NPHY 111 EC
BASIC PHYSICS I
Faculty of Natural and Agricultural Sciences
Study guide compiled by: Mrs H. Vosloo
Copyright © 2020 edition. Review date 2020.
North-West University
No part of this study guide may be reproduced in any form or in any way without the written permission of the publishers.
It all starts here
•
•
Ranked in the top 5% of universities globally by the QS-rankings
Contributes the second largest number of graduates annually to the labour market
Dit begin alles hier
•
•
As een van die top 5% universiteite wêreldwyd deur die QS-ranglys aangewys
Lewer jaarliks die tweede meeste graduandi aan die arbeidsmark
Gotlhe go simolola fano
•
•
Re beilwe mo gare ga diyunibesiti tse 5% tse di kwa godimo go ya ka peo ya
maemo ya QS
Ngwaga le ngwaga go abelwa palo ya bobedi ka bogolo ya badiri mo maketeng ya
badiri
MODULE CONTENTS
Module information ................................................................................................................iii
Welcome ................................................................................................................................iii
Module outcomes...................................................................................................................iii
Prerequisite............................................................................................................................iv
Contents of this module .........................................................................................................iv
Time schedule .......................................................................................................................iv
General module information and contact details ....................................................................iv
Study material ........................................................................................................................vi
Working method in physics and how to study.........................................................................vi
Assessment ........................................................................................................................... x
Priorities ................................................................................................................................xii
Action words ........................................................................................................................ xiii
Before we start – a bit of inspiration: .................................................................................... xiv
Icons ....................................................................................................................................xiv
Warning against plagiarism ...................................................................................................xv
Study division A: Kinematics and vectors ............................................................................... 1
Study unit 1
Measurement ........................................................................................ 1
Study unit 2
Motion along a straight line ................................................................. 3
Study unit 3
Vectors.................................................................................................. 6
Study unit 4
Motion in two and three dimensions .................................................. 9
Study division B: Dynamics .............................................................................................. 12
Study unit 5
Force and motion I ............................................................................. 12
Study unit 6
Force and motion ii ............................................................................ 15
Study unit 7
Kinetic energy and work .................................................................... 17
Study unit 8
Potential energy and conservation of energy .................................. 20
Study unit 9
Centre of mass and linear momentum ............................................. 23
Study unit 10
Rotation .............................................................................................. 26
Study unit 11
Rolling, torque andangular momentum ............................................ 29
Study division C: Statics ................................................................................................... 32
Study unit 12
Equilibrium ......................................................................................... 32
Study unit 13
Gravitation .......................................................................................... 34
Study division D: Hydrostatics and hydrodynamics ....................................................... 36
Study unit 14
Fluids .................................................................................................. 36
Study division E: Periodic motion and waves ................................................................ 39
Study unit 15
Oscillations......................................................................................... 39
i
Study unit 16
Waves ................................................................................................. 42
Study unit 17
Waves ii .............................................................................................. 45
Study division F: Study of heat......................................................................................... 48
Study unit 18
Temperature, heat and the first law of thermodynamics ................. 48
Study unit 19
The kinetic theory of gases ............................................................... 51
Study unit 20
Entropy and the second law of thermodynamics ............................ 54
List of the most important key words .................................................................................... 56
Meertalige kernkonsepte / Multilingual key concepts / Dikakanyokgolo ................................ 61
ii
Module information
Module code
NPHY 111
Module credits
12
Module name
Basic Physics I
Name of lecturer(s)
Mr. Ruhann Steyn (PC)
Dr. Donald Ngobeni (MC)
Office telephone
Email address
Ruhann.Steyn@nwu.ac.za (PC)
Donald.Ngobeni@nwu.ac.za (MC)
Building and Office no.
G5-124 (PC)
..............(MC)
Consulting hours
By appointment only
Welcome
The subject-group Physics welcomes you to the module NPHY111. This module will
equip you with the basic knowledge and understanding about physical phenomena that
you will meet in everyday life and that you will need for your further studies. This module
is also a preparation for students intending to continue with Physics as one of their major
subjects.
Module outcomes
After completion of the module NPHY111, the student should demonstrate:
•
•
•
•
•
Formal mathematical knowledge and informed understanding of the
fundamental concepts underpinning the subthemes of physics, i.e., kinematics,
Newtonian laws of motion, work and energy, momentum, rotation and rolling,
equilibrium, gravity, fluid mechanics, simple harmonic motion, waves, the study of
heat, and thermodynamics.
An awareness of the development of physical measurements and theories that
shaped the progress of physics;
The ability and skills to explain certain parts of the theory by means of the basic
differential and integral calculus; to solve a variety of natural science problems in
the above-mentioned subthemes and to evaluate the answers and apply them to
phenomena within a well-defined and familiar environment.
Effective utilisation of basic research skills, such as conducting experiments,
measuring basic observable quantities related to special and controlled cases of
natural processes, and processing these data. The ability to reliably communicate
these discipline-specific ideas by writing a report in an accurate and coherent way
while showing respect for conventions related to copyright and plagiarism.
The ability to manage his or her learning and implement the discipline-specific
learning strategies given in the NPHY111 study guide to address learning
problems.
iii
•
The ability to work in a group and make appropriate contributions and sharing
resources to successfully complete the practical sessions and thereby taking coresponsibility for the attainment of the outcomes by the group.
Conduct in the academic environment that adheres to the rules as stipulated by
the North-West University code of conduct.
•
Prerequisite
University Admission (with Mathematics and Physical Sciences)
It is preferable that you should already have completed school level science successfully,
since there are some parts of study units that suppose Physics school knowledge as
background knowledge.
Furthermore, we depend upon the algebra knowledge you acquired at school.
Contents of this module
A brief summary of the contents of this module is given below. The approximate number
of periods to be spent on each of the study divisions is also provided.
Study division
Number of
hours
% of
module
A
KINEMATICS
6
± 15
B
DYNAMICS
13
± 35
C
STATICS
4
± 10
D
HYDROSTATICS AND HYDRODYNAMICS
4
± 10
E
PERIODIC MOTION AND WAVES
6
± 15
F
STUDY OF HEAT
6
± 15
You will find that you have already encountered at high school some of the work that we
are going to do. We are repeating it in order to ensure a firm and uniform basis on which
we can continue to work.
The STUDY UNITS of this module have been divided according to the chapters in the
prescribed textbook and the STUDY SECTIONS correspond with the paragraphs in the
textbook. We will strictly adhere to this order.
Time schedule
This module consists of 12 credits that are the equivalent of 120 hours of study. The
lectures periods and the study hour (self-study) are indicated with each Study Unit.
General module information and contact details
Consultation hours
Please make an appointment if necessary.
Potchefstroom campus: Make enquiries at G5-116 if the lecturer is not in his office. All
arrangements about the practical work can be obtained from Mr. Moerdyk, G5-308.
iv
Mafikeng campus:
…………………………………………………………………………......................................
...........................................................................................................................................
Lectures
Monday: ______________________________________________________________
Tuesday: ______________________________________________________________
Wednesday: ___________________________________________________________
Thursday: _____________________________________________________________
Friday:________________________________________________________________
Study facilitator
_____________________________________________________________________
Some successful and capable senior undergraduate or post-graduate students have
been appointed as facilitators. They have been thoroughly trained in the techniques of
study facilitation in order to assist you in mastering the strategy for study and in achieving
the desired outcomes of your subjects. The section on “Study techniques” in this Study
Guide gives more information about this system of facilitation. We shall introduce the
facilitator for NPHY111 to you at the earliest opportunity.
Tutorial period
We will arrange for a few tutorial sessions to ensure that every one has the opportunity
to ask their questions. The tutorial sessions offers you another golden opportunity to ask
questions if there should be anything that you do not understand, as well as an
opportunity to do additional exercises and solve problems with the required guidance
and assistance. Keep in mind that every test and examination paper will also include a
number of problems and applications.
Semester test
During assessment week: ________________________________________________
Autumn recess
_____________________________________________________________________
_____________________________________________________________________
Final ending of lectures
_____________________________________________________________________
_____________________________________________________________________
Examination
You will write one paper of 3 hours.
Duration
examination):
of
examination
(first
v
_____________________________________________________________________
_____________________________________________________________________
Duration of examination (second examination): ________________________________
Examination date: _______________________________________________________
Study material
Prescribed textbook
Printed: Halliday, Resnick and Walker: Principles of Physics. 10th Edition 2014
Online: The online edition of this textbook on WileyPlus will/can be incorporated.
NB NB NB: Please consult your lecturer during the first lecture about which textbook
(online or printed) will be used and to what extent. It will not be necessary to buy both,
the online and printed form of this textbook is EXACTLY the same, therefore consult with
your lecturer before making any purchase.
Study guide
The purpose of the study guide for NPHY111 is to guide you through your study, use it!
Working method in physics and how to study
General Outcomes:
The main aim of this module is to equip you with the knowledge about physical
phenomena that you will meet in everyday life and that you will need in further studies.
We trust that you will develop an understanding of them. The module also aims to
prepare you for further studies in Physics. We shall pursue the following outcomes in
particular:
•
•
•
vi
Insight or understanding: Understanding the work is important. One understands
work if you can answer the why question about everything. Why is a definition
defined like this and not in any other way? How does step 2 follow from step 1?
Insight is to understand which steps are necessary for a certain derivation, and
why only those steps will do. When one struggles to solve problems, the reason is
usually that one does not yet know and understand the work.
Accuracy: In Physics something is not “almost right”, for then it is “totally wrong”.
You have to learn to get the precisely correct formulation for a definition, a law, or
whatever.
Communication: It is important to learn to express yourself logically and clearly in
good English (or Afrikaans). Poor grammar and language will be penalized in tests
or in the examination. Language remains the medium through which you
communicate with your colleagues. In this course, you are required to associate a
concept, an object, an idea or an action with a specific word. Since English is
evolving on a daily basis, it is necessary that it should also be developing as a
technical language owing to the addition of new terminology. One should strive
always to let a technical term have one meaning only by associating it with a
particular concept. The term needs to be appropriate, descriptive and typical of the
concept, object, idea or action concerned. You should therefore pay careful
attention to the way in which the lecturer uses the terminology and make certain
that you do likewise. You should then never experience problems with regard to
the understanding and communication of the relevant technical terminology.
Mathematical symbols and formulae:
Measured results based on what has been observed in nature are summed up in physics
as mathematical formulae so that these provide a compact reproduction of the mutual
relationships that are implied in the measurements. Theoretic models are then
formulated for the measurements. Quantities therefore need to be defined in order that
we may all know what we are measuring. Quantities are represented by a mathematical
symbol that has content and meaning in physics. It is therefore always essential that you
should clearly define the symbols that you use otherwise these will amount to mere
mathematical manipulations.
Describing nature by making use of defined mathematical symbols, formulae or
equations therefore forms a powerful communication method in physics.
Take care that you always explain or record the meaning of the mathematical symbols
that you are using. The examiner will also want to know whether you understand the
meaning and significance of the mathematical symbols that you write down. You are
therefore required to take note of the meaning and content that the lecturer attaches to
mathematical symbols and how the relationships between physical quantities in
mathematical equations are read. You must become familiar with these and must be able
to do likewise.
Models and a description there of:
As we are all aware, reality is extremely complicated.
In class, we theorise with regard to the simplified reality. In theorising we make use of
models in order to describe the simplified reality. Such a model can often be presented
by means of a sketch using for instance arrows for forces and electric fields, a dot for a
charge and an arrow to indicate the direction of movement of a charge. Distances, forces,
magnetic fields, etc. are indicated by means of symbols in sketches of this nature. Often
a sketch is essential to explain symbols and meanings and also to let derivations and
discussions make sense. Take note of the large number of sketches / illustrations that
you can find in your textbook and how frequently these are used in order to explain the
learning material. It is therefore very important that you should understand the sketches
and symbols used in your textbook. In tests and examinations you are also required to
make meaningful use of sketches with symbols in them so that it will be clear to the
examiner that you do indeed understand the work. Many questions cannot possibly be
answered in a meaningful way without the use of appropriate sketches.
In the laboratory, on the other hand, we create simple conditions so that only a few
variables (or parameters) play a role and so that it is easy to control the variables. In that
manner we are in a position to verify how different quantities change in respect of one
another and what legitimate connection they have with regard to one another.
Why study Physics?
Each of the natural sciences studies the physical reality by looking at some or other
aspect of it.
Let us give a few examples:
•
Mathematics is a study of the number- and space-aspects of reality.
•
Physics covers the motion- and energy-aspects of nature. (As such Chemistry is
actually a part of Physics). In Physics numbers, space, motion and energy play an
vii
important role. For this reason we cannot study Physics without a basic knowledge
of Mathematics. To do Physics, we have to know Mathematics!
•
The biotic (life-) aspects of plants, animals or humans designate the biological,
zoological and physiological fields of study. In these biological subjects numbers,
space, motion, energy and the biotic aspects all come into play. To work in the
biological subjects, one therefore needs a thorough knowledge of Mathematics,
Physics and Chemistry.
There is no aspect of our physical reality (objects, plants, animals, humans) that is not
subjected to the laws of physics.
•
Gravity determines the direction of growth of plants;
•
The heartbeat is regulated by electrical pulses;
•
Engineers (whether mechanical, electrical, electronic or chemical) apply the laws
of physics and chemistry in their everyday work. Therefore engineers study the
applications of physics and chemistry. An engineer who does not understand the
physics which is basic to these laws, will not be able to enjoy his work;
•
Physical measuring instruments and methods of measurements are being used in
all natural sciences and cultural sciences (such as engineering, computer science
and home economics);
•
The engineer, biologist, medical doctor, chemist or dietician cannot perform his or
her tasks without using mass meters, pressure gauges, gauges of mechanical
stress, voltmeters, X-ray machines, centrifuges, electron microscopes, gas
chromatography systems, radiation detectors and computers (to name a few). The
operation of all these instruments is based on physical principles and laws and to
use them intelligently, one has to understand these principles and laws.
In our modern lives we live and work in a physical -technological society. Just consider
the modern car that abounds in modern technology. Consider the role that computers
play in today’s life. Without an elementary knowledge of the basic laws and principles of
nature that govern this technical environment, we may develop insecurity and become
neurotic.
The purpose of your study is not to make you one day performing a job like a robot. It is
to enable you to become a balanced person who will lead an interesting and rewarding
life in a satisfying career. This will only be possible if you could pursue your career as an
intelligent, thinking person who does not feel threatened by modern technology, because
you would understand your environment.
Of course it is important that you should pass your exams, but it is even more important
that you should understand and be in charge of yourself and your environment.
Study practice:
It is very important to develop the correct study methods. If you need help, consult me
or someone else immediately. Should any problem occur during the semester,
something that has a negative influence on your studies, do not hesitate to come and
discuss it with me, your lecturer. Consult me timeously – do not wait until it is too late.
Other forms of formal support are also available on the campus.
The facilitator system is a programme that makes use of Subject Guardians and Student
Facilitators, to assist first, second and sometimes third year students. It aims to empower
them by developing a study strategy so that they can achieve the study outcomes in their
viii
modules. Cooperative study is promoted and it is hoped that a dynamic culture of study
will develop on the campus.
Students meet on a weekly basis in small groups. Group study sessions are being
conducted by the facilitators. These facilitators are senior students that have been
trained in guiding students towards correct study techniques. These facilitators have
weekly consultations with the subject guardian (usually the first or second year lecturer
in the subject) to identify the outcomes and decide which skills should be receiving more
attention.
During the group study sessions special attention is given to academic problems.
The facilitators create a safe learning environment in which learners are encouraged to
be active participants to the learning process. They are prompted to ask questions, pose
problems and suggest answers to questions. In this way an insight into the subject matter
is developed while communication skills, study strategies and other scientific abilities like
critical thinking, analysis, organizing, etc. are being cultivated.
The facilitator for NPHY111 will be introduced to you at the earliest opportunity.
If you want to complete the module without experiencing any problems, it is essential
that you should prepare thoroughly for every lesson. You are furthermore required to
make yourself a set of core notes by availing yourself of the textbook (which is excellently
written), the study guide, and the lecturer’s lectures. Also have a look at the Review and
summary which is a good indication of what you are suppose to know as well as a
summary of the key concepts of each Study.
Furthermore you will be expected to be motivated and also to do self-study with the
necessary self-discipline.
The writing of definitions and laws:
The most important laws in every study unit are indicated with an arrow () next to the
most important concepts in each chapter.
The writing of definitions is an art you have to master yourself. The lecturer is not going
to rewrite each of the definitions from the textbook for you. Note that it has to be written
concise, but still contain all relevant information, consisting of the following components:
•
Concise description of relevant aspects
•
A mathematical expression of the quantity defined (if relevant)
•
Declaration of all symbols
•
Scientific units of the quantity you are defining.
•
A sketch with captions (if relevant)
Derivations (Proofs):
The study guide provides you with a list of the derivations with which you need to be
familiar and be able to reproduce in tests and in the examination. The number of marks
that you earn will depend on the completeness of the derivation. Study the derivation
and then make your own summary by taking the following into consideration:
•
What are the initial conditions? They should typically start with “Consider a system
/ particle / charge …”
•
Draw a sketch and explain.
•
With which law / equation(s) should you start? Next, apply it and explain the
symbols.
ix
•
Don’t merely write down equations; explain what you are doing and the reason for
doing so.
•
Indicate how you progress from one step to the next.
•
The derivation is completed only when you have proved what you have been asked
(final expression).
•
You will be awarded no marks at all if you just write down a number of formulas.
Solving problems:
Problem solving tactics are given in each chapter. Make use of it. Answer the
Questions listed at the end of each chapter and the Checkpoints in every chapter.
By answering the questions that appear at the end of each study unit and by solving the
problems you will be exercising your understanding of and insight into the work that has
been dealt with in that study unit. Try to find solutions for all the exercises and problems
of each study unit independently in order to ensure that you understand the laws and
principles and are able to apply them. Discuss the problems with the lecturer or with your
fellow students. You will thus develop an insight of your own regarding the subject. The
textbook provides complete information and advice in virtually every chapter with regard
to the way you should handle problems. At the back of the textbook you are given the
answers to all the checkpoints, to the odd number questions as well as the odd number
exercises and problems that appear in each chapter. We will also spend time on the
exercises in the tutorial lessons. Keep in mind that the tests and examinations will contain
some problems (≈50%).
Assessment
Class tests, open book tutorials or e-learning tests
During the semester, you will write a number of class tests as well as a test during the
assessment week. The purpose of the class tests is to let you work diligently every day
so that you may develop a full understanding of the knowledge presented to you and that
you do not fall behind with the work. This will simultaneously contributes towards your
participation mark, which is very important. The class tests will also contain a number of
problems, laws, definitions and derivations. If there are multiple choice questions in the
tests, it must be answered on a computer card by colouring in the circle that concurs with
the correct answer. You will need a HB pencil for this purpose. If you don’t colour in
the circles neatly, the card reader will ignore it and you will lose marks.
After the class tests have been assessed it will be placed in the Physics mailboxes in the
Physics building. It is your own responsibility to go and fetch it. The marks will be placed
in a document on eFundi. You must check your marks.
Besides the class tests you will also do a number of open book tutorials and any
eLearning tests on eFundi will be announced in class.
Assessment dates:
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
x
Homework and assignments
A very important aspect of any Physics course is the solving of problems. As soon as a
chapter has been finished you should start working on the homework in the chapter.
Some of the homework problems will be done in class or during the tutorial periods; the
answers of the others will be put on eFundi.
During the semester you will occasionally be asked to submit a few exercises as
assignments. The assignments will be given in class and published on eFundi.
The purpose of these homework and assignments is to help you to think about the
Physics. It will do you no good to copy the work from someone else.
The homework and assignments are important since they help you to understand the
basic applications of physics, and you should therefore complete them meticulously, thus
make sure that you regularly do this homework. The marks that you obtain with
assignments also contribute towards your participation mark.
The following rules apply when you submit assignments:
•
No late assignments will be accepted.
•
Each assignment is to be completed and submitted on A4-size lined pages and
must be stapled in the top left-hand corner. You may not use pins or paper clips.
Books, covers, etc. are not acceptable.
•
Use the same numbering for each problem as in the textbook or as on eFundi.
•
Draw a neat line across the page at the end of each answer to a problem.
•
Make certain that your surname and all your registered initials as well as your
student number are clearly written on the cover of each completed assignment.
•
After the assignments have been assessed it will be placed in the mailboxes on
the third floor on your way to the Physics practical laboratory. It is your own
responsibility to go and fetch it. The marks will be placed on the board on the first
floor in the Physics building; you must check your marks there.
Dates for submission of assignments: ____________________________________
Absence
•
•
•
Students, who have been successful in the past, regard regular class attendance
as one of the most important reasons for their success. If you have been unable to
write a test owing to illness (or any other valid reason), you are required to submit
at the first opportune moment to the Secretary at Enquiries in the Physics
building, an original medical certificate (or any other original official document in
verification of any other valid reason for your absence).
Medical certificates and other supporting documentation must be submitted within
ten days of the date of absence and it has to be the original document. The
secretary will make a copy and hand the original back to you.
N.B.: There will be no rewriting of tests that students have missed owing to their
absence due to illness or any other reasons.
Participation mark and final mark
Requirements for examination admission:
xi
To gain entrance to the examination, you must obtain proof of participation. You will find
the complete requirements for this in the yearbook of the Faculty of Natural and
Agricultural Sciences. One requirement is a minimum participation mark of 40% (35%
for bona fide first year students). Please note that the completion of practical work and
satisfactory class attendance are required for proof of participation. The participation
mark is made up of the final mark for the practical work and the final mark for theory. The
mark for theory is made up of the marks obtained for the class tests, semester test, open
book tutorials, class work (class attendance), eLearning tests on eFundi and the
assignments. The final mark for the practical work and the final mark for theory are taken
in a ratio of 1:3 when the participation mark is calculated.
Requirements for a pass:
A minimum module mark of 50%, provided that you have obtained 40% or more in the
examination, is required for you to pass the module. The ratio of the examination mark
in relation to the participation mark is 1:1.
Examination
All those students who have qualified for a participation mark in this module are entitled
to two opportunities for writing the module examination. Both these module examinations
consist of a single 3-hour paper. You may use either both of these opportunities or any
one of your choice. Should you, however, opt to write both papers, the mark that you
obtain at the second opportunity will be used to determine your module mark. No
certificate is required if you do not write the first examination. Please note that it would
be rather risky not to avail yourself of the opportunity to write the first examination. Should
you, for instance, be unable to make use of the second opportunity for unforeseen
reasons such as illness, there will not be a third (special) examination opportunity.
Students who do not avail themselves of these two opportunities to write the examination
or who have failed to pass the module after having written one or both of the
examinations, will need to re-register for the module, pay the class fees again, and attend
all classes in order to qualify for proof of participation anew and thus gain entrance to
the next scheduled opportunity to write the examination.
If there are multiple choice questions in the exam you will be handed a computer card
on which you must answer these questions by colouring in the circle that concur with the
correct answer. You will need a HB pencil for this purpose. If you don’t colour in the
circles neatly, the card reader will ignore it and you will lose marks.
Priorities
In order to determine what is of importance, we make use of the following system: a
specific priority and icon is allocated to each paragraph. We explain the meaning of this
in the table below. Make sure that you understand the content of the table well, because
it is the key to success in your studies.
Priority
Meaning
Examination
weight
Number of lessons (hours) required by lecturer;
number of hours of self-study by student
a
xii
This is essential knowledge (which includes all
laws,
derivations
and
definitions);
a
comprehensive, in-depth knowledge of the work
Approximately
30%
is required. You are required not only to know
and to understand the work, but must be able to
apply it also as in the examples that have been
worked out.
b
You need to go through this work (derivations,
discussions and examples that have been
worked out) and make absolutely certain that
you understand it. It is essential that you should
master the work. The definitions and basic
principles of physics supported by mathematics
are very important.
Approximately
25%
c
Only a few central ideas are important in these
sections. Make your own summary and
interpretation as required in the study guide.
This includes all exercises, questions and
assignments.
At most 30%
d
Self-study – mainly a repetition of schoolwork
that is essential for mastering the work. We will
deal with it but briefly or perhaps not at all in
class.
At most 10%
e
Supplementary study material, additional points
of interest, and background information that is
not of necessity of direct importance
At most 5%
Outcomes of the specific study unit or chapter
Priority (a) determines the core study material. A student who has mastered priorities (a)
and (b) can pass the module. In order to qualify for a distinction you need to do more
than is required by priority (a) only. It is essential that you should know priority (d) very
well since the omission of that will create a gap in your background knowledge. The
assignments and homework afford you with an opportunity to prove that you have indeed
mastered the work.
Action words
Test and examination questions always contain certain key or action words. It is essential
for you to be familiar with the meanings of such action words and to know exactly what
is required of you when you need to answer a question. With this in mind, a brief list of
such verbs is given below:
•
Name
In this instance, you need to write down the facts in a nutshell.
•
Describe
You are required to perform at knowledge level. Characteristics, facts or results must be
given in a logical, well-structured way. No comments or debating is required.
•
Define / State
A mere reproduction of information / knowledge is required. It entails a clear, concise
and authoritative description of a concept so that its meaning becomes clear. If you
should make use of a mathematical equation in this instance, you need to explain all the
symbols that you use in the equation, explain the meaning of each symbol, and also
supply the SI unit of each.
xiii
•
Give a mathematical expression for:
You are required to explain all symbols used in the expression: you need to state what
each symbol represents and give its SI unit.
•
Give an overview
A large volume of knowledge must be summarised and reproduced logically and
systematically while retaining the essence of the matter.
•
Explain
A matter is stated simply in order that the reader may understand it fully. You must make
use of examples, illustrations and descriptions, while also providing reasons for
statements and results.
•
Prove
Bear out the facts by producing proof in support of them. Look again at the heading
“WORKING METHOD IN PHYSICS AND HOW TO STUDY”, for how to tackle a
“derivation” or prove a “statement”.
•
Compare / Distinguish between
You should approach this with care. Do not first discuss one matter and then the next
one. Facts, events or problems are contrasted and similarities or differences are
highlighted. Hint: answer this type of question in tabular format
Before we start – a bit of inspiration:
We as lecturers are very enthusiastic about our field, Physics. The world of physics is so
wide and each individual lecturer has become an expert on his or her field of research.
Lecturers will most definitely share their experience of their specific research fields with
their students when teaching physics since the lecture’s mandate is not only to teach
technical physics with real-life examples, but also to inspire the scientists (you) of the
future. Absorb as much as possible from your lecturers and use this module to lay the
foundation to be the best scientist you can be.
Icons
xiv
Time allocation
Learning outcomes
Study material
Assessment /
Assignments
Individual exercise
Group Activity
Example
Reflection
Warning against plagiarism
ASSIGNMENTS ARE INDIVIDUAL TASKS AND NOT GROUP ACTIVITIES. (UNLESS
EXPLICITLY INDICATED AS GROUP ACTIVITIES)
Copying of text from other learners or from other sources (for instance the study guide,
prescribed material or directly from the internet) is not allowed – only brief quotations
are allowed and then only if indicated as such.
You should reformulate existing text and use your own words to explain what you have
read. It is not acceptable to retype existing text and just acknowledge the source in a
footnote – you should be able to relate the idea or concept, without repeating the original
author to the letter.
The aim of the assignments is not the reproduction of existing material, but to ascertain
whether you have the ability to integrate existing texts, add your own interpretation and/or
critique of the texts and offer a creative solution to existing problems.
Be warned: students who submit copied text will obtain a mark of zero for the
assignment and disciplinary steps may be taken by the Faculty and/or University.
It is also unacceptable to do somebody else’s work, to lend your work to them or
to make your work available to them to copy – be careful and do not make your
work available to anyone!
Plagiarism is a serious offence and you should familiarise yourself with the
plagiarism policy of the NWU. http://library.nwu.ac.za/copyright-and-plagiarism
Please refer to the Policy on Academic Integrity which is found on the following
website: http://www.nwu.ac.za/content/policy_rules
xv
Study unit 1
Study division A: Kinematics and vectors
Study unit 1
MEASUREMENT
Study material
This self-study Study Unit consists of Chapter 1 in the textbook. You will not be
examined about this, but it is important that you study this attentively.
Study the following attentively
The most important concepts in this chapter are:
The SI-system
Base units
Standard kilogram
Derived units
Standard meter
Changing units
Study outcomes
After completion of this Study Unit you should be able to:
•
•
•
•
know certain concepts you need to complete this module successfully.
know and understand the SI-system.
convert units, e.g. from km/h to m/s.
know how we deal results with colleague scientists.
Study time
Contact sessions: 0 periods
Self-study: 2 hours
1
Study Unit 1
Important information
D What is Physics?
Read through.
D Measuring things:
Read through.
D The International System of Units:
Make sure you know the base units and the derived units. You must know Table 1.2.
D Changing units:
The rule explained here and the examples are very important. Take note of the “problem
solving tactics” – it helps to simplify your work.
D Length:
Read through and take note of Table 1.3. The example is not important.
D Time:
Read through.
D Mass:
Read through. Take note of Table 1.5. Make sure that you know what is meant by atomic
mass units (u).
Reflection
Review and Summary
Why do we measure things? How do we deal results with colleague scientists? What
is the SI system? How are units changed? See the “Review and summary” which is
a good summary of what you should know.
The core facts of this Study Unit is summarised here.
2
Study unit 2
Study unit 2
MOTION ALONG A STRAIGHT LINE
Study material
This Study Unit consists of Chapter 2 in the textbook and is the key Chapter to describe
any kind of motion. This is also revision of school work. It is important to that you
master this work.
Study the following attentively
The most important concepts in this chapter are:
Kinematics
Instantaneous speed
Position
Average acceleration
Distance
Instantaneous acceleration
Displacement
Constant acceleration
Average velocity
Equations of motion
Instantaneous velocity
Free fall
Average speed
Terminal speed
Study outcomes
After completion of this Study Unit you should be able to:
•
•
•
define and discuss the above-mentioned concepts and be able to derive and
apply them where applicable.
describe motion along a straight line.
derive and apply the equations of motions.
Study time
Contact sessions: 2 hours
Self-study: 4 hours
3
Study Unit 2
Important information
D What is Physics?
Read through.
C Motion:
Make sure that you know and understand the three assumptions that are made in this
Chapter.
A Position and Displacement:
Always give the definition of displacement (equation 2.1) in terms of a point of reference.
Displacement has both magnitude and direction and is thus a vector quantity. Difference
between displacement and distance.
“Checkpoint 1”: Do them all to check whether you understand what is done.
A Average velocity and speed:
Know both definitions (Equations 2.2 and 2.3). What are the units?
Figures 2.2, 2.3 and 2.4 are essential to understand the basic concepts – NB “x vs t”
graphs are not pictures of the path of the motion on the ground.
Thoroughly work through the Sample Problem – which will guide you in the correct
approach while doing problems.
A Instantaneous velocity and speed:
Know the definition (Equation 2.4) and the unit.
Make sure that you understand it is the tangent to x vs t graph.
Understand the remark about speed at the bottom of the page.
The Sample Problem and Checkpoint 2 are important.
A Acceleration:
Know the definitions (Equations 2.7, 2.8 and 2.9) as well as the SI unit.
Take note of g as a unit for acceleration.
Work through the Sample Problem and Checkpoint 3.
A Constant acceleration: A Special case
Derivation 1: You must be able to derive the Equations of motion (Equations 2.11, 2.15
and 2.16) for constant acceleration.
Checkpoint 4 is important.
Another look at Constant acceleration II:
4
Study unit 2
You can omit this.
B Free-fall acceleration:
Free fall – what is meant by this?
Do the Sample Problem and Checkpoint 5.
C Graphical Integration in Motion Analysis:
What does the area below a graph represent?
Reflection
Review and Summary
This is a good summary of the core facts of this Study Unit.
Individual activity
Homework:
2, 28, 37, 43, 62
5
Study Unit 3
Study unit 3
VECTORS
Study material
This Study Unit consists of Chapter 3 in the textbook and contains the core information
for the extension from one to more dimensions. You will need this Chapter a few times
during this year, so it will be great if you understand it from now on.
Important information
ur
To represent a vector, the textbook uses an arrow above the symbol, e.g. a . In hand
writing we underline the symbol, e.g. a. Other textbooks use bold letters, e.g. a.
Study the following attentively
The most important concepts in this chapter are:
Scalar
Vector components
Vector
Unit vectors
Displacement vector
Component Addition
Addition of vectors
Scalar product
Resultant
Vector product
Study outcomes
After completion of this Study Unit you should be able to:
•
•
•
define and discuss the above-mentioned concepts and be able to derive and
apply them where applicable.
know when a physical quantity is a vector or a scalar.
know and apply the rules for vector calculations.
Study time
Contact sessions: 2 hours
Self-study: 4 hours
6
Study Unit 3
Important information
D What is Physics?
Read through.
A Vectors and Scalars:
Scalars are quantities with magnitude only.
Vectors have magnitude and direction and are represented by an arrow. (e.g.
displacement)
D Adding vectors geometrically:
This is revision of known work.
Addition and subtraction.
Commutative and associative laws
Make sure that you understand all the figures.
Do the first Sample Problem and Checkpoint 1.
B Components of vectors:
The components of a vector are scalars and thus easy to work with. The components
can be written as component vectors by using unit vectors (see the next paragraph).
Equations 3.5 and 3.6 give the method to find the components and also to combine them
again.
Checkpoint 2 and the Sample Problem are important.
The Problem-Solving Tactics do significant revision of the angular units and trigonometry
functions.
B Unit vectors:
A formal way to write a vector in terms of its components.
B Adding vectors by components:
Make sure that you understand equations 3. 9 – 3.12 and the Sample Problem.
E Vectors and the laws of Physics:
Read through.
A `Multiplying Vectors:
Al three ways in which vectors can be multiplied are important.
(i) Multiplying a vector by a scalar: Increase a vector a with a quantity s. The direction is
the direction of a if s is positive but the opposite direction if s is negative.
7
Study Unit 3
(ii) Scalar Product or dot product: Multiplying a vector by a vector and the result is a
scalar.
The method is given in equation 3.20. Make sure that you understand figure 3.18.
Equation 3.23 gives it in terms of components. Do Checkpoint 4 and the
Sample Problem.
(iii) Vector- or cross product: This produces a third vector that is perpendicular on the
other two vectors.
The method is given in equation 3.27. Make sure that you understand the right-hand rule
in figure 3.19.
Do Checkpoint 5 and the Sample Problems.
Reflection
Review and Summary
Individual activity
Homework:
15, 18, 38
8
Study Unit 4
Study unit 4
MOTION IN TWO AND THREE DIMENSIONS
Study material
This Study Unit consists of Chapter 4 in the textbook. By writing the definitions of
motion in terms of vectors we can describe the two- and three dimensional motions in
terms of motion in a straight line and can thus apply the results of Study Unit 2.
Study the following attentively
The most important concepts in this chapter are:
Position and displacement
Uniform circular motion
Velocity
Centripetal acceleration
acceleration
Relative motion
Projectile motion
Study outcomes
After completion of this Study Unit you should be able to:
•
•
•
•
•
define and discuss the above-mentioned concepts and be able to derive and
apply them where applicable.
know that all the cases done in this study unit can be described in terms of motion
in a straight line and that we can thus apply the results of Study Unit 2.
do projectile motion with confidence.
understand circular motion, because you will need it again.
understand relative motion.
Study time
Contact sessions: 2 hours
Self-study: 4 hours
9
Study Unit 4
Important information
D What is Physics?
Chapters 2 and 3 are combined – read through.
B Position and displacement:
Both are vectors. Make sure you know equations 4.1, 4.2 and 4.3.
Do the Sample Problem.
B Velocity:
Another vector quantity. The definitions are given in equations 4.8 and 4.10. Make sure
that you know the component notation in equation 4.11 and the implication there of in
equation in 4.12.
Instantaneous velocity is the tangent to the path of the particle.
Checkpoint 1 and the Sample Problem are important.
B Acceleration:
Also a vector quantity with its definitions in equations 4.15 – 4.18.
Do the Sample Problem as well as Checkpoint 2.
A Projectile motion:
Projectile motion is the motion of a particle that is launched with an initial velocity v and
with its vertical acceleration the free-fall acceleration (air friction is negligible).
NB: The horizontal and vertical motions are independent of each other and have different
equations of motion – see figure fig 4.9. See figures 4.10, 4.11 and 4.12 together with
its discussions to convince you about it.
Only the parts on horizontal and vertical motion are of importance. Omit the equation for
the path, the horizontal range and the effects of the air.
Do Checkpoint 4 and the first Sample Problem.
A Uniform circular motion:
Circular motion with constant speed. The particle accelerates because the direction of
its velocity changes continuously.
Derivation 2: The calculation of the magnitude and direction of the acceleration – also
called the centripetal acceleration (make sure about the unit vectors).
Do Checkpoint 5 and the sample Problem.
B Relative motion in one dimension:
10
Study Unit 4
Make sure that you understand and know figure 4.18 and equation 4.41. The conclusion
that follows equation 4.42 is very important.
Do the Sample Problem.
B Relative motion in two dimensions:
Expansion of the previous paragraph – read through.
Reflection
Review and Summary
Individual activity
Homework:
14, 30, 61, 70
11
Study Unit 5
Study division B: Dynamics
Study unit 5
FORCE AND MOTION I
Study material
This Study Unit consists of Chapter 5 in the textbook. Now that we know how to
describe motion, we ask ourselves about the cause of motion.
Study the following attentively
The most important concepts in this chapter are:
Force

Inertial mass
Newton’s first law

Newton’s second law
Inertial frames

Newton’s third law
Study outcomes
After completion of this Study Unit you should be able to:
•
•
•
define and discuss the above-mentioned concepts and be able to derive and
apply them where applicable.
know what is meant by a force and its action.
know and apply Newton’s laws.
Study time
Contact sessions: 2 hours
Self-study: 4 hours
Important information
D What is Physics?
Read through.
12
Study unit 5
D Newtonian Mechanics:
Read through.
B Newton’s first law:
Memorise the law and take note that friction is negligible in this Chapter.
B Force:
A force is measured by the acceleration caused by it. It is thus also a vector quantity
and the unit is the newton (N).
Note that all vector calculations also hold for forces and that we always look at the
resultant force on a body. Note that all the vector calculations are also true for forces
and that we always work with the resultant force on a body. Thus Newton’s first law may
be re formulated. What is an inertial frame? This is important in mechanics. See that you
understand the discussion of figure 5.2.
Do Checkpoint 1 as revision of vectors.
D Mass:
Mass is an intrinsic property of matter. Work through this.
b Newton’s second law:
Memorise the law in words as well as the mathematical expression (equation 5.1).
You must understand the fact that this law is also true for the components of forces and
that the component equations are independent.
Do the two Sample Problems and Checkpoint 2.
B Some particular forces:
(1) Gravitational force: The force of attraction of the earth on a body with mass m.
(2) Weight: The magnitude of the gravitational force on a body. – How do we measure
weight? – It is not the mass of the body.
(3) Normal force: When an object rests on a surface, the normal force equals the
magnitude of the weight and acts in opposite direction. Checkpoint 3 is important.
(4) Friction: Is a force that opposes motion.
(5) Tension: Study figure 5.9 and its description where the tension is the magnitude of
the force on the body.
Checkpoint 4 is important.
B Newton’s third law:
13
Study Unit 5
Work through. Make sure that you understand the law and that you know it in words and
mathematically. Figures 5.10 and 5.11 as well as Checkpoint 5 are important.
B Applying Newton’s laws:
The first Sample Problem will be done in class. Work through the other Sample Problems
Reflection
Review and Summary
Individual activity
Homework:
14, 38, 64
14
Study unit 6
Study unit 6
FORCE AND MOTION II
Study material
This Study Unit consists of Chapter 6 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Static friction
Drag force and terminal speed
Kinetic friction
Uniform circular motion
Coefficient of static friction
Centripetal acceleration
Coefficient of kinetic friction
Study outcomes
After completion of this Study Unit you should be able to:
•
define and discuss the above-mentioned concepts and be able to apply them in
simple calculations.
•
realise that we come closer to reality by the discussion of friction.
•
know how to determine friction and understand its connection with the normal
force and the weight of a body.
Study time
Contact sessions: 2 hours
Self-study: 4 hours
15
Study Unit 6
Important information
D What is Physics?
Read through.
B Friction:
Figure 6.1 and its discussion are important to understand friction (static and kinetic) and
how it influences motion.
Work through the part that describes the microscopic cause of friction.
C Properties of friction:
You must know the properties of friction and equations 6.1 and 6.2 as well as the
connection between the coefficient of static and kinetic friction.
Do Checkpoint 1 as well as the two Sample Problems
D Drag force and terminal speed:
Read through. You must know the meaning of drag force and terminal speed. Omit the
Sample Problem
E Uniform circular motion:
See Chapter 4 and consider the different types of circular motion. Read through and omit
the Sample Problems. Do Checkpoint 2.
Reflection
Review and Summary
Individual activity
Homework:
20, 23, 28
16
Study unit 7
Study unit 7
KINETIC ENERGY AND WORK
Study material
This Study Unit consists of Chapter 7 in the textbook. It is sometimes difficult to
describe motion in terms of vector quantities. We therefore develop a scalar theory in
this chapter and the following chapters to simplify those cases.
Study the following attentively
The most important concepts in this chapter are:
Kinetic energy
Work done by a variable force
Work
Work done by a spring force
Work-kinetic energy theorem
Power
Work done by Gravity
Study outcomes
After completion of this Study Unit you should be able to
•
•
•
•
define and discuss the above-mentioned concepts and be able to derive and
apply them where applicable.
ensure yourself that you thoroughly understand the alternative description of
motion.
master the core concepts Work and Kinetic energy.
know and apply the Work-kinetic energy theorem.
:Study time
Contact sessions: 2 hours
Self-study: 4 hours
Important information
D What is Physics?
Read through.
17
Study Unit 7
D What is Energy?
Read through.
A Kinetic Energy:
This is a new concept with lots of meanings. It is a scalar quantity that simplifies the study
of motion. In this chapter we will concentrate on kinetic energy (K), which depends on
the state of motion of a system (see the definition in equation7.1).
The unit is the joule (J) – see equation 7.2.
Read the Sample Problem.
A Work:
If the state of motion of a system changes, it accelerates and according to Chapter 5 a
force then acts on it. We say then that work was done on the system by the force that
caused the change in the state of the motion. Work and energy are thus closely related.
A Work and kinetic energy:
(1) An expression for work:
Derivation 3: Derive equation 7.8 from equation 7.3.
Thus work depends on the displacement of a system and the force component in the
direction of the displacement.
When is the work done positive and when negative?
What is the unit of work (see equation 7.8)?
(2) The work-kinetic energy theorem: Equation 7.10 and 7.11 are very important, but
is just another notation for equation 7.5.
Do Checkpoint 1 as well as the two Sample Problems.
B Work done by a Gravitational force:
Only equation 7.12 is important.
Work through the rest of the paragraph. This will give you the necessary exercise in the
work of §7.5.
Do the first Sample Problem.
B Work done by a spring force:
You must understand figure 7.10 (7.9 in the 9th edition) to understand Hooke’s law
(equation 7.21). This force is thus a variable force (non uniform).
Derivation 4: Work done by the spring force (equation 7.25)
18
Study unit 7
Do the Sample Problem as well as Checkpoint 2.
A Work done by a variable force
Make sure that you understand the General concepts of integration on this page very
clearly – especially the transformation of equation 7.29 to equation 7.32.
You will find the integrals on page A11.
Omit the rest of this paragraph.
b
Power:
This is an important quantity that is used very often to describe energy consumption.
This is thus the rate at which work is done.
There are different units for power, but we use the watt (W).
Make sure that you remember equations 7.43 and 7.48 to use later on.
Reflection
Review and Summary
Individual activity
Homework:
3, 15, 37, 41, 46
19
Study Unit 8
Study unit 8
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
Study material
This Study Unit consists of Chapter 8 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Potential energy
Elastic potential energy
conservative force
Conservation of mechanical energy
Work-potential energy theorem
Work done by an external force
Gravitational potential energy
Dissipative force
Path independence of
conservative forces

Law of conservation of energy
Study outcomes
After completion of this Study Unit you should be able to:
•
•
define and discuss the above-mentioned concepts and be able to derive and
apply them where applicable.
know and apply the work-energy theorems and laws of conservation.
Study time
Contact sessions: 2 hours
Self-study: 4 hours
Important information
D What is Physics?
20
Study unit 8
Read through.
B Work and Potential energy:
Most bodies have the potential to do work. There are multiple reasons for this. The
concept “potential energy” (U) together with kinetic energy forms a powerful whole to
describe the motion of bodies.
The example in figure 8.2 and its discussion are important. Take note of equation 8.1.
Make sure that you know what a conservative force is – it simplifies lots of problems.
C Path independence of conservative forces:
When is a force a conservative force? The two arrows and figure 8.4 are important. Omit
the proof.
Do Checkpoint 1
Do the Sample Problem.
B Determining potential energy values:
Derivation 5: Expressions for Gravitational potential energy and elastic potential energy.
A body has gravitational potential energy because of its position that means because it
is on a distance away from the earth.
A spring has elastic potential energy because of its deformation, in other words because
it is stretched or compressed.
Do the Sample Problem and Checkpoint 2.
B Conservation of mechanical energy:
The definition of mechanical- or total energy (equation 8.12) is very important.
Derivation 6: Conservation of mechanical energy (equation 8.17).
The part from equation 8.17 to the bottom of the page, as well as figure 8.7 with its
description is very important.
Do Checkpoint 3 and the Sample Problem.
C Reading a potential energy curve:
Equation 8.22 will be used very often.
You must be able to interpret the potential energy curve in figure 8.9.
Read the part about turning points and equilibrium points – this will help you with the
problem solving.
Do Checkpoint 4.
B Work done on a system by an external force:
Read thoroughly about the connection between work and energy.
The work-energy concept (equation 8.26) is very important.
21
Study Unit 8
Note the part about friction, but omit Checkpoint 5. It is important to note that when
conservative and non-conservative forces (e.g. friction) act on an object and thus do
work, then the work-kinetic energy theorem (in Chapter 7) can still be used. The
conservation of mechanical energy does not hold here anymore.
Do the Sample problem.
D Conservation of energy:
Read thoroughly – this gives us a good insight in the discussed conservation laws.
Do the Sample Problem. Again have a look at the previous paragraph about what to do
if friction is involved.
Reflection
Review and Summary
Individual activity
Homework:
2, 27, 33, 54, 60
22
Study unit 9
Study unit 9
CENTRE OF MASS AND LINEAR MOMENTUM
Study material
This Study Unit consists of Chapter 9 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Centre of mass
Linear momentum


Linear momentum for a system of
particles
Newton’s second law in terms of 
momentum
Law of conservation
momentum
Collisions
Elastic collisions
Impulse
Inelastic collisions
The Impulse-momentum theorem
Collisions in two dimensions
of
Linear
Law of conservation of momentum
during collisions
Study outcomes
After completion of this Study Unit you should be able to:
•
•
•
•
•
define and discuss the above-mentioned concepts and be able to apply them
where applicable.
know how to handle systems of particles.
master the important concept of momentum as well as the law of conservation
that goes with it.
know what collisions are and how we handle it together with the conservation
laws.
know that the concept impulse and its connection with momentum are important
to describe collisions.
23
Study Unit 9
Study time
Contact sessions: 2 hours
Self-study: 4 hours
Important information
D What is Physics?
Read through and make sure that you understand figure 9.1.
C Centre of mass:
Systems of particles – make sure you understand this concept.
Omit the part on solid bodies as well as Checkpoint 1 and the two Sample Problems.
D Newton’s second law for a system of particles:
Work through – it is identical to that of a single particle.
A Linear momentum I:
This is a very important concept – make sure that you know the definition (equation 9.22).
Newton’s second law in terms of momentum will be used very often.
Ensure that you understand Checkpoint 3.
D Linear momentum of a system of particles:
Equation 9.25 and the definition in words are important.
A Collision and Impulse:
You have to master this new concept “impulse”. (To do so, you must understand figure
9.9).
It is important to remember the connection between momentum and impulse (equation
9.31) – also that it is actually three independent equations. The Sample Problem is for
self-study.
Omit ‘Series of collisions’. Do Checkpoints 4 and 5.
A Conservation of linear momentum:
An important and usable theorem. Make sure that you know the conservation of
momentum (equation 9.42) in words. Do Checkpoint 6 and the Sample Problems.
B Momentum and kinetic energy in collisions:
24
Study unit 9
Important approaches in the handling of collisions. Make quite sure that you can
distinguish between elastic and inelastic collisions. Also make certain that you know the
conservations during the different type of collisions.
C Inelastic collisions in one dimension:
Make use of the approach definition to write down equation 9.50.
The equation may be simplified for stuck-together bodies.
The motion of the centre of mass; figure 9.16 is important.
Do the Sample Problem.
C Elastic collisions in one dimension:
What is the approach for elastic collisions?
Derivation 7: Derive equations 9.67 and 9.68.
You must know the three special situations.
‘Moving Target’: read through.
Do the Sample Problem and Checkpoint 8.
E Collisions in two dimensions:
This is an extension of the previous paragraphs. Read through.
An example will be done in class.
C Rockets:
Another example will be done in class.
Reflection
Review and Summary
Individual activity
Homework:
22, 24, 35, 49, 51
25
Study Unit 10
Study unit 10
ROTATION
Study material
This Study Unit consists of Chapter 10 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Translation and rotation
Constant angular acceleration
Angular position
Relation between linear and angular
variables
Angular displacement
Average angular velocity
Kinetic energy of rotation
Instantaneous angular velocity
Moment of inertia
Average angular acceleration
Torque
Instantaneous angular
acceleration
Study outcomes
After completion of this Study Unit you should be able to:
•
•
define and discuss the above-mentioned concepts and be able to apply them
where applicable.
know which variables to use in the description of rotation and what their
equivalents in rectilinear motion are.
Study time
Contact sessions: 2 hours
Self-study: 4 hours
26
Study Unit 10
Important information
D What is Physics?
Read through.
A Rotation variables:
We consider the rotation of a rigid body about a fixed axis...
- Angular position (equation 10.1) measured in radians (equations 10.2 and 10.3). (Also
see figure 10.3).
- Angular displacement (equation 10.4) also in radians. The sign rule is important.
- Angular velocity (equation 10.6) in rad/s. It is the same for the whole body although
the speed is different.
- Angular acceleration (equation 10.8) and its unit.
Do the first Sample Problem and Checkpoint 1.
D Are angular quantities vectors?
Very strange properties.
D Rotation with constant angular acceleration:
Take note of Table 10.1. It shows that the equations of motion for pure rotation are
similar to those for linear motion in a straight line.
Do Checkpoint 2.
Do the two Sample Problems.
B Relating the linear and angular variables:
Derivation 8.
Important paragraph that connect the linear variables to the angular variables. Make
certain that you know, understand and are able to derive (prove) and use equations
10.17, 10.18, 10.22 and 10.23.
Do Checkpoint 3.
b Kinetic energy of rotation:
Understand the concept of rotational inertia (equation 10.33) – it replaces mass in
rotational motion.
Derivation 9: The kinetic energy of a rotating body.
Do Checkpoint 4.
D Calculating the rotational inertia:
27
Study Unit 10
A Torque:
read together with §11.4 (§11.6 in 9th edition)
Torque plays the role of force in rotational motion. This is the first time that we use the
vector product to define a quantity (equations 10.39 and 11.14).
Line of action and momentum are handy concepts which are also used in the practicals.
The unit is newton-metre (which is also the unit for work done – do not confuse the two).
Do Checkpoint 6.
E Newton’s second law for rotation:
Equation 10.42 is the rotation equivalent.
E Work and rotation kinetic energy:
Read through.
Reflection
Review and Summary
Individual activity
Homework:
4, 10, 23
28
Study Unit 11
Study unit 11
ROLLING, TORQUE ANDANGULAR MOMENTUM
Study material
This Study Unit consists of Chapter 11 in the textbook.
Study the following attentively
The most important concepts in this chapter are:

Rolling
Angular momentum
Newton’s second law in angular 
form
Law of conservation of angular
momentum
Study outcomes
After completion of this Study Unit you should be able to:
•
•
define and discuss the above-mentioned concepts and be able to apply them
where applicable.
be familiar with these rotation equivalents of the linear variables.
Study time
Contact sessions: 1 hour
Self-study: 2 hours
29
Study Unit 11
Important information
D What is Physics?
Read through.
D Rolling:
Rolling is a combination of rotation and translational motion.
D The kinetic energy of rolling:
Read through.
E The forces of rolling:
Omit
E The yo-yo:
Omit, but very interesting to read through.
A Torque:
Read with §10.6 (§10.8 in 9th edition).
Equation 11.14 and figure 11.10 are important.
Do the Sample Problem and Checkpoint 3.
A Angular momentum:
Another important quantity for rotation; it is equivalent to momentum in linear motion. It
is defined by equation 11.18 and figure 11.12.
Make sure that you also know the unit.
The meaning of the direction of the angular momentum is important.
Do Checkpoint 4 and the Sample Problem.
D Newton’s second law in angular form:
The vector sum of all the torques on a particle equals the rate of change of the angular
momentum of the particle.
D The angular momentum of a system of particles:
The angular momentum L of a system of particles is the vector sum of the angular
momentum of the individual particles.
C The angular momentum of a rigid body:
30
Study Unit 11
The component of the angular momentum parallel to the rotation-axis of a rigid body that
rotates about a fixed axis is given by L = Iω .
Table 11.1 is handy to use. Do Checkpoint 6
A Conservation of angular momentum:
This is again the rotational equivalent of the linear motion.
The examples with the figures from 11.16 to 11.20 are very interesting and incredible
implications of the law of conservation.
D Precession of a Gyroscope:
Read through.
Reflection
Review and Summary
Individual activity
Homework:
21, 46
31
Study Unit 12
Study division C: Statics
Study unit 12
EQUILIBRIUM
Study material
This Study Unit consists of Chapter 12 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Static-and dynamic equilibrium
Requirements of equilibrium
Stable-, unstableequilibrium
Centre of gravity
and
neutral
Study outcomes
After completion of this Study Unit you should be able to:
•
•
define and discuss the above-mentioned concepts and be able to apply them
where applicable.
know the requirements of equilibrium and be able to apply it.
Study time
Contact sessions: 3 hours
Self-study: 6 hours
Important information
D What is Physics?
Read through.
D Equilibrium:
32
Study Unit 12
Read through attentively – this is a summary of what is done already.
A Requirements of equilibrium:
You must know the whole paragraph and be able to apply it.
Do Checkpoint 1.
D Centre of gravity:
This will be done completely in the practicals. Take note that it is in most cases the body’s
centre of gravity is coincident with the body’s centre of mass.
Omit the derivation and Checkpoint 2.
A Examples of static equilibrium:
Do the Sample Problems. Some will be done in class.
E Indeterminate structures:
Read through.
C Elasticity:
Reflection
Review and Summary
Individual activity
Homework:
3, 4, 12 (10th edition)
10, 28, 12 (9th edition)
33
Study Unit 13
Study unit 13
GRAVITATION
Study material
This Study Unit consists of Chapter 13 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Force of gravity

Newton’s law of Gravitation
Study outcomes
After completion of this Study Unit you should be able to
•
•
define and discuss the above-mentioned concept and law and be able to apply
them where applicable.
know the law of Gravitation and be able to apply it.
Study time
Contact sessions: 1 hour
Self-study: 2 hours
Important information
D What is Physics?
Read through.
A Newton’s law of Gravitation:
You must know the law and be able to apply it.
D Gravitation and the principle of superposition:
Read through.
34
Study Unit 13
D Gravitation near the Earth’s surface:
Important to take note of.
D Gravitation inside the Earth:
Same as previous paragraph.
E Gravitational potential energy:
Already done.
E Kepler’s laws:
For those who are interested – the principles that controls the motion of planets.
E Satellites:
Read through.
E Einstein and gravitation:
Read through this – especially if you are going to study Physics further.
Reflection
Review and Summary
Individual activity
Homework:
18 (10th edition)
11 (9th edition)
35
Study Unit 14
Study division D: Hydrostatics and
hydrodynamics
Study unit 14
FLUIDS
Study material
This Study Unit consists of Chapter 14 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Fluid

Pascal’s principle
Density

Archimedes’ principle
Pressure, absolute pressure, gauge pressure

Equation of continuity
Manometer

Bernoulli’s equation
Study outcomes
After completion of this Study Unit you should be able to:
•
•
Define and discuss the above-mentioned concept and law and be able to apply
them in simple calculations.
Analyze fluids in motion by

derive and apply the Equation of continuity

derive and apply Bernoulli’s equation
Study time
Contact sessions: 4 hours
Self-study: 8 hours
36
Study Unit 14
Important information
D What is Physics?
Read through.
A What is a fluid?
Read through. You must know what a fluid is.
A Density and pressure:
Know the definitions for density and pressure.
Work through the Sample Problem.
A Fluids at rest:
The pressure at a point in a fluid in static equilibrium depends on the depth of that point
but not on any horizontal dimension of the fluid or its container.
Derivation 10: Determine an equation for the pressure at a point in a fluid as a
function of depth.
Do Checkpoint 1 and the two Sample Problems.
A Measuring Pressure:
Know the operation of a mercury barometer and an open-tube manometer.
A Pascal’s principle: Derivation 11
You most know Pascal’s principle and its derivation. Also see the application of the
hydraulic lever. Can you think about some other applications?
A Archimedes’ principle:
Make sure that you know and understand Archimedes’ principle and that you are able to
apply it. Do Checkpoint 2 and the Sample Problem.
A Ideal fluids in motion:
Know the properties of an ideal fluid.
A The Equation of continuity: Derivation 12
The Equation of continuity is an important concept; you must know its derivation and
applications. It is also an example of a conservation law.
Do Checkpoint 3 and the Sample Problem.
37
Study Unit 14
A Bernoulli’s equation: Derivation 13
You must know Bernoulli’s equation and be able to derive and apply it. The Equation of
continuity is about the conservation of matter in a liquid, but Bernoulli’s equation is about
the conservation of energy in liquids.
Do Checkpoint 4 and the two Sample Problems.
Reflection
Review and summary
Individual activity
Homework:
11, 15, 37, 53, 67 (10th edition)
10, 2, 58, 53, 33 (9th edition)
38
Study Unit 15
Study division E:
Periodic motion and waves
Study unit 15
OSCILLATIONS
Study material
This Study Unit consists of Chapter 15 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Free oscillations
Phase angle
SHM
Angular frequency
Frequency
Pendulum
Period
Damping
Amplitude
Forced oscillations
Phase
Resonance
Study outcomes
After completion of this Study Unit you should be able to:
•
•
•
•
define, discuss and derive this kind of motion and the above-mentioned concepts
and be able to apply it in simple calculations.
know where oscillations occur in nature
explain oscillations mathematically
solve simple problems on oscillations
Study time
Contact sessions: 2 hours
Self-study: 4 hours
39
Study Unit 15
Important information
D What is Physics?
Read through. Here you get a brief scope about the occurrence of oscillations in
everyday life. This kind of motion forms the base of a variety of phenomena.
A Simple harmonic Motion
As in lots of other cases in Physics, we use the simplest case to describe a natural
phenomenon mathematically. Simple harmonic Motion (SHM) is the simplest case in the
study of oscillations. The following important definitions concerning SHM are given in this
section:
Frequency
Period
Amplitude
Phase
Phase angle
Angular frequency
Make sure that you understand these definitions. The mathematical expression for a
SHM is very important. It is given by equation15-3:
x(t) = xm cos (ωt + φ)
and the symbols are explained in Figure 15-3 (15-2 in 9th edition). Figure 15-5 (15-3 in
9th edition) is a plot of x versus t. Do Checkpoint 1.
B The Force law: Derivation 14
Work through. Note the negative sign in equation 15-10 which indicates that the direction
of the restoring force is opposite to the direction of the displacement. Work through the
two Sample Problems, Checkpoint 2 (this one is not in the 9th edition) and Checkpoint 3
(Checkpoint 2 in 9th edition).
c Energy in SHM: Derivation 15
Like with all mechanical motion, the total energy is the sum of the potential energy and
the kinetic energy. See whether you can prove that the energy of a SHM is constant and
depends only on k and (amplitude)2. Refer back to Chapter 8 in order to understand the
origin of the relation for potential energy. Do Checkpoint 4 (Checkpoint 3 in 9th edition)
and the Sample Problem.
E Angular SHM:
Read Through.
C Pendulums: (Period of a pendulum)
We will only study the simple harmonic pendulum.
40
Study Unit 15
C 15.7 SHM and Uniform Circular motion:
SHM is the projection of uniform circular motion on a diameter of the circle in which the
circular motion occurs. Example: Jupiter’s moons.
E Damped SHM:
Motion is always damped by forces. This is thus closer to the truth than the models we
studied. Read through.
D Forced oscillations and Resonance:
This is one of the most general phenomena in nature and in industry. Make sure that
you know what resonance is.
Make a list of resonance phenomena.
Reflection
Review and Summary
Study time
Homework:
5, 13, 20, 42 (10th edition)
13, 33, 30, 2 (9th edition)
41
Study Unit 16
Study unit 16
WAVES
Study material
This Study Unit consists of Chapter 16 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Waves
Wave number
Transverse waves
Period
Longitudinal waves
Speed of a travelling wave
Wave length
Energy and Power
Frequency and angular frequency
Principle of Superposition
Amplitude
Standing waves
Phase
Resonance
Study outcomes
After completion of this Study Unit you should be able to:
•
•
•
•
•
•
•
42
define, discuss and derive the above-mentioned concepts and be able to apply
it in simple calculations.
know what waves are and how to handle it.
know the difference and similarities between oscillations and waves.
know where waves occur in nature.
distinguish between longitudinal and transverse waves.
describe waves mathematically
solve simple problems about waves.
Study Unit 16
Study time
Contact sessions: 2 hours
Self-study: 4 hours
Important information
D What is Physics?
Read through
D Types of waves:
Tale note of examples of mechanical waves, electromagnetic waves and matter waves.
B Transverse and longitudinal waves:
Make sure that you are able to define the two types (longitudinal and transverse) and
that you know examples of each. Water waves are transverse waves and sound waves
are longitudinal.
A Wavelength and frequency:
The basic description of waves is given here. Know the difference between a wave and
an oscillation. Their mathematical explanation is very similar. In the case of an oscillator
it is only necessary to describe the displacement in terms of the rest position. The latter
is also true for a wave, but also how this displacement propagates through space, for
example in the x–direction.
Make sure that you know the meaning of each of the following concepts:- amplitude,
phase, wavelength, wave number, period, frequency and angular frequency.
The wave equation 16.2 and figures 16.3 and 16.4 are important.
- Amplitude and phase are as for oscillations
- Wavelength and wave number typify the spatial aspect of the wave.
- Period, frequency and angular frequency typify the time aspect of the wave.
Do Checkpoint1.
A The speed of a travelling wave:
Derivation 16: derive equation 16.13.
Make sure how to determine the direction of motion of a wave.
Do Checkpoint 2.
E Wave speed on a stretched string:
Read through.
43
Study Unit 16
e Energy and power:
Read through.
E The wave equation:
A Principle of Superposition:
A simple but cogent principle that is used very often and formulated as follows:
Overlapping waves algebraically add to produce a resultant wave. Overlapping waves
do not in any way alter the travel of each other.
A Interference:
The interaction between waves is illustrated in this paragraph. Interference of waves is
a result of the principle of superposition. The superposition of waves is mathematically
very simple and makes use of known trigonometric relations. You must understand
concepts like phase; constructive interference and destructive interference and also
know the conditions for both to take place.
Derivation 17: Derive equation 16.51 and understand figure 16.14 (16.13 in the 9th
edition).
See Table 16.1.
E Phasors:
This is used in advanced work. Read through.
D Standing waves:
Very interesting application. Standing waves are a special case of superposition of
waves that are moving in opposite directions, like waves on a string. The outstanding
feature of the resultant standing waves is that there are places along the string where
the string never moves. Remember that the two waves that are moving in opposite
directions are still present. The standing wave is the resultant of the superposition of the
two waves. If any one of the two waves does not exist anymore, so be the standing wave.
D Standing waves and Resonance:
Very interesting application. This is about standing waves in a string being made to
oscillate by an oscillator at the one end.
Reflection
Review and Summary
Individuele aktiwiteit
Homework:
13, 31, 42 (10th edition)
5, 13, 10 (9th edition)
44
Study Unit 17
Study unit 17
WAVES II
Study material
This Study Unit consists of Chapter 17 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Displacement Amplitude
Intensity
Pressure amplitude
Decibel
Interference
Beats
Wave front
Sound level
Longitudinal waves
Doppler effect
Path length difference
Mach cone and Mach number
Study outcomes
After completion of this Study Unit you should be able to:
•
•
•
•
•
define and know the above concepts.
use the decibel scale with confidence.
describe the superposition of waves mathematically and to determine the end
result of such a superposition.
describe and know the importance of the Doppler effect.
solve simple problems.
Study time
Contact sessions: 2 hours
Self-study: 4 hour
45
Study Unit 17
Important information
D What is Physics?
Read through
B Sound waves:
In this chapter we pay attention to longitudinal waves. Sound waves have important
medical applications, for example in sonar en physiotherapy treatments. Sound waves
are not limited to the earth. They play an important role in outer space in the so called
molecular clouds, in supernova explosions etc.
B The speed of sound:
Speed of a mechanical wave (transversal or longitudinal) depends on the inertial
properties of the medium (to store kinetic energy), and the elastic properties (to store
potential energy) of the medium.
B Travelling sound waves:
Like in the case of a transverse wave; it is not the medium that propagates although the
medium does oscillate in the direction of propagation. It is only the disturbance that
moves through the medium.
B Interference:
Sound waves undergo interference. Know the conditions for constructive and destructive
interference.
B Intensity and sound level:
Know the definitions of intensity and sound level. Work through Checkpoint 2.
E Sources of musical sound:
Read through.
B Beats: Derivation 18
If sounds of two different frequencies reach our ears simultaneously, then we hear a
sound whose frequency is the average of the two combining frequencies. We also hear
a striking variation in the intensity of this sound; this is called beats.
A The Doppler effect: Derivation 19
The Doppler effect plays an important role, not only in the case of sound waves, but also
for transverse waves like electromagnetic waves. Equation 17-47 and its derivation are
important.
46
Study Unit 17
B Supersonic speeds, shock waves:
Make sure that you know what a Mach number is.
Reflection
Review and Summary
Individual activity
Homework:
32, 29, 46 (10th edition)
28, 57, 56 (9th edition)
47
Study Unit 18
Study division F: Study of heat
Study unit 18
TEMPERATURE, HEAT AND THE FIRST LAW OF
THERMODYNAMICS
Study material
This Study Unit consists of Chapter 18 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Thermodynamics
Heat capacity
Temperature
Heat and work
Triple point
Phase changes
Constant volume gas
thermometer
Heat transfer
Thermal expansion

Thermodynamic transformations
and the first law of thermodynamics
Study outcomes
After completion of this Study Unit you should be able to:
•
•
•
•
•
•
•
•
48
know and define the above concepts.
explain what is meant by “temperature”.
formulate the Zeroth Law of thermodynamics and be able to apply it.
explain what is “heat” and the relation between heat and temperature.
formulate the relation between heat and work and be able to apply it.
apply the First law of Thermodynamics.
represent a thermodynamic transformation on a PV diagram.
do a variety of problems and applications on thermodynamics.
Study Unit 18
Study time
Contact sessions: 2 hours
Self-study: 4 hour
Important information
D What is Physics?
A few examples of thermodynamics in everyday life are given here. Read through.
A Temperature:
What is temperature? We normally use this word very easily, but do we really know what
we are talking about? By touching two objects, we can say the one is hotter than the
other one. This is very subjective and sometimes wrong. It is important to use the correct
definition for temperature.
A The Zeroth Law of Thermodynamics:
Know the law.
C Measuring Temperature:
A reference temperature is firstly defined in this paragraph and the concept of thermal
equilibrium is used then to describe the constant-volume gas thermometer. You must be
able to explain the operation of the constant-volume gas thermometer.
D Die Celsius and Fahrenheit Scales:
Take note of this paragraph because it may be applicable in the problems. In SA we
normally do not use the Fahrenheit scale any more. It is still used in the USA for the
maximum and minimum day temperatures.
C Thermal Expansion:
Make sure that you understand the definitions of the coefficients of linear and volume
expansion.
B Temperature and Heat:
Heat is the energy transferred between a system and its environment because of a
temperature difference that exists between them.
B The absorption of heat by solids and liquids:
As seen before, temperature differences between bodies in thermal contact lead to heat
transfer. This section deals with the calculation of heat transfer and is thus important. Do
Checkpoint 3.
49
Study Unit 18
A Heat and Work:
A proper understanding of this section is important for the work that follows. Do
Checkpoint 4.
A The First Law of Thermodynamics:
Know the law and work through Checkpoint 5.
B Special cases of the First Law of Thermodynamics:
Know the four different thermodynamic processes in table 18.5.
C Heat Transfer Mechanisms:
The mechanism of heat transfer is discussed here, namely: conduction, convection and
radiation.
Reflection
Review and Summary
Individual activity
Homework:
61, 58, 4, 25, 40 (10th edition)
9, 28, 22, 45, 48 (9th edition)
50
Study Unit 19
Study unit 19
THE KINETIC THEORY OF GASES
Study material
This Study Unit consists of Chapter 19 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Avogadro’s number
Equation of state
Ideal gas
rms speed
Universal gas constant
Study outcomes
After completion of this Study Unit you should be able to:
•
•
understand and define the above concepts.
do a variety of problems and applications of the kinetic gas theory.
Study time
Contact sessions: 2 hours
Self-study: 4 hour
Important information
D What is Physics?
This chapter relates the motion of atoms of a gas with the volume, pressure and
temperature. Read through
51
Study Unit 19
A Avogadro’s number:
One mole of a substance contains Avogadro’s number elementary particles.
A Ideal gases:
Know the law. Do the first Sample Problem and Checkpoint 1.
C Pressure, temperature and rms speed:
The pressure exerted by n mole of an ideal gas is given here in terms of the speed of its
molecules.
C Translational Kinetic energy:
The average translational kinetic energy of a gas particle (atom or molecule) is given in
terms of the macroscopic temperature, namely:
K gem =
3
kT
2 .
E Mean Free path:
Read through.
E The Distribution of molecular speeds:
Read through.
C The Molar Specific Heats of an Ideal Gas:
See notes.
E egrees of Freedom and Molar Specific Heats:
Read through.
E
A Hint of Quantum Theory:
Read through.
C The Adiabatic Expansion of an Ideal Gas:
Adiabatic transformations (this is where Q = 0) are very important in lots of classic
thermodynamic applications. Note in Figure 19-15; an adiabatic transformation is not
isothermal and that an isothermal transformation is not adiabatic. The curve describing
an adiabatic transformation on a pV- diagram is given by equation 19-53 and does not
follow directly from the equation of state of an ideal gas.
52
Study Unit 19
Reflection
Review and Summary
Study time
Homework:
54, 40, 57 (10th edition)
4, 10, 7 (9th edition)
53
Study Unit 20
Study unit 20
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
Study material
This Study Unit consists of Chapter 20 in the textbook.
Study the following attentively
The most important concepts in this chapter are:
Irreversible transformations
Entropy

Second law of Thermodynamics
Efficiency of engines
Study outcomes
After completion of this Study Unit you should be able to:
•
understand and define the above concepts and be able to apply it in simple
calculations.
Study time
Contact sessions: 2 hours
Self-study: 4 hours
Important information
D What is Physics?
Read through
Irreversible Processes and Entropy:
Some transformations take place in one direction only and are called irreversible
processes. Know the difference between reversible and irreversible processes. Note
that only isothermal and adiabatic processes are reversible. This paragraph discusses
these transformations and brings in the concept of “entropy”.
54
Study Unit 20
When an irreversible transformation takes place in a closed system, the entropy of the
system will always increase, never decrease.
A Change in Entropy:
The change in entropy is defined in equation 20-1.
A Second Law of Thermodynamics:
In general it is found in practice that the entropy of a closed system will never decrease
during an irreversible process.
B Entropy in the Real World: Engines
The Carnot engine is important.
A heat engine extracts energy from its environment in the form of heat and does useful
work.
Figure 20-9 shows the pV-diagram of the cycle followed by the working substance (gas)
of the Carnot engine
Do the two Sample Problems.
D Entropy in the Real World: Refrigerators
D Die Efficiencies of Real Engines:
You must know the definition and be able to apply it.
D A Statistical View of Entropy:
This section gives a simple introduction to the statistical view of entropy and also how
physical systems of particles are described in Statistical Mechanics.
Reflection
Review and Summary
Study time
Homework:
36, 46, 1, 43 (10th edition)
4, 6, 25, 27 (9th edition)
55
List of the most important key words
List of the most important key words
AFRIKAANS
56
ENGLISH
Afstand
Distance
Arbeid
Work
Arbeid-energiestelling
Work Energy Theorem
Behoud van energie
Conservation of energy
Behoud van momentum
Conservation of momentum
Bewegingsvergelykings
Equations of motion
Botsing
Collision
Digtheid
Density
Dinamika
Dynamics
Dotproduk (puntproduk)
Dot product
Druk
Pressure
Drywing
Power
Eenheidsvektore
Unit vectors
Elastiese botsing
Elastic collision
Elastiese herstelkrag
Elastic restoring force
Elastiese Potensiële energie
Elastic Potential energy
Ewewig
Equilibrium
Gewig
Weight
Gravitasiekrag
Force of Gravity
Gravitasie Potensiële energie
Gravitational Potential energy
Grootte en Rigting
Magnitude and Direction
Herstelkrag
Restoring force
Hoekmomentum,
hoekposisie,
hoeksnelheid
hoekverplasing,
hoekversnelling
Angular momentum,
angular position,
angular velocity,
angular displacement,
angular acceleration
Horisontale Afstand
Range
Impuls
Impulse
Inersiaalsisteem
Inertial frame
Kinematika
Kinematics
List of the most important key words
Kinetiese energie
Kinetic energy
Kinetiese Wrywing
Kinetic Friction
Kinetiese wrywingskoëffisiënt
Coefficient of kinetic friction
Komponente
Components
Konserwatiewe Krag
Conservative Force
Krag
Force
Kragveld
Force Field
Kruisproduk
Cross product
Massamiddelpunt
Centre of Mass
Meganiese energie
Mechanical energy
Momentum
Momentum
Nie-Elastiese botsing
Inelastic collision
Normaalkrag
Normal Force
Oombliklike snelheid,
oombliklike spoed en
oombliklike versnelling
Instantaneous velocity,
instantaneous speed, and
instantaneous acceleration
Oppervlakspanning
Surface Tension
Posisie
Position
Potensiële energie
Potential energy
Projektiel Beweging
Projectile Motion
Relatiewe Beweging
Relative Motion
Resultant
Resultant
Rotasie
Rotation
Sentripetale versnelling
Centripetal acceleration
Sirkelbeweging
Circular motion
Skalaar(produk)
Scalar(product)
Sleurkrag
Drag force
Snelheid
Velocity
Spankrag (Spanning)
Tension
Spoed
Speed
Statiese Wrywing
Static Friction
Statiese wrywingskoëffisiënt
coefficient of static friction
Swaartepunt
Centre of Gravity
Terminaalsnelheid /spoed
Terminal Velocity / speed
Traagheidsisteem
Inertial Frame of Reference
Traagheidsmassa
Inertial mass
57
List of the most important key words
Traagheidsmoment
Moment of inertia
Translasiebeweging
Translational motion
Uniforme sirkelbeweging
Uniform circular motion
Veerkrag
Spring force
Vektor(produk)
Vector(product)
Verplasing
Displacement
Versnelling
Acceleration
Vryval
Free Fall
Wringkrag
Torque
Wrywing
Friction
ENGLISH
58
AFRIKAANS
Acceleration
Versnelling
Angular acceleration,
angular displacement,
angular momentum,
angular position,
angular velocity
Hoekversnelling,
hoekverplasing
hoekmomentum,
hoekposisie,
hoeksnelheid
Centre of Gravity
Swaartepunt
Centre of Mass
Massamiddelpunt
Centripetal acceleration
Sentripetale versnelling
Circular motion
Sirkelbeweging
Coefficient of kinetic friction
Kinetiese wrywingskoëffisiënt
Coefficient of static friction
Statiese wrywingskoëffisiënt
Collision
Botsing
Components
Komponente
Conservation of energy
Behoud van energie
Conservation of momentum
Behoud van momentum
Conservative Force
Konserwatiewe Krag
Cross product
Kruisproduk
Density
Digtheid
Displacement
Verplasing
Distance
Afstand
Dot product
Dotproduk
Drag force
Sleurkrag
Dynamics
Dinamika
List of the most important key words
Elastic collision
Elastiese botsing
Elastic Potential energy
Elastiese Potensiële energie
Elastic restoring force
Elastiese herstelkrag
Equations of motion
Bewegingsvergelykings
Equilibrium
Ewewig
Force
Krag
Force Field
Kragveld
Force of Gravity
Gravitasiekrag
Free Fall
Vryval
Friction
Wrywing
Gravitational Potential energy
Gravitasie Potensiële energie
Impulse
Impuls
Inelastic collision
Nie-Elastiese botsing
Inertial frame
Inersiaalsisteem
Inertial Frame of Reference
Traagheidsisteem
Inertial mass
Traagheidsmassa
Instantaneous acceleration,
instantaneous speed, and
instantaneous velocity
Oombliklike versnelling,
oombliklike spoed en
oombliklike snelheid
Kinematics
Kinematika
Kinetic energy
Kinetiese energie
Kinetic Friction
Kinetiese Wrywing
Magnitude and Direction
Grootte en Rigting
Mechanical energy
Meganiese energie
Moment of inertia
Traagheidsmoment
Momentum
Momentum
Normal Force
Normaalkrag
Position
Posisie
Potential energy
Potensiële energie
Power
Drywing
Pressure
Druk
Projectile Motion
Projektiel Beweging
Range
Horisontale Afstand
Relative Motion
Relatiewe Beweging
Restoring force
Herstelkrag
Resultant
Resultant
59
List of the most important key words
60
Rotation
Rotasie
Scalar(product)
Skalaar(produk)
Speed
Spoed
Spring force
Veerkrag
Static Friction
Statiese Wrywing
Surface Tension
Oppervlakspanning
Tension
Spankrag (Spanning)
Terminal Velocity / speed
Terminaalsnelheid /spoed
Torque
Wringkrag
Translational motion
Translasiebeweging
Uniform circular motion
Uniforme sirkelbeweging
Unit vectors
Eenheidsvektore
Vector(product)
Vektor(produk)
Velocity
Snelheid
Weight
Gewig
Work
Arbeid
Work Energy Theorem
Arbeid-energiestelling
Multilingual key concepts
Meertalige kernkonsepte / Multilingual key
concepts / Dikakanyokgolo
Kernbegrip/Afrikaans
Kakanyokgolo ka
Setswana
Key-concept/English
1
Afstand
Distance
Sekgala
2
Arbeid
Work
Tiro
3
Arbeid-energiestelling
Work Energy Theorem
Tioreme ya TiroMaatla
4
Behoud van energie
Conservation of energy
Tshomarelo ya maatla
5
Behoud van momentum
Conservation of
momentum
Tshomarelo ya
momenthamo
6
Bewegingsvergelykings
Equations of motion
Ditekano tsa motsamao
7
Botsing
Collision
Thulano
8
Diffusie
Diffusion
Phasalalo
9
Digtheid
Density
Kitlano
10
Dinamika
Dynamics
Tinamiki
11
Dotproduk
Dot product
Katisi khutlo
12
Druk
Pressure
Kgatelelo
13
Drukverskil
Gauge Pressure
Selekanyi sa kgatelelo
14
Dryfkrag
Buoyant Force
Thata ya phaphamalo
15
Drywing
Power
Maatla-a-tiro
16
Eenheidsvektore
Unit vectors
Dibeketara nngwe
17
Effektiwiteit
Efficiency
Bokgoni
18
Elastiese botsing
Elastic collision
Ngaologo ya Thulano
19
Elastiese herstelkrag
Elastic restoring force
Thata ya pusetso ya
ngaologo
20
Elastiese Potensiële
energie
Elastic Potential energy
Ngaologo ya
Maatlakgonego
21
Ewewig
Equilibrium
Tekatekano
22
Gewig
Weight
Bokete
23
Gravitasiekrag
Force of Gravity
Maatlakgogedi
24
Gravitasie Potensiële
energie
Gravitational Potential
energy
Kgogedi ya
Maatlakgonego
25
Grootte en Rigting
Magnitude and Direction
Bokanakang le Ntlha
26
Herstelkrag
Restoring force
Thata pusetso
61
Multilingual key concepts
62
27
Hidrouliese Sisteem
Hydraulic System
Thulaganyo kgatelokedi
28
Hoekmomentum, -posisie,
-snelheid -verplasing, versnelling
Angular momentum, position, -velocity, displacement, acceleration
Momenthamo sekhutlo, kemo, -belosithi, sekgalantlha, -kelolebelo
29
Horisontale Afstand
Range
Renje
30
Impuls
Impulse
Imphalese
31
Inersiaalsisteem
Inertial frame
Kgatlha ya
kelolebelotshwano
32
Kinematika
Kinematics
Kinimatiki
33
Kinetiese energie
Kinetic energy
Maatlatsamao
34
Kinetiese Wrywing
Kinetic Friction
Kgotlhanotsamao
35
Kinetiese
wrywingskoëffisiënt
Coefficient of kinetic
friction
Khoefišente ya
kgotlhanotsamao
36
Komponente
Components
Dikarolo
37
Konserwatiewe Krag
Conservative Force
Thata e e khonsebetifi
38
Krag
Force
Thata
39
Kragveld
Force Field
Lefelo la thata
40
Kruisproduk
Cross product
Katiso kgaoganyo
41
Laminêre Vloei
Laminar Flow
Kelelo e e lamina
42
Massamiddelpunt
Centre of Mass
Ntlhagare ya Mmase
43
Meganiese energie
Mechanical energy
Maatla ka motšhini
44
Momentum
Momentum
Momenthamo
45
Nie-Elastiese botsing
Inelastic collision
Thulano e e ngaologeng
46
Normaalkrag
Normal Force
Thata Tlwaelo
47
Oombliklike snelheid, spoed en –versnelling
Instantaneous velocity, speed, and –acceleration
Belosithi pong, -lebelo, le kelelobelo
48
Oombliklike Versnelling
Instantaneous
Acceleration
Kelebelopong
49
Oppervlakspanning
Surface Tension
Kgagamalo Boalo
50
Posisie
Position
Kemo
51
Potensiële energie
Potential energy
Maatlakgonego
52
Projektiel Beweging
Projectile Motion
Motsamao wa
Sethunngwa
53
Relatiewe Beweging
Relative Motion
Motsamaomabapi
54
Resultant
Resultant
Sephethokopanyo
55
Rotasie
Rotation
Modikologo
Multilingual key concepts
56
Sentripetale versnelling
Centripetal acceleration
Kelolebelo go ya
ntlhagareng
57
Sirkelbeweging
Circular motion
Motsamaotshekeletsa
58
Skalaar(produk)
Scalar(product)
Sekalara (katisi)
59
Sleurkrag
Drag force
Thata ya kgogô
60
Snelheid
Velocity
Belosithi
61
Soortlike Gravitasie
Specific Gravity
Kgogedi e e rileng
62
Spankrag (Spanning)
Tension
Kgagamalo
63
Spoed
Speed
Lebelo
64
Statiese Wrywing
Static Friction
Kgotlhano-e-e-sa-suteng
65
Statiese
wrywingskoëffisiënt
coefficient of static friction
Khoefišente ya kgotlhano
e e sa suteng
66
Swaartepunt
Centre of Gravity
Ntlhagare ya
Maatlakgogedi
67
Terminaalsnelheid /spoed
Terminal Velocity / speed
Belosithi/lebelo le le
khutlang
68
Spoed
Uniform circular motion
Motsamaotshekeletsa o o
sa fetogeng
69
Veerkrag
Spring force
Thata ya seporeng
70
Vektor(produk)
Vector(product)
Beketara (katiswa)
71
Verplasing
Displacement
Sekgalantlha
72
Versnelling
Acceleration
Kelolebelo
73
Viskose Krag
Viscous Drag
Kgogô e e kgomarelang
74
Viskositeit
Viscosity
Go kgomarela
75
Vryval
Free Fall
Go wa ka kgololosego
76
Wringkrag
Torque
Maatlatikoloso
77
Wrywing
Friction
Kgotlhano
63