Contents
1. SI Base Units
Every physical quantity has a standard unit. The seven SI base units are the foundation — all derived units (like N, J, W) come from combinations of these.
| Quantity | Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Temperature | kelvin | K |
| Electric current | ampere | A |
| Amount of substance | mole | mol |
Common prefixes
| Prefix | Symbol | Multiplier |
|---|---|---|
| milli | m | × 10⁻³ (e.g. 500 mA = 0.5 A) |
| centi | c | × 10⁻² (e.g. 25 cm = 0.25 m) |
| kilo | k | × 10³ (e.g. 2 km = 2000 m) |
| mega | M | × 10⁶ (e.g. 5 MHz = 5×10⁶ Hz) |
Always convert to SI base units before substituting into a formula. 5 cm → 0.05 m; 200 g → 0.2 kg; 3 ms → 0.003 s.
2. Scalars and Vectors
Has magnitude (size) only — fully described by a number and unit.
Has both magnitude and direction — must include a number, unit, and direction to be complete.
| Scalars | Vectors |
|---|---|
| Distance | Displacement |
| Speed | Velocity |
| Mass | Weight / Force |
| Energy, Work, Power | Acceleration |
| Temperature, Time | Momentum |
"Speed is 10 m/s east" — wrong. Speed is scalar, it has no direction. Correct term is velocity: "velocity is 10 m/s east". This is a frequent 1-mark trap.
3. Measuring Instruments
| Instrument | Measures | Precision |
|---|---|---|
| Metre rule | Length | 1 mm |
| Vernier callipers | Length | 0.1 mm |
| Micrometer screw gauge | Small length | 0.01 mm |
| Stopwatch (digital) | Time | 0.01 s |
| Thermometer | Temperature | 1 °C (typical) |
Parallax error occurs when your eye is not perpendicular to the scale — the reading looks different from different angles. Always read at eye level, directly in line with the scale marking.
For a liquid in a tube, read the bottom of the meniscus at eye level to avoid parallax error.
4. Significant Figures
- All non-zero digits are significant: 3.45 → 3 s.f.
- Zeros between non-zero digits are significant: 3.04 → 3 s.f.
- Trailing zeros after a decimal point are significant: 3.40 → 3 s.f.
- Leading zeros are NOT significant: 0.0034 → 2 s.f.
How many significant figures in 0.04560 m?
Leading zeros are not significant. Digits 4, 5, 6, 0 are all significant. Answer: 4 significant figures.
Give your final answer to the same number of significant figures as the least precise measurement given. Only round at the final step — not mid-calculation.
5. Percentage Error
A metre rule (smallest division 1 mm) measures a length of 0.50 m. Find the percentage error.
% error = (0.001 ÷ 0.50) × 100% = 0.2%
Random vs systematic error
| Random error | Systematic error |
|---|---|
| Varies unpredictably each reading | Consistent — same direction every time |
| Reduced by taking more repeats and averaging | Cannot be fixed by repeating — must be identified |
| Example: reaction time when pressing stopwatch | Example: zero error on a balance |
Time 20 complete oscillations and divide by 20. This reduces the percentage error in each period by a factor of 20 compared to timing a single swing.
- SI base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd)
- Scalar: magnitude only (speed, distance, mass, energy, temperature)
- Vector: magnitude + direction (velocity, displacement, force, acceleration, weight, momentum)
- Random error: unpredictable, reduces precision. Reduce by taking many repeats and averaging.
- Systematic error: consistent offset (e.g. zero error). Reduces accuracy. Cannot be reduced by repeating.
- Vernier calliper reads to 0.1 mm; micrometer screw gauge reads to 0.01 mm
6. Common Exam Traps
Always write the unit in every numerical answer. "The length is 0.25" scores zero. "The length is 0.25 m" scores the mark.
Distance is total path length (scalar). Displacement is the straight-line distance from start to finish in a specified direction (vector). A runner who completes a 400 m lap has distance 400 m but displacement 0 m.
Before using a micrometer or vernier calliper, check the zero reading when fully closed. If it reads 0.02 mm, subtract 0.02 mm from every measurement taken.
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