Scalars & Vectors (Oxford AQA IGCSE Physics)

Revision Note

Scalars & Vectors

  • All quantities can be one of two types:

    • A scalar

    • A vector

Scalars

  • Scalars are quantities that have only a magnitude

    • Mass is scalar since it has magnitude without a direction

    • Energy and speed are also examples of scalar quantities

Vectors

  • Vectors have both magnitude and direction

    • Velocity is a vector since it has a magnitude and a direction

      • When describing the velocity of a car it is necessary to mention both its speed and the direction in which it is travelling

      • For example, the velocity might be 60 km per hour (magnitude) due west (direction)

  • Distance is a value describing only how long an object is or how far it is between two points - this means it is a scalar quantity

  • Displacement on the other hand also describes the direction in which the distance is measured - this means it is a vector quantity

    • For example, a displacement might be 100 km north

Table of Common Scalar & Vector Quantities

Scalar

Vector

Distance

Displacement

Speed

Velocity

Mass

Weight

Energy

Volume

Density

Temperature

Power

Force

Acceleration

Momentum

Worked Example

An instructor is in charge of training junior astronauts. For one of their sessions, they would like to explain the difference between mass and weight.

Suggest how the instructor should explain the difference between mass and weight, using definitions of scalars and vectors in your answer.

Answer:

Step 1: Recall the definitions of a scalar and vector quantity

  • Scalars are quantities that have only a magnitude

  • Vectors are quantities that have both magnitude and direction

Step 2: Identify which quantity has magnitude only

  • Mass is a quantity with magnitude only

  • So mass is a scalar quantity

    • The instructor might explain to their junior astronauts that their mass will not change as their location in the Universe changes

Step 3: Identify which quantity has magnitude and direction

  • Weight is a quantity with magnitude and direction (it is a force)

  • So weight is a vector quantity

    • The instructor might explain that their weight - the force on them due to gravitational field strength - will vary depending on their location. For example, the force of weight acting on them would be less on the Moon than it is on Earth

Examiner Tip

Make sure you are comfortable with the differences between similar scalars and vectors, the most commonly confused pairings tend to be:

  • Distance and displacement

  • Speed and velocity

  • Weight and mass

Vector arrows

A vector can be represented by using an arrow

  • The length of the arrow represents the magnitude of the vector

  • The direction of the arrow indicates the direction of the vector

Forces represented as vectors

Two forces represented by arrows, for GCSE & IGCSE Physics Revision Notes
Force A has a greater magnitude than Force B, and each force has a different direction
  • Pairs of objects exerting a force on one another can be represented by vectors

Vector diagram for a pair of objects exerting a force on one another

The Earth and a book with vector arrows of equal length pointing towards one another
The gravitational pull of the Earth acts on the book (weight) and the gravitational pull of the book acts on the Earth (weight)
  • In the example above:

    • The vectors are equal in length showing that the forces are equal in magnitude

    • The vectors are opposite in direction showing that the forces are acting in opposing directions

Worked Example

A tennis ball is thrown at an angle of 45° to horizontal at a speed of 5 m/s. A second tennis ball is thrown in the same direction at a speed of 10 m/s.

Draw the velocity vectors of the balls.

Answer:

Step 1: Draw the first tennis ball and its velocity vector

  • Measure the 45° angle with a protractor

Tennis ball vector drawn at 45 degrees to the horizontal

Step 2: Draw the second tennis ball and its velocity vector

  • The second ball has a speed of 10 m/s, so the arrow will be twice as long

Second tennis ball vector drawn at the same angle but twice as long

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