# Edexcel IGCSE Physics: Double Science 复习笔记：1.2.2 Scalar & Vectors

### Scalar & Vector Quantities

• All quantities can be one of two types:
• scalar
• vector

#### Scalars

• Scalars are quantities that have only a magnitude
• For example, mass is a scalar quantity since it is a quantity that has no direction to it

#### Vectors

• Vectors have both a magnitude and a direction
• Velocity is a vector quantity since it is described with both 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, 60 km per hour in a Westerly 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, 100 km in a Northern direction

#### Examples of Scalars & Vectors

• The table below lists some common examples of scalar and vector quantities:

Scalars & Vectors Table

• Some vectors and scalars are similar to each other
• For example, the scalar quantity distance corresponds to the vector quantity displacement

• Corresponding vectors and their scalar counterparts are aligned in the table where applicable

#### Worked Example

Blu is in charge of training junior astronauts. For one of his sessions, he would like to explain the difference between mass and weight.Suggest how Blu should explain the difference between mass and weight, using definitions of scalars and vectors in your 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
• Blu might explain to his junior astronauts that their mass will not change if they travel to outer space

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
• Blu might explain that to his junior astronauts that their weight - the force on them due to gravity - will vary depending on their distance from the centre of the Earth

### Forces as Vectors

• Force is a vector quantity because it describes both magnitude and direction
• The length of the arrow represents the magnitude of the force
• The direction of the arrow indicates the direction of the force

A free body diagram of an object with two forces acting on it

• Not all forces are directed perfectly horizontally or vertically and thus need to have an angle described
• It is useful to describe an angle with respect to the vertical or the horizontal

A force of magnitude 100 N directed 40° to the horizontal