Scalars & Vectors | Physics for Grade 10 PDF Download

Introduction

All quantities can be one of two types:

• A scalar
• A 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

Comparing 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

Exam Tip

• Distance and displacement
• Speed and velocity
• Weight and mass

Representing Vectors

• 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
  
  Two forces represented by arrows.

Force A has a larger magnitude than Force B. Force A is directed to the right and slightly upwards, whereas Force B is directed to the left and slightly upwards.

Solved Example

Step 1: Draw the first tennis ball and its velocity vector
(i) Measure the 45° angle with a protractor

Step 2: Draw the second tennis ball and its velocity vector
(i) The second ball has a speed of 10 m/s, so the arrow will be twice as long