Module 00 — Foundations
Duration: 1–2 weeks | Prereq: None
This module isn't exciting — but it's load-bearing. Everything in later modules uses these tools. The good news: it's short, and most of it will feel familiar once you see it.
1. SI Units — The Language of Physics
Physics quantities are meaningless without units. The international standard is the SI system (Système International).
The seven base units
| Quantity | Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
Everything else is derived from these. For example:
- Speed = distance / time → m/s (or m s⁻¹)
- Force = mass × acceleration → kg m s⁻² = newton (N)
- Energy = force × distance → kg m² s⁻² = joule (J)
Prefixes you'll use constantly
| Prefix | Symbol | Multiplier |
|---|---|---|
| Giga | G | × 10⁹ |
| Mega | M | × 10⁶ |
| kilo | k | × 10³ |
| — | — | × 10⁰ (baseline) |
| milli | m | × 10⁻³ |
| micro | μ | × 10⁻⁶ |
| nano | n | × 10⁻⁹ |
| pico | p | × 10⁻¹² |
Example: A wavelength of 500 nm = 500 × 10⁻⁹ m = 5 × 10⁻⁷ m
Unit checking (dimensional analysis)
Before trusting any answer, check the units work out. If you're calculating speed and your units don't simplify to m/s, you've made an error somewhere. This habit catches a huge number of mistakes.
2. Standard Form and Orders of Magnitude
Physics deals with extremes — from the radius of a proton (~10⁻¹⁵ m) to the distance to the edge of the observable universe (~10²⁶ m). Standard form keeps numbers manageable.
Standard form: a × 10ⁿ where 1 ≤ a < 10
Examples:
- 6,400,000 m = 6.4 × 10⁶ m
- 0.000000045 s = 4.5 × 10⁻⁸ s
Multiplying in standard form: multiply the numbers, add the exponents
(3 × 10⁴) × (2 × 10³) = 6 × 10⁷
Dividing in standard form: divide the numbers, subtract the exponents
(6 × 10⁸) ÷ (2 × 10³) = 3 × 10⁵
3. Significant Figures and Uncertainty
The short version: Never write down more precision than your data justifies.
- 9.81 m/s² has 3 significant figures
- 9.8 m/s² has 2 significant figures
- 0.0045 has 2 significant figures (leading zeros don't count)
In practice, working to 3 significant figures is standard for most A Level problems.
Uncertainty is the acknowledgement that every measurement has limits. You'll encounter it when reading about experiments. The key idea: if a ruler can measure to ±1 mm, then a measurement of 23 cm is really 23.0 ± 0.1 cm.
4. Maths Toolkit
4.1 Rearranging Equations
The single most important algebraic skill in A Level Physics. The rule: whatever you do to one side, do to the other.
Example: The equation for speed is v = d / t
To find d: multiply both sides by t → d = v × t
To find t: divide both sides by v → t = d / v
A useful trick: think of the equation as a triangle. Write v at the top, d and t at the bottom. Cover the one you want, and the arrangement of the remaining two tells you the operation.
Practice: Rearrange E = mc² to find m. (Answer: m = E / c²)
4.2 Proportionality
Physics is full of proportional relationships. Understanding them stops you needing to memorise every equation.
- Direct proportion: y ∝ x means "if x doubles, y doubles"
- Inverse proportion: y ∝ 1/x means "if x doubles, y halves"
- Square proportion: y ∝ x² means "if x doubles, y quadruples"
Example: Gravitational force ∝ 1/r² (inverse square law). Double the distance → force drops to 1/4.
4.3 Trigonometry
You need sin, cos, and tan — specifically for resolving vectors (covered next) and wave problems.
hypotenuse
/|
/ |
/ | opposite
/θ |
------
adjacent
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
Memory aid: SOH-CAH-TOA
The angles you'll use most: 30°, 45°, 60°, 90°.
Handy values to remember:
- sin 30° = 0.5, cos 30° = 0.866
- sin 45° = cos 45° = 0.707
- sin 60° = 0.866, cos 60° = 0.5
4.4 Graphs — Gradients and Areas
Two graph operations matter in physics:
Gradient (slope) = Δy / Δx (change in y divided by change in x)
The gradient tells you the rate of change. On a distance-time graph, the gradient is speed. On a velocity-time graph, the gradient is acceleration.
Area under a graph tells you accumulated quantity. On a velocity-time graph, the area is displacement (net change in position). If the object reverses direction partway through, areas above and below the time axis partially cancel — giving displacement, not total distance travelled.
This is secretly calculus. The gradient is the derivative (rate of change); the area is the integral (accumulated total). You don't need to use calculus notation at A Level, but recognising what's happening conceptually will serve you well if you go further.
5. Vectors and Scalars
This is one of the most important distinctions in all of physics.
Scalar: a quantity described by magnitude (size) alone.
Examples: speed, distance, mass, temperature, energy, time
Vector: a quantity described by both magnitude and direction.
Examples: velocity, displacement, force, acceleration, momentum
Subtle but important: Speed and velocity are different.
- Speed = 60 mph (scalar — just a size)
- Velocity = 60 mph north (vector — size and direction)
Adding vectors
Scalars add normally: 5 kg + 3 kg = 8 kg.
Vectors must account for direction. If two forces both act in the same direction, add them. If they act at 180° (opposite), subtract. If they act at an angle, you need trigonometry.
The component method (most useful approach):
Any vector can be split into a horizontal (x) component and a vertical (y) component.
For a vector of magnitude F at angle θ to the horizontal:
- Horizontal component: F cos θ
- Vertical component: F sin θ
To find the resultant of multiple vectors:
- Resolve each into x and y components
- Sum all x components → Rₓ
- Sum all y components → Rᵧ
- Resultant magnitude: R = √(Rₓ² + Rᵧ²)
- Angle: θ = tan⁻¹(Rᵧ / Rₓ)
Worked Example: Two forces act on a box: 6 N east and 8 N north. What is the resultant?
Rₓ = 6 N, Rᵧ = 8 N R = √(36 + 64) = √100 = 10 N θ = tan⁻¹(8/6) = tan⁻¹(1.33) ≈ 53° north of east
6. Self-Check Questions
Try these before moving on. Don't worry if you need to look back — that's the point.
- Convert 45 nm to metres in standard form.
- The equation for kinetic energy is Eₖ = ½mv². Rearrange to find v.
- A force of 50 N acts at 30° to the horizontal on a box. What are its horizontal and vertical components?
- On a velocity-time graph, what does the area under the curve represent?
- Is "temperature" a vector or scalar? What about "force"?
Answers:
- 45 × 10⁻⁹ m = 4.5 × 10⁻⁸ m
- v = √(2Eₖ / m)
- Horizontal: 50 cos 30° = 50 × 0.866 = 43.3 N. Vertical: 50 sin 30° = 50 × 0.5 = 25 N
- Displacement (net change in position)
- Temperature is a scalar. Force is a vector.
Go Deeper
If you're finding the maths more enjoyable than expected, these are worth a look:
- "The Language of Physics" — any introductory chapter in Halliday & Resnick (a classic university text, often findable in libraries)
- Khan Academy: Algebra and Trigonometry sections — short videos, good for specific gaps
- 3Blue1Brown "Essence of Calculus" (YouTube) — if you want the intuition behind gradients and areas, this series is beautiful. Not required, but outstanding.