Scalars and vectors (AQA GCSE Physics Combined Science): Revision Notes
Scalars and vectors
What are scalars and vectors?
All the things we measure in physics can be put into two groups. They are either scalar quantities or vector quantities. The main difference is whether they have direction or not.
The key distinction in physics measurements is simple: scalars have only magnitude, while vectors have both magnitude and direction.
Scalar quantities
Scalar quantities only have size (also called magnitude). They don't have any direction.
Think of scalars as just numbers with units. You can say "the mass is 5 kg" or "the temperature is 20°C" but you don't need to say which way they're pointing.
Examples of scalars include:
- Mass (like 50 kg)
- Speed (like 10 m/s)
- Distance (like 100 m)
- Energy (like 500 J)
- Temperature (like 25°C)
Vector quantities
Vector quantities have both size and direction. You need to know both pieces of information to fully describe them.
When we talk about vectors, we often use arrows to show them. The length of the arrow shows the size, and the arrow points in the direction.
Vector Representation with Arrows:
- Arrow length = magnitude (size)
- Arrow direction = direction of the vector
Examples of vectors include:
- Force or weight (like 10 N downwards)
- Velocity (like 5 m/s to the right)
- Displacement (like 20 m north)
- Acceleration (like 2 m/s² forwards)
- Momentum (like 15 kg⋅m/s eastwards)
The difference between speed and velocity
This is a really important difference that comes up a lot in exams.
Speed vs Velocity - A Critical Distinction:
Speed is a scalar. It just tells you how fast something is moving. For example, "the car is moving at 30 m/s."
Velocity is a vector. It tells you how fast something is moving AND which direction it's going. For example, "the car is moving at 30 m/s to the north."
A helpful example
Worked Example: Speed vs Velocity
Imagine two people running:
- A girl runs to the right at 8 m/s
- A boy runs to the left at 4 m/s
For Speed (scalar):
- Girl's speed: 8 m/s
- Boy's speed: 4 m/s
For Velocity (vector):
- Girl's velocity: +8 m/s (positive because she's going right)
- Boy's velocity: -4 m/s (negative because he's going left)
Notice how the speeds are just the magnitudes, but velocities include direction information through positive and negative signs.
Positive and negative values for vectors
Vector quantities can have positive and negative values to show their direction.
For example:
- A force of +4 N might be balanced by a force of -4 N acting in the opposite direction
- If you accelerate forwards at +2 m/s², you could decelerate (slow down) at -2 m/s²
- Walking 20 m to the right gives a displacement of +20 m, walking the same distance back gives -20 m
The + and - signs in vectors don't mean "good" or "bad" - they simply indicate opposite directions along the same line.
Remember!
Key Points to Remember:
- Scalars have size only (like speed, mass, energy)
- Vectors have size AND direction (like velocity, force, displacement)
- Speed is how fast you're going, velocity is how fast and which way
- Vectors can be positive or negative to show opposite directions
- Arrows represent vectors - length shows size, direction shows which way