Scalar and vector quantities revision notes

Edexcel International GCSE Physics (4PH1), chapter 2: Forces and shape, specification point 1.13, 1.14. Free lesson.

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A scalar has size only, while a vector has both size and direction. This distinction helps you describe motion and forces accurately, especially when directions change or quantities act in opposite directions.

How scalars differ from vectors

Every physical quantity is either a scalar or a vector. The difference is whether direction is part of the quantity. The size of a quantity is also called its magnitude, meaning how big it is. A scalar has size only. Examples include distance, speed, mass, energy, time and temperature. A vector has size and direction. Examples include displacement, velocity, weight, force, acceleration and momentum. Weight is a force acting downwards, so it has a direction and is a vector.

How distance and displacement differ

Distance is how far you travel in total, so it does not depend on direction. Displacement is how far you end up from your starting point and in which direction. This means opposite parts of a journey add for distance but subtract for displacement.

Why a change in direction changes velocity

Speed tells you how fast something moves, without its direction. Velocity includes direction, so it can change even when speed stays constant. A car moving round a roundabout at a steady 10 m/s has constant speed. Its direction keeps changing, so its velocity changes too.

How to show and combine forces

A force is a vector, so it can be drawn as an arrow. The arrow points in the direction of the force. Its length shows the force's size. When forces act on the same object, forces in the same direction add; forces in opposite directions leave a difference. The single force that has the same effect as the forces together is the resultant. Two pushes to the right, 400 N and 250 N, give a resultant of 650 N to the right. Pushes in opposite directions, 400 N right and 250 N left, give a resultant of 150 N to the right.

How to define and identify a vector

For a definition, include both parts: a vector has size and direction. Saying only that it has a direction is incomplete, because direction without size is not enough. From energy, mass, speed, temperature, velocity and weight, the vectors are velocity and weight. Speed is a common trap: it has size only, so it is a scalar.