AQA GCSE Scalar and Vector Quantities

Scalar quantities

A scalar quantity has a magnitude only.

Magnitude means size.

Speed is a scalar quantity. If an object has a speed of 5m/s, then its magnitude is 5.

Vector quantities

A vector quantity has both magnitude and direction.

Velocity is an example of a vector quantity. A velocity could be 5m/s in the forward direction.

Scalar Quantities	Vector Quantities
Time(s)	Acceleration(m/s²)
Temperature(⁰C)	Velocity(m/s)
Mass(kg)	Force(N)
Density(kg/m³)	Weight(N)
Volume(m³)	Momentum(kg m/s)
Speed(m/s)	Displacement(m)
Power(W)
Energy(J)
Distance(m)

Explanation of these terms

Some of these terms are obvious, but some need to be defined, so below is a definition for some of the terms:

Mass – The amount of matter in an object

Density- The amount of mass per unit volume

Speed – Distance an object travels per unit time

Power – Rate of energy transfer

Acceleration – Rate of change of velocity

Weight – Force of gravity that acts on the mass of an object

Momentum – Product (multiply) of mass and velocity

Displacement – Distance travelled in a certain direction

Vectors

Remember a vector is a quantity that has both a magnitude and a direction.

We can show a vector on a piece of paper by using an arrow. The length of the arrow denotes the magnitude and the arrow’s direction indicates its direction.

These arrows are often drawn to scale.

Lets take an example, using a scale of 1cm = 1N, draw a vector to represent a ball falling that has a force of 5N. So, we will draw an arrow 5cm long directly downwards.

Two forces act on an object. The first force of 50N occurs at a bearing of 270º, whilst the second force of 30N occurs at a bearing of 180º. Using a scale diagram where 1cm =10N draw a vector diagram.

We need two force arrows, one directly downwards with a length of 3cm for 180º and a second force arrow of 5cm for 270º.

Practice Questions

1. Explain the difference between a scalar quantity and a vector quantity

2. Give 3 examples of scalar quantities and 3 examples of vector quantities.

3. Draw a vector diagram for an arrow that has a force of 20N at a bearing of 090º and weight force of 5N at a bearing of 180º, using a scale of 1cm = 5N.