<< Chapter < Page Chapter >> Page >

Introduction

This chapter focuses on vectors. We will learn what is a vector and how it differs from everyday numbers. We will also learn how to add, subtract and multiply them and where they appear in Physics.

Are vectors Physics? No, vectors themselves are not Physics. Physics is just a description of the world around us. To describe something we need to use a language. The most common language used to describe Physics is Mathematics. Vectors form a very important part of the mathematical description of Physics, so much so that it is absolutely essential to master the use of vectors.

Scalars and vectors

In Mathematics, you learned that a number is something that represents a quantity. For example if you have 5 books, 6 apples and 1 bicycle, the 5, 6, and 1 represent how many of each item you have.

These kinds of numbers are known as scalars .

Scalar

A scalar is a quantity that has only magnitude (size).

An extension to a scalar is a vector, which is a scalar with a direction. For example, if you travel 1 km down Main Road to school, the quantity 1 km down Main Road is a vector. The “ 1 km ” is the quantity (or scalar) and the “ down Main Road ” gives a direction.

In Physics we use the word magnitude to refer to the scalar part of the vector.

Vectors

A vector is a quantity that has both magnitude and direction.

A vector should tell you how much and which way .

For example, a man is driving his car east along a freeway at 100 km · h - 1 . What we have given here is a vector – the velocity. The car is moving at 100 km · h - 1 (this is the magnitude) and we know where it is going – east (this is the direction). Thus, we know the speed and direction of the car. These two quantities, a magnitude and a direction, form a vector we call velocity.

Notation

Vectors are different to scalars and therefore have their own notation.

Mathematical representation

There are many ways of writing the symbol for a vector. Vectors are denoted by symbols with an arrow pointing to the right above it. For example, a , v and F represent the vectors acceleration, velocity and force, meaning they have both a magnitude and a direction.

Sometimes just the magnitude of a vector is needed. In this case, the arrow is omitted. In other words, F denotes the magnitude of the vector F . | F | is another way of representing the magnitude of a vector.

Graphical representation

Vectors are drawn as arrows. An arrow has both a magnitude (how long it is) and a direction (the direction in which it points). The starting point of a vector is known as the tail and the end point is known as the head .

Examples of vectors
Parts of a vector

Directions

There are many acceptable methods of writing vectors. As long as the vector has a magnitude and a direction, it is most likely acceptable. These different methods come from the different methods of expressing a direction for a vector.

Relative directions

The simplest method of expressing direction is with relative directions: to the left, to the right, forward, backward, up and down.

Compass directions

Another common method of expressing directions is to use the points of a compass: North, South, East, and West. If a vector does not point exactly in one of the compass directions, then we use an angle. For example, we can have a vector pointing 40 North of West. Start with the vector pointing along the West direction: Then rotate the vector towards the north until there is a 40 angle between the vector and the West. The direction of this vector can also be described as: W 40 N (West 40 North); or N 50 W (North 50 West)

Questions & Answers

at what age does development of bone end
Alal Reply
how many bones are in the human upper layers
Daniel Reply
bones that form the wrist
Priscilla Reply
yes because it is in the range of neutrophil count
Alexander Reply
because their basic work is to fight against harmful external bodies and they are always present when chematoxin are released in an area in body
Alexander
What is pathology
Samuel Reply
what is anatomy
ESTHER Reply
drowning and level female reproductive system
Anas Reply
what are the types of homeostasis
Odey Reply
diagram of the digestive system
Zainab Reply
drown and level female reproductive system
Anas
anatomy
Anas
What is the best way to indicate the sperm
ADAM Reply
Definition of pathology
Promise Reply
what are the body organs and their functions
Comforter Reply
what are the body organs and their functions
Ruth
musculoskeletal
Ruth
what is cell
Oppicial Reply
a cell is the smallest structural and functional unit of life.
Patrick
To know how bones are functions
DAUDA Reply
diagram of the heart
Victoria Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Physics - grade 10 [caps 2011]. OpenStax CNX. Jun 14, 2011 Download for free at http://cnx.org/content/col11298/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics - grade 10 [caps 2011]' conversation and receive update notifications?

Ask