Scalars and Vectors

Question 1

What is a physical quantity?

Answer 1

A physical quantity is something that can be measured. Physical quantities describe measurable properties such as mass, temperature, distance, force, or energy.

Question 2

Into what two groups can all measurable (physical) quantities be divided?

Answer 2

All measurable quantities can be divided into two groups: scalars and vectors.

Question 3

What is a scalar quantity?

Answer 3

A scalar quantity is a physical quantity that has magnitude only. Magnitude means the size or numerical value of the quantity. Scalars have no direction.

Question 4

What does “magnitude” mean in physics?

Answer 4

Magnitude means the size or numerical value of a physical quantity. It tells you how much of something there is, but not the direction.

Question 5

Example - Why is temperature a scalar quantity?

Answer 5

Temperature is a scalar quantity because it only has magnitude (for example, 10°C) and no direction.

Question 6

Give examples of scalar quantities.

Answer 6

• Distance
• Mass
• Temperature
• Time
• Density
• Speed
• Energy
• Power

Question 7

Give examples of scalar quantities with units.

Answer 7

Temperature, e.g. 10 degrees Celsius (°C)

Mass, e.g. 5 kilograms (kg)

Energy, e.g. 2,000 joules (J)

Distance, e.g. 19 metres (m)

Speed, e.g. 8 metres per second (m/s)

Density, e.g. 1,500 kilograms per metre cubed (kg/m³)

Question 8

How do you add scalar quantities?

Answer 8

To add scalar quantities, you simply add their numerical values together.

Question 9

How do you subtract scalar quantities?

Answer 9

To subtract scalar quantities, you subtract one numerical value from another.

Question 10

What is a vector quantity?

Answer 10

A vector quantity is a physical quantity that has both magnitude (size) and direction.

Question 11

Why is force a vector quantity?

Answer 11

Force is a vector quantity because when describing a force, you must state both its magnitude (for example, the number of newtons) and its direction (for example, to the left or upwards). It is not enough to state the size alone.

Question 12

Why is it not enough to only state the size of a force acting on an object?

Answer 12

It is not enough to state only the size of a force because force is a vector. You must also know its direction to fully describe its effect on an object.

Question 13

Give examples of vector quantities.

Answer 13

• Force
• Displacement
• Velocity
• Acceleration
• Momentum
• Weight

Question 14

Give examples of vector quantities with magnitude and direction included.

Answer 14

Force, e.g. 20 newtons (N) to the left

Displacement, e.g. 50 kilometres (km) east

Velocity, e.g. 11 metres per second (m/s) upwards

Acceleration, e.g. 9.8 metres per second squared (m/s²) downwards

Momentum, e.g. 250 kilogram metres per second (kg m/s) south west

Question 15

How can the direction of a vector be given?

Answer 15

The direction of a vector can be given either in a written description (such as “to the left” or “east”) or by drawing it as an arrow.

Question 16

How are vectors usually represented?

Answer 16

By an arrow.

Question 17

What does the length of a vector arrow represent?

Answer 17

The length of a vector arrow represents the magnitude (size) of the vector.

Question 18

What does the direction of a vector arrow represent?

Answer 18

The direction the arrow points represents the direction of the vector quantity.

Question 19

Can vectors be drawn to different scales?

Answer 19

Yes, vectors can be drawn to different scales, meaning the length of the arrow can represent different amounts depending on the chosen scale.

Question 20

Example - Describe how a velocity of 35 m/s at 45° to the horizontal would be represented as a vector.

Answer 20

It would be represented by an arrow. The length of the arrow would represent the magnitude (35 m/s), and the arrow would point at an angle of 45° to the horizontal to show the direction.

Question 21

Example - What happens to a vector diagram if the magnitude of velocity increases from 35 m/s to 60 m/s?

Answer 21

The length of the arrow becomes longer to represent the greater magnitude.

Question 22

Example - What happens to a vector diagram if the direction changes from 45° to 60° to the horizontal?

Answer 22

The arrow changes direction and points at 60° instead.

Question 23

What is the difference between speed and velocity?

Answer 23

Speed is a scalar quantity because it only has magnitude. Velocity is a vector quantity because it has both magnitude and direction.

Question 24

How can two objects have the same speed but different velocities?

Answer 24

Two objects can have the same speed if they are moving at the same magnitude (for example, the arrows representing them are the same length). However, they have different velocities if they are travelling in different directions, because velocity includes direction as well as magnitude.