Other scalar and vector quantities

AshPhys · Revision cheat sheet

AS Level9702 AS Ch.1Chapter 1: KinematicsLesson 1.8Sections 1.8

Goal: Classify common quantities as scalars or vectors, and explain why.

01The big picture

A quantity is a vector if its direction matters and it adds like a vector (tip to tail). Otherwise it is a scalar, and scalars add as ordinary numbers.

Multiplying a vector by a scalar gives a vector in the same direction: weight $W = mg$ and momentum $p = mv$ are vectors because $g$ and $v$ are.

Scalars [paraphrase]: distance, speed, time, mass, energy (including kinetic and potential), power, temperature, density, pressure, charge, current.
Vectors [paraphrase]: displacement, velocity, acceleration, force (including weight), momentum, electric and gravitational field strength.

02Key equations

Weight: scalar × vector

\vec{W} = m\,\vec{g}

Momentum: scalar × vector

\vec{p} = m\,\vec{v}

Symbols and units

$m$ mass (scalar) $\mathrm{kg}$
$\vec{g}$ acceleration of free fall (vector) $\mathrm{m\,s^{-2}}$
$\vec{v}$ velocity (vector) $\mathrm{m\,s^{-1}}$

03Sample problems with solutions

Sample 1 · Mass and weight
Explain why weight is a vector but mass is a scalar.

Weight is a force: the gravitational pull on an object, which acts in a direction (downwards, towards the centre of the Earth).
Mass is the amount of matter; it has size only and is the same whichever way the object faces or moves.

Answer: Weight (a force) has a direction; mass has size only.

04Practice problems

P1
Is kinetic energy a scalar or a vector?
Final answer
Scalar
Answer: Scalar
P2
Is momentum a scalar or a vector?
Final answer
Vector
Answer: Vector
P3
Pressure is force ÷ area. Is it a scalar or a vector?
Final answer
Scalar (it acts equally in all directions in a fluid)
Answer: Scalar (it acts equally in all directions in a fluid)
P4
Two masses of 3 kg and 4 kg are joined. What is the total mass?
Final answer
7 kg (scalars add as numbers)
Answer: 7 kg (scalars add as numbers)

05Other useful information

Common mistakes

✗ Wrong: Speed and velocity are the same quantity.
✓ Right: Speed is a scalar; velocity is a vector.
✗ Wrong: A negative value means a quantity is a vector.
✓ Right: Scalars can be negative too (temperature in °C, charge).

Exam tips

Ask: does it make sense to say which way it points? If yes, it is a vector.

What the syllabus asks

9702 topic 1: understand the difference between scalars and vectors and give examples. Coursebook 1.8.

Explore: Practice questions for this lesson