Base quantities and SI units
Key idea: Recall the six base quantities listed for O-Level Physics, distinguish base and derived quantities, and keep units consistent in calculations.
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The core idea
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Learning objectives
- Represent a physical quantity with a numerical magnitude and unit
- Recall the six prescribed SI base quantities and their units
- Use the prescribed SI prefixes from nano to tera
- Compare orders of magnitude from a typical atom to the Earth
- Select and justify measuring instruments by range and precision
- Distinguish scalar and vector quantities and give examples
- Add two vectors graphically to determine a resultant
1. Definitions
A physical quantity is a measurable property written as a number and a unit, such as 2.5 m.
A base quantity is defined independently. A derived quantity is defined using other quantities, usually through an equation.
2. Key Ideas
For Singapore–Cambridge O-Level Physics 6091, recall these six base quantities and SI units:
| Base quantity | Quantity symbol | SI unit | Unit symbol |
|---|---|---|---|
| mass | m | kilogram | kg |
| length | l | metre | m |
| time | t | second | s |
| electric current | I | ampere | A |
| temperature | T | kelvin | K |
| amount of substance | n | mole | mol |
SI globally has seven base quantities. The seventh is luminous intensity, measured in candela (cd). The 6091 syllabus recall requirement lists the six in the table above.
3. Detailed Explanations
| Derived quantity | Relationship | Unit |
|---|---|---|
| speed | distance ÷ time | m s⁻¹ |
| acceleration | change in velocity ÷ time | m s⁻² |
| density | mass ÷ volume | kg m⁻³ or g cm⁻³ |
| force | mass × acceleration | N |
Named derived units such as newton (N), joule (J) and pascal (Pa) are SI units too.
Using units in calculations
Use mutually consistent units throughout a calculation, then express the answer in the unit requested. Converting every value to an SI base unit is unnecessary when the equation works consistently in another suitable unit system.
For example, density may be calculated directly in g cm⁻³ when mass is in grams and volume is in cubic centimetres. Convert only if the answer is required in kg m⁻³.
4. Common Mistakes
- Treating a familiar derived quantity such as speed as a base quantity. Test whether its unit can be written using base units.
- Giving a quantity name when the question asks for its SI unit, or giving only a unit symbol when the quantity is required.
- Combining prefixes before converting them to consistent powers of ten.
5. Exam Tips
- Write the quantity, unit name and unit symbol as three distinct pieces of information.
- Reduce a derived unit to base units one relationship at a time; this exposes missing powers and inconsistent prefixes.
- In a data table, place the unit in the column heading so every recorded value has an unambiguous unit.
6. Worked Examples
Modelled example 1
Identify base quantities
Problem
Study the worked solution
Test whether each quantity is independently defined
Method
Separate quantities that can be formed from other quantities.Reason
Base quantities are independent; derived quantities follow relationships.Working
Speed is length divided by time; force is mass multiplied by acceleration.Classify the list
Method
Select mass, time and electric current as base quantities.Reason
They appear directly in the 6091 base-quantity list.Working
Base: mass, time, electric current. Derived: speed, force.
Guided practice 2
Convert for the requested unit
Problem
Match both inputs to the requested unit
Hints
Hint 1: read the requested unit
Hint 2: convert both inputs
View solution step by step
Convert distance and time
Method
Express the inputs in metres and seconds.Reason
These units are consistent with the requested m s⁻¹.Working
1.2 km = 1200 m, 2.5 min = 150 sCalculate average speed
Method
Divide distance by time.Reason
Average speed is total distance divided by total time.Working
v = 1200/150 = 8.0 m s⁻¹
Common misconception 3
A newton is not a base unit
Learner response
Use the defining relationship
View solution step by step
Identify the derived relationship
Method
Use F = ma.Reason
Force is defined from mass and acceleration, so it is derived.Working
[F] = [m][a]Substitute base units
Method
Replace mass by kilograms and acceleration by metres per second squared.Reason
A named SI unit can still be derived.Working
1 N = 1 kg m s⁻²
7. Practice
- From length, area, time and energy, identify the base quantities and explain why the other two are derived.
- A runner covers 1.5 km in 5.0 min. Calculate the average speed in m s⁻¹.
- A sample has mass 54.0 g and volume 20.0 cm³. Calculate its density in g cm⁻³. Explain why you do not need to convert the measurements to kilograms and cubic metres first.
Check your answers
- Length and time are base quantities. Area is derived from length multiplied by length, and energy is derived from other quantities.
- 1.5 km = 1500 m and 5.0 min = 300 s, so v = 1500/300 = 5.0 m s⁻¹.
- ρ = 54.0/20.0 = 2.70 g cm⁻³. Grams and cubic centimetres are mutually consistent and directly produce the requested unit.
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Course and syllabus information
- Course
- SEC G3 Physics
- Edition
- SEC G3 Physics 2027