (m)
- The base unit of length
- Since 1983: the distance light travels in a vacuum in 1/299,792,458 of a second
- This definition ensures it never changes with environmental conditions
The Second (s)
- The base unit of time
- Defined using atomic clocks: the time for 9,192,631,770 vibrations of a caesium-133 atom
- So precise that two such clocks would differ by less than 1 second in 300,000 years!
Kelvin (K) and Ampere (A)
- Kelvin: unit of temperature (you don’t need the exact definition for CSEC)
- Ampere: unit of electric current (named after André-Marie Ampère)
4. Derived Quantities & Units
Derived quantities are created by combining fundamental quantities through multiplication or division. Their units are called derived units.
| Derived Quantity | Formula | Derived Unit | Unit Symbol |
|---|---|---|---|
| Area | length × length | square metre | m² |
| Volume | length × length × length | cubic metre | m³ |
| Speed/Velocity | distance ÷ time | metre per second | m/s or m·s⁻¹ |
| Acceleration | velocity ÷ time | metre per second squared | m/s² or m·s⁻² |
| Density | mass ÷ volume | kilogram per cubic metre | kg/m³ or kg·m⁻³ |
| Force | mass × acceleration | newton | N (1 N = 1 kg·m·s⁻²) |
| Energy/Work | force × distance | joule | J (1 J = 1 N·m) |
| Power | energy ÷ time | watt | W (1 W = 1 J/s) |
| Pressure | force ÷ area | pascal | Pa (1 Pa = 1 N/m²) |
Important Formatting Rules:
- No dots or dashes between unit symbols: write A s not A·s or A-s
- Leave a space between symbols: m s⁻¹ not ms⁻¹ (which could mean millisecond)
- Use index notation (m·s⁻¹) in your exam answers
5. Units Named After Scientists
Many derived units honor famous physicists. Remember these rules:
- When written in full: lowercase (e.g., 10 newtons, 5 joules)
- When using symbols: capitalize first letter (e.g., 10 N, 5 J)
| Unit | Symbol | Named After | Quantity Measured |
|---|---|---|---|
| Newton | N | Isaac Newton | Force |
| Joule | J | James Joule | Energy/Work |
| Watt | W | James Watt | Power |
| Pascal | Pa | Blaise Pascal | Pressure |
| Kelvin | K | Lord Kelvin | Temperature |
| Ampere | A | André-Marie Ampère | Electric Current |
6. Multiple and Sub-multiple Units
Sometimes base units are too large or too small for practical measurement. We use prefixes to create multiples and sub-multiples:
| Prefix | Symbol | Multiplier | Example |
|---|---|---|---|
| kilo | k | 10³ | kilometre (km) = 1000 m |
| centi | c | 10⁻² | centimetre (cm) = 0.01 m |
| milli | m | 10⁻³ | millimetre (mm) = 0.001 m |
| micro | µ | 10⁻⁶ | micrometre (µm) = 0.000001 m |
| nano | n | 10⁻⁹ | nanometre (nm) = 10⁻⁹ m |
Special Notes:
- Micrometre (µm) is sometimes called a micron
- Litre (L) = 1 dm³ = 10⁻³ m³ (common in chemistry)
- Hectare = 10,000 m² (used for land area)
7. Standard Form (Scientific Notation)
For very large or very small numbers, we use standard form:
- Write as: a × 10^n where 1 ≤ a < 10
- n is positive for large numbers, negative for small numbers
Examples:
- Speed of light:
3.00 × 10⁸ m/s - One nanometre:
1.00 × 10⁻⁹ m - Avogadro’s number:
6.02 × 10²³
8. Worked Examples
Example 1: Unit Conversion
A stock bottle contains tablets each of mass 250 mg. The total mass is 0.5 kg. How many tablets?
Solution:
Convert to same units (mg):
0.5 kg = 0.5 × 10³ g = 0.5 × 10³ × 10³ mg = 0.5 × 10⁶ mg
Number of tablets = (0.5 × 10⁶ mg) / (250 mg) = 2 × 10³ = 2000
Example 2: Density Calculation
A piece of cork has mass 10 g and volume 40 cm³. Find its density.
Solution:
Density = mass/volume = 10 g / 40 cm³ = 0.25 g/cm³
(or 0.25 g·cm⁻³ in index notation)
9. CSEC Exam Tips
- Always include units in your answers (marks are deducted if you don’t!)
- Use correct symbols and formatting
- Convert to consistent units before calculations
- Show your working clearly
- Express final answers with appropriate significant figures
Next Steps in Your CSEC Physics Journey
Now that you’ve mastered physical quantities and units, you’re ready to tackle:
- Accuracy, Precision, and Significant Figures
- Measurement Techniques with Vernier Calipers and Micrometers
- Graph Plotting and Analysis
- Forces and Motion