Sample Notes: Physical Quantities And Units
AS Level Physics – Topic 1: Physical Quantities and Units
1.1 Physical Quantities
- A physical quantity is any quantity that can be measured and consists of:
- A numerical magnitude (e.g. 5.2)
- A unit (e.g. meters)
- Examples of physical quantities:
- Distance (m), Time (s), Mass (kg), Speed (m/s), Temperature (K)
- Reasonable estimates:
- Mass of an apple ≈ 0.2 kg
- Height of a door ≈ 2 m
- Time for a heart to beat once ≈ 1 s
- Speed of walking ≈ 1.5 m/s
1.2 SI Units
Base Quantities and SI Units
| Physical Quantity | SI Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Temperature | kelvin | K |
| Electric Current | ampere | A |
Derived Units
Derived units are combinations of base units, either as products or quotients.
| Derived Quantity | SI Unit | Base Unit Expression |
|---|---|---|
| Area | m² | m × m |
| Volume | m³ | m × m × m |
| Velocity | m/s | m ÷ s |
| Acceleration | m/s² | m ÷ s² |
| Force | N | kg·m/s² |
| Energy | J | kg·m²/s² |
| Power | W | kg·m²/s³ |
| Pressure | Pa | N/m² = kg/m·s² |
Homogeneity of Equations
- All physical equations must be dimensionally homogeneous.
- Each term must have the same base unit combination.
- Example:
Equation: s = ut + ½at²
Units: m = (m/s)(s) + (1/2)(m/s²)(s²)
→ All terms simplify to meters (m)
SI Prefixes
| Prefix | Symbol | Multiple | Example |
|---|---|---|---|
| pico | p | 10⁻¹² | 1 pm = 10⁻¹² m |
| nano | n | 10⁻⁹ | 1 ns = 10⁻⁹ s |
| micro | μ | 10⁻⁶ | 1 μA = 10⁻⁶ A |
| milli | m | 10⁻³ | 1 mm = 10⁻³ m |
| centi | c | 10⁻² | 1 cm = 10⁻² m |
| deci | d | 10⁻¹ | 1 dm = 10⁻¹ m |
| kilo | k | 10³ | 1 km = 10³ m |
| mega | M | 10⁶ | 1 MW = 10⁶ W |
| giga | G | 10⁹ | 1 GW = 10⁹ W |
| tera | T | 10¹² | 1 TB = 10¹² B |
1.3 Errors and Uncertainties
Types of Errors
- Systematic error:
- Repeated error in one direction (e.g. zero error on instruments)
- Affects accuracy
- Random error:
- Unpredictable variations
- Affects precision
Accuracy vs Precision
| Term | Definition |
|---|---|
| Accuracy | Closeness to the true value |
| Precision | Repeatability or consistency of measurements |
Uncertainty Calculations
- Absolute uncertainty:
- ± smallest division (e.g. ±0.01 cm)
- Percentage uncertainty:
- (absolute uncertainty / measured value) × 100%
Combining Uncertainties
- For addition/subtraction:
Add absolute uncertainties - For multiplication/division:
Add percentage uncertainties
1.4 Scalars and Vectors
Scalar Quantities
- Have only magnitude
- Examples: mass, speed, time, distance, temperature
Vector Quantities
- Have magnitude and direction
- Examples: displacement, velocity, acceleration, force
Vector Addition and Subtraction
- Same direction: Add magnitudes directly
- Opposite direction: Subtract magnitudes
- At angles: Use vector diagrams, Pythagoras, or trigonometry
Components of Vectors
- Any vector can be broken into:
- Horizontal component: Aₓ = A * cosθ
- Vertical component: Aᵧ = A * sinθ
- Use components to add vectors algebraically:
- Resultant vector:
- Rₓ = Aₓ + Bₓ
- Rᵧ = Aᵧ + Bᵧ
- R = √(Rₓ² + Rᵧ²)
- θ = tan⁻¹(Rᵧ / Rₓ)
- Resultant vector: