Physical quantities and SI units

Overview

Physics depends on measurement. A physical quantity is a property that can be measured and expressed using a number and a unit. For example, a length of $2\ \text{m}$, a mass of $5\ \text{kg}$, and a time of $10\ \text{s}$ are physical quantities written with numbers and SI units.

This chapter introduces fundamental and derived physical quantities and their SI units. It prepares learners for measuring instruments, linear motion, force, density, pressure, work, power, energy, and experiments.

Key idea: a number without a suitable unit is often incomplete in Physics. The statement "$4$" is not enough. The statement "$4\ \text{m}$" tells us a length, while "$4\ \text{s}$" tells us a time.

Prerequisites

• Concept of Physics: meaning of Physics, observation, measurement, matter, energy, and physical phenomena.
• Basic arithmetic with multiplication and division.
• Reading simple decimals and whole numbers.
• Recognizing common measuring ideas from daily life, such as length, mass, and time.
• Useful Mathematics bridge: Meaning, branches, relationships, and importance of mathematics for using numbers, units, and relationships.

Learning Scope

This page covers:

• Meaning of physical quantity.
• Difference between fundamental and derived physical quantities.
• SI units and common symbols used in Form I Physics.
• Measurable objects and measurable properties.
• Unit writing, unit conversion within simple metric prefixes, and unit checking.
• How quantities and units prepare learners for measuring instruments and motion.

This page does not give detailed instrument-reading practice. That belongs to Measuring instruments in Physics and Measuring instruments and physical quantities. It does not teach full motion calculations beyond basic preparation for Linear motion.

The 2022 examination format is not used here to define the topic scope. It may later provide assessment signals only after review.

Subtopics

Physical Quantities

A physical quantity is a measurable property of an object, material, event, or system. It is written using a numerical value and a unit.

Examples:

• Length of a table: $1.5\ \text{m}$
• Mass of a stone: $2\ \text{kg}$
• Time for a runner: $12\ \text{s}$
• Temperature of water: $30\ \text{^\circ C}$
• Speed of a bicycle: $5\ \text{m/s}$

Key insight: the number tells how much, and the unit tells what kind of quantity is being measured.

For example:

$$ 5\ \text{m} \ne 5\ \text{kg} $$

Both have the number $5$, but they describe different physical quantities.

Measurable Objects and Measurable Properties

An object is the thing being studied. A physical quantity is the measurable property of that object or event.

Examples:

• Object: desk. Measurable properties: length, width, height, mass.
• Object: cup of water. Measurable properties: volume, mass, temperature.
• Event: a student walking. Measurable properties: distance, displacement, time, speed.
• Material: wooden block. Measurable properties: mass, volume, density.

Key insight: one object can have many physical quantities. A stone can have mass, volume, density, temperature, and weight. The learner must identify which quantity is required before choosing a unit or instrument.

SI Units

SI units are internationally agreed units used in science and measurement. They make measurements clear and comparable between people, schools, laboratories, and countries.

In Form I Physics, learners meet several important SI units:

| Physical quantity | SI unit | Unit symbol | | --- | --- | --- | | Length | metre | $\text{m}$ | | Mass | kilogram | $\text{kg}$ | | Time | second | $\text{s}$ | | Electric current | ampere | $\text{A}$ | | Temperature | kelvin | $\text{K}$ | | Amount of substance | mole | $\text{mol}$ | | Luminous intensity | candela | $\text{cd}$ |

The seven quantities in the table are called base or fundamental quantities in SI. In school Physics, the first three - length, mass, and time - are especially important early because they appear in measurement, motion, force, density, pressure, work, power, and energy.

Temperature is often measured in degrees Celsius in school and daily life, written as $\text{^\circ C}$. The SI base unit for thermodynamic temperature is kelvin, written as $\text{K}$. Learners should follow the unit required by the topic or instrument context.

Fundamental Physical Quantities

Fundamental physical quantities are quantities that are treated as independent base quantities in SI. Other quantities can be formed from them.

Examples include:

• Length, measured in metre, $\text{m}$.
• Mass, measured in kilogram, $\text{kg}$.
• Time, measured in second, $\text{s}$.
• Electric current, measured in ampere, $\text{A}$.
• Temperature, measured in kelvin, $\text{K}$.
• Amount of substance, measured in mole, $\text{mol}$.
• Luminous intensity, measured in candela, $\text{cd}$.

Key insight: fundamental quantities are building blocks. Derived quantities are built from these blocks.

For example, speed uses length and time:

$$ \text{speed} = \frac{\text{distance}}{\text{time}} $$

Therefore, the SI unit of speed is:

$$ \frac{\text{m}}{\text{s}} = \text{m/s} $$

Derived Physical Quantities

A derived physical quantity is formed by combining fundamental quantities. Its unit is also formed by combining SI base units.

Common Form I examples include:

| Derived quantity | Relationship | SI unit | | --- | --- | --- | | Area | length $\times$ length | $\text{m}^2$ | | Volume | length $\times$ length $\times$ length | $\text{m}^3$ | | Speed | distance $\div$ time | $\text{m/s}$ | | Acceleration | velocity change $\div$ time | $\text{m/s}^2$ | | Density | mass $\div$ volume | $\text{kg/m}^3$ | | Force | mass $\times$ acceleration | $\text{N}$ | | Pressure | force $\div$ area | $\text{Pa}$ | | Work | force $\times$ distance | $\text{J}$ | | Power | work $\div$ time | $\text{W}$ |

Some derived units have special names:

• The unit of force is newton, $\text{N}$.
• The unit of pressure is pascal, $\text{Pa}$.
• The unit of work and energy is joule, $\text{J}$.
• The unit of power is watt, $\text{W}$.

Key insight: a derived unit often reveals the quantities used to calculate it. For example, density has unit $\text{kg/m}^3$, showing that it compares mass with volume.

Writing Quantities and Units Correctly

A measurement should usually be written as:

$$ \text{physical quantity} = \text{number} \ \text{unit} $$

Examples:

$$ \begin{aligned} \text{length} &= 3\ \text{m} \\ \text{mass} &= 0.5\ \text{kg} \\ \text{time} &= 20\ \text{s} \end{aligned} $$

Good unit writing habits:

• Leave a space between the number and unit: write $5\ \text{m}$, not $5\text{m}$ in formal work.
• Use standard unit symbols: $\text{m}$ for metre, $\text{s}$ for second, $\text{kg}$ for kilogram.
• Do not add plural letters to unit symbols: write $10\ \text{kg}$, not $10\ \text{kgs}$.
• Keep the unit with the answer, especially in measurement and calculation.
• Use the correct case: $\text{m}$ means metre, while $\text{M}$ is not the SI symbol for metre.

Simple Metric Prefixes and Conversions

Physics often uses prefixes for very small or large measurements. At Form I level, learners commonly meet:

| Prefix | Symbol | Meaning | | --- | --- | --- | | kilo | $\text{k}$ | $1,000$ times | | centi | $\text{c}$ | $\frac{1}{100}$ | | milli | $\text{m}$ | $\frac{1}{1,000}$ |

Common conversions:

$$ \begin{aligned} 1\ \text{km} &= 1,000\ \text{m} \\ 1\ \text{m} &= 100\ \text{cm} \\ 1\ \text{m} &= 1,000\ \text{mm} \\ 1\ \text{kg} &= 1,000\ \text{g} \end{aligned} $$

Key insight: convert quantities to consistent units before using a formula. If distance is in metres and time is in seconds, speed will be in $\text{m/s}$.

Unit Checking

Unit checking means using units to test whether a calculation is sensible. It helps learners notice mistakes before accepting an answer.

For example, speed is distance divided by time:

$$ \text{speed} = \frac{\text{distance}}{\text{time}} $$

If distance is in metres and time is in seconds, the unit becomes:

$$ \frac{\text{m}}{\text{s}} = \text{m/s} $$

If a learner calculates speed and writes the answer in $\text{kg}$, the unit reveals an error because kilogram is a mass unit, not a speed unit.

Link to Measuring Instruments and Linear Motion

Physical quantities tell what is measured. Units tell how the result is expressed. Measuring instruments tell how the measurement is obtained.

Examples:

| Quantity | SI unit | Possible instrument | | --- | --- | --- | | Length | $\text{m}$ | metre rule or tape measure | | Mass | $\text{kg}$ | beam balance or electronic balance | | Time | $\text{s}$ | stopwatch or clock | | Temperature | $\text{K}$ or $\text{^\circ C}$ | thermometer |

This link leads directly to Measuring instruments in Physics and Measuring instruments and physical quantities.

Linear motion then uses measured quantities:

$$ \text{speed} = \frac{\text{distance}}{\text{time}} $$

So a learner studying Linear motion must already understand distance, time, SI units, and unit conversion.

Key Terms

• Physical quantity: a measurable property expressed using a number and a unit.
• Measurement: the process of finding the value of a physical quantity.
• Unit: an agreed standard used to express a measurement.
• SI units: internationally agreed units used in science.
• Fundamental quantity: an SI base quantity treated as independent, such as length, mass, or time.
• Derived quantity: a quantity formed from fundamental quantities, such as area, speed, density, or pressure.
• Unit symbol: a short standard symbol for a unit, such as $\text{m}$, $\text{kg}$, or $\text{s}$.
• Prefix: a symbol or word added to a unit to show a multiple or fraction, such as kilo, centi, or milli.
• Unit conversion: changing a measurement from one unit to an equivalent unit.
• Unit checking: using units to test whether a calculation is physically sensible.

Worked Examples

Example 1: Identify quantity, value, and unit

A book has a mass of $0.8\ \text{kg}$. Identify the physical quantity, numerical value, and unit.

The physical quantity is mass.

The numerical value is $0.8$.

The unit is kilogram, written as $\text{kg}$.

Therefore:

$$ \text{mass} = 0.8\ \text{kg} $$

Example 2: Classify fundamental and derived quantities

Classify length, speed, time, and density as fundamental or derived quantities.

Length is fundamental because its SI unit is a base unit, metre.

Time is fundamental because its SI unit is a base unit, second.

Speed is derived because:

$$ \text{speed} = \frac{\text{distance}}{\text{time}} $$

Density is derived because:

$$ \text{density} = \frac{\text{mass}}{\text{volume}} $$

Therefore, length and time are fundamental quantities, while speed and density are derived quantities.

Example 3: Find the SI unit of speed

A student travels $20\ \text{m}$ in $4\ \text{s}$. Find the speed and its unit.

Use:

$$ \text{speed} = \frac{\text{distance}}{\text{time}} $$

Substitute:

$$ \begin{aligned} \text{speed} &= \frac{20\ \text{m}}{4\ \text{s}} \\ &= 5\ \text{m/s} \end{aligned} $$

The speed is $5\ \text{m/s}$. This prepares for the detailed study of speed in Linear motion.

Example 4: Convert centimetres to metres

Convert $250\ \text{cm}$ to metres.

Since:

$$ 100\ \text{cm} = 1\ \text{m} $$

Then:

$$ \begin{aligned} 250\ \text{cm} &= \frac{250}{100}\ \text{m} \\ &= 2.5\ \text{m} \end{aligned} $$

Therefore, $250\ \text{cm} = 2.5\ \text{m}$.

Example 5: Use units to identify a derived quantity

A calculation gives:

$$ \frac{12\ \text{kg}}{3\ \text{m}^3}=4\ \text{kg/m}^3 $$

What derived quantity is being calculated?

The unit $\text{kg/m}^3$ compares mass with volume. The relationship is:

$$ \text{density} = \frac{\text{mass}}{\text{volume}} $$

Therefore, the derived quantity is density.

Common Mistakes

• Mistake: Writing a number without a unit.

Correction: In Physics, write the value and unit, such as $6\ \text{m}$ or $12\ \text{s}$.

• Mistake: Confusing object and quantity.

Correction: A table is an object. Length, width, height, and mass are quantities that can be measured on the table.

• Mistake: Treating all quantities as fundamental.

Correction: Some quantities are derived from others. Speed is derived from distance and time.

• Mistake: Using $\text{m}$ for both metre and minute.

Correction: In SI, $\text{m}$ means metre. Time in seconds is written $\text{s}$. If minutes are used in a context, write them clearly as minutes or convert them to seconds when needed.

• Mistake: Adding plural letters to symbols.

Correction: Write $5\ \text{kg}$, not $5\ \text{kgs}$.

• Mistake: Mixing units in a formula without conversion.

Correction: Convert units first, such as centimetres to metres, before calculating speed, density, area, or volume.

• Mistake: Thinking instruments define the topic scope.

Correction: Instruments support measurement. The official syllabus topic here is physical quantities and SI units; detailed instrument work belongs to related measurement pages.

Practice Tasks

1. Define physical quantity.
2. Explain why a unit is needed when writing a measurement.
3. Write the SI unit and symbol for length, mass, and time.
4. Identify the physical quantity, numerical value, and unit in each measurement:
• $12\ \text{m}$
• $5\ \text{kg}$
• $30\ \text{s}$
• $2\ \text{m/s}$
5. Classify each quantity as fundamental or derived: mass, area, time, volume, speed, density, length.
6. Convert:
• $3\ \text{km}$ to metres.
• $450\ \text{cm}$ to metres.
• $2.5\ \text{kg}$ to grams.
• $75\ \text{mm}$ to metres.
7. A cyclist travels $60\ \text{m}$ in $12\ \text{s}$. Calculate the speed and write the correct unit.
8. A box has length $2\ \text{m}$ and width $0.5\ \text{m}$. Calculate its top area and write the SI unit.
9. A block has mass $6\ \text{kg}$ and volume $2\ \text{m}^3$. Calculate its density and write the SI unit.
10. For each quantity, name a suitable measuring instrument: length of a desk, mass of a stone, time for a race, temperature of water.
11. Explain how this topic prepares a learner for Linear motion.
12. A learner writes that the speed of a toy car is $8\ \text{kg}$. Explain the error using unit checking.

Generated Question Layer

Future generated practice for this page should include:

• Direct recall questions on physical quantities, SI units, and unit symbols.
• Sorting questions for fundamental and derived quantities.
• Matching questions for quantities, units, and measuring instruments.
• Unit conversion tasks using kilo, centi, and milli.
• Short calculations for speed, area, volume, and density with unit checking.
• Bridge questions leading from measurement to Measuring instruments in Physics, Measuring instruments and physical quantities, and Linear motion.

Generated questions should remain original and should not be presented as official past-paper questions.

Learner Aid Opportunities

• chart: Quantity-unit-symbol table for fundamental and common derived quantities.
• diagram: Measurement triangle linking object, quantity, unit, and instrument.
• interactive: Unit conversion practice with immediate feedback.
• interactive: Matching activity for quantities, SI units, and measuring instruments.
• LLM tutor: Adaptive hints for deciding whether a quantity is fundamental or derived.

Exam-Derived Signals

• No past-paper or examination-format mappings have been reviewed for this Physics topic yet.
• The 2022 CSEE examination format may provide future assessment signals, but it does not define the scope of this page.
• Any future exam-derived examples should be clearly marked as assessment signals and checked against the official syllabus topic placement.

Source And Review Notes

• Official syllabus status: topic identity, form placement, competence, sequence, hub, and summary are taken from the 2023 CSEE Physics curriculum extraction.
• Existing repo context used: Form I Physics topic spine, Physics measurement hub, Physics foundations topic, Math chapter standard, and docs/rulebook.md.
• External enrichment status: no external web enrichment used.
• Exam signal status: not mapped in this milestone.
• Textbook status: not used.
• Review risk: the learner expansion should be checked by a Physics reviewer for local classroom wording, unit conventions, and depth before being treated as reviewed content.