Types of physical quantity

Physics· Unit 1: Physical quantities and units· 15 min read

1. Classification of Scalars and Vectors★☆☆☆☆⏱ 5 min

📘 Definition

Scalar quantity

Written as plain symbol, e.g. $m$ for mass

A physical quantity that has only magnitude (size) and no direction. Fully described by a single number and unit.

Example:

Mass, temperature, energy, distance, speed, time

📘 Definition

Vector quantity

Written with an arrow over the symbol, e.g. $v$ for velocity

A physical quantity that requires both magnitude and direction to be fully described.

Example:

Displacement, velocity, acceleration, force, momentum

Common scalars: mass, energy, temperature, distance, speed, time, density, work, power
Common vectors: displacement, velocity, acceleration, force, weight, momentum, electric field strength

📐 Worked Example

Classify each of the following as scalar or vector: (a) kinetic energy, (b) acceleration, (c) weight, (d) density

1
Check if the quantity requires direction to be fully described.
2
(a) Kinetic energy only has size, no direction: scalar.
3
(b) Acceleration needs magnitude and direction of change of velocity: vector.
4
(c) Weight is a force acting towards the centre of the Earth, so has direction: vector.
5
(d) Density is mass per unit volume, only has size: scalar.

2. Adding Vectors to Find the Resultant★★☆☆☆⏱ 5 min

When two or more vectors act at the same point, their combined effect is called the resultant vector. For parallel vectors, add magnitudes if they act in the same direction, subtract magnitudes if opposite. For non-parallel vectors, we use geometry to find the resultant.

📘 Definition

Resultant vector

A single vector that produces the same effect as the combination of all original vectors.

📐 Worked Example

A hiker walks 4.0 km east, then 3.0 km north. Calculate the resultant displacement from the starting point.

1
The two displacement vectors are perpendicular, so use Pythagoras' theorem for magnitude.
2
$|\vec{s}| = \sqrt{(4.0)^2 + (3.0)^2} = \sqrt{25} = 5.0 \text{ km}$
3
Calculate direction, measured from east towards north:
4
$\theta = \tan^{-1}\left(\frac{3.0}{4.0}\right) = 37^\circ$
5
Final resultant displacement is 5.0 km at 37° north of east.

3. Resolving Vectors into Perpendicular Components★★☆☆☆⏱ 5 min

Any vector can be split into two independent, perpendicular components. This process (called resolution) is the most used vector skill in A-Level mechanics, used for projectile motion, inclined planes, and equilibrium.

V_x = V \cos\theta \\ V_y = V \sin\theta

📐 Worked Example

A force of 30 N acts at 40° above the horizontal. Find the horizontal and vertical components of the force.

1
Identify $F = 30$ N, $θ = 4 0^{\circ}$ from the horizontal axis.
2
Calculate the horizontal (x) component:
3
$F_x = 30 \times \cos(40^\circ) = 30 \times 0.766 = 23 \text{ N (2 s.f.)}$
4
Calculate the vertical (y) component:
5
$F_y = 30 \times \sin(40^\circ) = 30 \times 0.643 = 19 \text{ N (2 s.f.)}$
6
Final components: 23 N horizontal, 19 N vertical.

4. Common Pitfalls

Wrong move:

Confusing speed (scalar) and velocity (vector) as the same quantity type

Why:

This is a common multiple-choice trap set by examiners

Correct move:

Always remember: speed is scalar (only magnitude), velocity is vector (speed + direction)

Wrong move:

Swapping sine and cosine when resolving vectors

Why:

Misremembering which side of the triangle matches the angle

Correct move:

Always label the triangle: the component along the angle direction uses cosine, perpendicular uses sine

Wrong move:

Adding scalar magnitudes of non-parallel vectors to get the resultant

Why:

Direction changes the total magnitude, so simple addition only works for parallel vectors

Correct move:

Use Pythagoras for perpendicular vectors, or trigonometry on a vector diagram for non-parallel vectors

Wrong move:

Forgetting to state the direction of a resultant vector

Why:

Examiners require full description of vectors, and will deduct marks for missing direction

Correct move:

Always add direction (e.g. 25° north of east) when giving a final vector answer

Wrong move:

Resolving vectors into non-perpendicular components for calculations

Why:

Non-perpendicular components are not independent, leading to wrong results

Correct move:

Always resolve into two perpendicular components for all standard A-Level problems

5. Quick Reference Cheatsheet

Concept	Key Rule
Scalar quantity	Only magnitude, no direction
Vector quantity	Both magnitude and direction
Resultant of 2 perpendicular vectors	$R = A^{2} + B^{2}$
Resolve $V$ at angle $θ$ to x-axis	x: $V cos θ$ , y: $V sin θ$
Parallel vectors same direction	Add magnitudes
Parallel vectors opposite direction	Subtract magnitudes

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 11
Identify scalar/vector quantities
2023 · 12
Resolve force into horizontal component
2021 · 21
Find resultant displacement

Going deeper

syllabusCIE 9702 Official SyllabusCheck for latest learning outcomes

What's Next

Understanding the classification of physical quantities and the core skills of vector addition and resolution is the foundation for almost all topics in CIE A-Level Physics. You will use vector resolution constantly in upcoming topics, including forces on inclined planes, static equilibrium, projectile motion, and even analysing electromagnetic fields. Mastering this early sub-topic eliminates common confusion later, and builds a strong problem-solving framework for all mechanics questions, which make up a large portion of your exam marks. Next, you will learn about SI units and measurement uncertainty, before applying vector skills to forces and motion.