1.1 Physical quantities and measurement techniques

Table of Contents

Physical Quantities and Measurement Techniques

Physical Quantities and Measurement Techniques – IGCSE Physics Study Notes

Physical Quantities and Measurement Techniques #

IGCSE Physics Topic 1.1 – How to measure length, volume, time, and understand different types of physical quantities

Why Measurement Matters: Physics is about understanding how the world works, and to do this we need to measure things accurately. This section teaches you how to use different measuring instruments correctly and how to get accurate measurements even when dealing with very small values. You will also learn the difference between scalar and vector quantities.

Measuring Length #

Using a Ruler #

A ruler is the simplest tool for measuring length. Most rulers are marked in centimetres (cm) and millimetres (mm). To use a ruler correctly:

How to Measure Length with a Ruler:

Place the ruler correctly: Put the ruler flat against the object. The zero mark (not the edge of the ruler) should line up with one end of the object
Keep your eye level with the scale: Look straight at the ruler from directly above, not from an angle. Looking from an angle causes parallax error
Read the measurement: Look at where the other end of the object reaches on the ruler scale
Estimate between the marks: If the end falls between two marks, estimate the value

IMAGE NEEDED: Diagram showing correct and incorrect ways to read a ruler, demonstrating parallax error

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Avoiding Parallax Error: Parallax error happens when you look at a scale from an angle instead of straight on. This makes the reading appear different from the true value. Always position your eye directly above or in front of the measurement mark.

Measuring Volume #

Using a Measuring Cylinder #

A measuring cylinder is used to measure the volume of liquids. The volume is measured in cubic centimetres (cm³) or millilitres (mL). Remember: 1 cm³ = 1 mL.

How to Read a Measuring Cylinder:

Place on a flat surface: Put the measuring cylinder on a level table so the liquid settles evenly
Wait for the liquid to settle: Let any bubbles rise and the liquid become still
Position your eye at the liquid level: Your eye must be at the same height as the surface of the liquid
Read from the bottom of the meniscus: Water curves upward at the edges (this curve is called the meniscus). Always read the volume from the bottom of this curve

IMAGE NEEDED: Diagram showing how to read a measuring cylinder correctly, with the meniscus clearly labeled and eye position shown

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Measuring the Volume of an Irregular Object #

For objects with irregular shapes (like a stone), we use a method called displacement. The object pushes water out of the way, and we measure how much water is displaced.

Displacement Method:

Pour water into a measuring cylinder: Note the initial volume of water ($V_1$)
Gently lower the object into the water: Use a string to lower it slowly to avoid splashing
Read the new volume: The water level rises. Note this new volume ($V_2$)
Calculate the object’s volume: Volume of object = $V_2 – V_1$

Worked Example: Finding the Volume of a Stone

A measuring cylinder contains 45 cm³ of water. When a stone is lowered into the water, the level rises to 52 cm³. What is the volume of the stone?

Solution:
Volume of stone = $V_2 – V_1$ = 52 cm³ − 45 cm³ = 7 cm³

Measuring Time #

Clocks and Digital Timers #

Types of Time-Measuring Instruments:

Analogue clocks: Have hour, minute, and second hands. Useful for longer time intervals
Digital stopwatches: Can measure time to 0.01 seconds or better
Light gates with timers: Electronic sensors that can measure very short time intervals (0.001 seconds or less) – useful when human reaction time would cause too much error

Human Reaction Time: When you use a handheld stopwatch, there is always some delay between when an event happens and when you press the button. This is called reaction time (usually about 0.2 to 0.3 seconds). For very short time intervals, this error becomes significant.

Measuring Short Time Intervals by Taking Multiples #

When we need to measure a very short time interval, we can measure multiple events and then divide to find the time for one event. This reduces the effect of reaction time error.

The Averaging Method: If one swing of a pendulum takes about 1 second, your 0.2 second reaction time error is 20% of your measurement. But if you time 20 swings (about 20 seconds), your 0.2 second error is only 1% of your measurement.

Measuring the Period of a Pendulum #

A pendulum is a weight (called a bob) hanging from a string that swings back and forth. The period is the time for one complete swing – from one side, to the other side, and back again.

IMAGE NEEDED: Diagram showing a pendulum with one complete oscillation (period) clearly marked

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How to Measure the Period of a Pendulum:

Choose a reference point: Pick a position where the bob passes (usually the centre/lowest point)
Start timing: Start the stopwatch as the bob passes your reference point in one direction
Count the oscillations: Count a set number of complete swings (for example, 20 oscillations)
Stop timing: Stop the stopwatch after the set number when the bob passes the reference point in the same direction
Calculate the period: Divide the total time by the number of oscillations

Formula for calculating the period:

$$\text{Period (T)} = \frac{\text{Total time for n oscillations}}{\text{Number of oscillations (n)}}$$

Worked Example: Finding the Period of a Pendulum

A student times 25 complete swings of a pendulum. The total time recorded is 38.5 seconds. Calculate the period of the pendulum.

Solution:
Period, T = $\frac{\text{Total time}}{n}$ = $\frac{38.5}{25}$ = 1.54 s

Measuring Small Distances by Taking Multiples #

The same idea works for measuring small distances. If you need to measure something very thin (like a sheet of paper), measure a stack of many sheets and divide.

Worked Example: Finding the Thickness of Paper

A student measures the thickness of a stack of 100 sheets of paper. The stack measures 8.5 mm. What is the thickness of one sheet?

Solution:
Thickness of one sheet = $\frac{8.5}{100}$ = 0.085 mm

Scalars and Vectors Supplement #

In physics, some quantities just need a number and a unit to describe them fully. Other quantities also need a direction. Understanding this difference is very important.

Scalar Quantities #

Definition of a Scalar: A scalar quantity has magnitude (size) only. It does not have a direction. You can describe a scalar completely with just a number and a unit.

Scalar Quantities (you must memorise these):

Distance – how far something has travelled (e.g., 50 m)
Speed – how fast something is moving (e.g., 20 m/s)
Time – how long something takes (e.g., 5 s)
Mass – how much matter is in an object (e.g., 2 kg)
Energy – the ability to do work (e.g., 100 J)
Temperature – how hot or cold something is (e.g., 30°C)

Vector Quantities #

Definition of a Vector: A vector quantity has both magnitude (size) AND direction. You cannot describe a vector completely without stating its direction.

Direction is essential for vectors. If someone pushes you with a force of 50 N, it matters a lot whether they push you forwards, backwards, or sideways!

Vector Quantities (you must memorise these):

Force – a push or pull (e.g., 50 N to the right)
Weight – the gravitational force on an object (e.g., 10 N downwards)
Velocity – speed in a particular direction (e.g., 20 m/s north)
Acceleration – rate of change of velocity (e.g., 5 m/s² upwards)
Momentum – mass × velocity (e.g., 100 kg m/s east)
Electric field strength – force per unit charge
Gravitational field strength – force per unit mass

Speed vs Velocity: Speed tells you how fast something moves (e.g., 30 m/s). Velocity tells you how fast AND in what direction (e.g., 30 m/s east). A car driving around a circular track at constant speed does NOT have constant velocity because its direction keeps changing.

Adding Vectors – The Resultant Supplement #

When two or more vectors act together, the single vector that has the same effect as all the original vectors combined is called the resultant.

Vectors in the Same Line #

Rules for Vectors in a Line:

Same direction: Add the magnitudes. The resultant is in the same direction.
Opposite directions: Subtract the smaller from the larger. The resultant is in the direction of the larger vector.

Vectors at Right Angles (90°) #

When two vectors are at right angles to each other, we use Pythagoras’ theorem. The two vectors form two sides of a right-angled triangle, and the resultant is the hypotenuse.

Pythagoras’ Theorem for Vectors at Right Angles:

$$R = \sqrt{a^2 + b^2}$$

Where $R$ = magnitude of the resultant, $a$ and $b$ = magnitudes of the two vectors

Finding the Direction (Angle):

$$\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$$

Then: $\theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right)$

Graphical Method (Scale Drawing) #

How to Find the Resultant Using a Scale Drawing:

Choose a scale: For example, 1 cm = 10 N
Draw the first vector: Draw an arrow of the correct length pointing in the correct direction
Draw the second vector from the tip of the first: Start where the first arrow ends
Draw the resultant: Draw an arrow from the start of the first vector to the end of the second vector
Measure: Measure the length and convert using your scale. Use a protractor to measure the angle

IMAGE NEEDED: Step-by-step diagram showing the graphical method for adding two perpendicular vectors, forming a vector triangle

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Worked Example: Two Forces at Right Angles

A force of 30 N acts towards the east. Another force of 40 N acts towards the north. Find the magnitude and direction of the resultant force.

Solution:

Step 1: Use Pythagoras’ theorem to find magnitude
$R = \sqrt{30^2 + 40^2} = \sqrt{900 + 1600} = \sqrt{2500}$ = 50 N

Step 2: Find the direction
$\tan \theta = \frac{40}{30} = 1.333$
$\theta = \tan^{-1}(1.333)$ = 53.1° north of east

Final Answer: The resultant force is 50 N at 53.1° north of east.

Remember the 3-4-5 Triangle: The numbers 3, 4, and 5 form a special right-angled triangle because $3^2 + 4^2 = 5^2$. You will often see this combination in exam questions. Multiples also work: 6-8-10, 30-40-50, etc.

Summary: Key Points for the Exam #

Measuring Instruments:

Ruler: Measure length in cm or mm. Avoid parallax error by looking straight at the scale
Measuring cylinder: Measure volume in cm³ or mL. Read from the bottom of the meniscus
Displacement method: Volume of irregular object = Final water level − Initial water level

Measuring Time:

Reduce timing errors by measuring multiple events and dividing to find the time for one event
Period of pendulum: Time for many complete swings ÷ Number of swings

Quick Reference Table: Scalars and Vectors

Scalar Quantities	Vector Quantities
Distance	Force
Speed	Weight
Time	Velocity
Mass	Acceleration
Energy	Momentum
Temperature	Electric field strength
	Gravitational field strength

Exam Tip – Resultant Vectors: When two vectors are at right angles, use Pythagoras: $R = \sqrt{a^2 + b^2}$. For the angle, use $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$. Always draw a diagram first.

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Updated on 31 January 2026