# WHAT IS 8.01?

8.01 is an introductory course in Classical Mechanics. Mechanics means that it deals with the motion of objects, how that motion changes with time, the conditions required to induce certain types of motion, etc. Classical Mechanics restricts us to circumstances where the speeds we encounter are small compared to the speed of light and the objects we deal with are generally of macroscopic size. Fortunately, almost any situation we are likely to meet in everyday life satisfies these restrictions, so the results of classical mechanics have a wide variety of applications in science and engineering. Furthermore, the most important principles of mechanics - the conservation laws for energy and momentum - can be fully explored within classical mechanics.

Why is 8.01 a required course for MIT students? There are three main reasons, one obvious and two more subtle.

• The contents of the course - the physical laws and principles you will learn, and the methods of applying them to practical problems - are important and relevant in many other fields. A civil engineer designing a bridge, an automobile designer laying out the specifications for the engine or the safety air-bag of a new model, a geologist estimating the likely severity of the next California earthquake: all are using, directly or indirectly, the principles of classical mechanics.
• The structure and development of classical mechanics is a good example of the aims and methods of scientific study. We shall see how experimental results and mathematical representations are combined to create testable scientific theories, and how the impossible complexities of most real-life physical situations can be reduced to soluble problems by concentrating on the basic physical features of the system. This way of working is what distinguishes the scientific approach to situations from the many other ways of looking at them (e.g. artistic, political, business...).
• Because the same basic principles can be used in a wide variety of different applications, the study of classical mechanics is an excellent introduction to the art of problem solving. By the end of the course you should be able to extract the essential features of a problem, use them to set up and solve the appropriate mathematical equations, and make quick and easy checks on your answer to catch simple mistakes.

The course will have succeeded in its aims if you come away from it with a grasp of the basic principles governing the motion of objects, a feel for the scientific method, and an understanding of the techniques of problem solving.

## HOW DOES THE COURSE WORK?

This course is designed in a way which is rather different from most of the other high school and MIT courses you will have encountered. The basic idea is that you are in charge of your own learning, while we provide you with the help and resources you will need. In this way you have the opportunity to structure your studies so that you take maximum advantage of what you already know (from physics and math courses at your high school, for example) and concentrate your efforts on material that is new and difficult. We monitor your progress through weekly homework and quizzes which contribute to your final grade.

### Resources

Your main resource and the starting point for your week's work is the written Study Guide. Each study guide covers one week's work and contains

• a brief overview setting out the main themes of the week's work;
• a list of aims detailing exactly what you're expected to know by the end of the week;
• a detailed summary explaining what you need to know and giving cross-references to problems to try;
• a list of new ideas to help you decide what to concentrate on in your study;
• a set of problems and questions designed for self-testing and learning problem-solving skills.
Answers are given to all problems. In addition, some come with hints to help you get started, while others come with fully worked-out solutions to show you how to apply the ideas and equations in the summary to problem solving.

Furthermore, many study guides include some supplementary notes which discuss some aspects of the material in a wider context, for example how particular points relate to the real world or how they may be developed into more advanced concepts. You don't need to know this material to get a good grade, but it should provide a starting point if you are curious to see how the artificial-seeming problems you may be doing fit into the rest of physics.

The study guide is designed to be used with the course textbook. The textbook provides the detailed derivations and explanations of the results and formulae quoted in the study guide summary, as well as more worked examples and problems, problem-solving hints, etc. You should certainly buy this book as it contains material essential to the course.

Of course, you're not expected to struggle on alone with only the written word to help. Each week begins with an introductory lecture, given by the Course Examiner. This consists of demonstrations showing you real-life illustrations of the physical principles you will be learning that week, together with brief discussions of important aspects of the material. The Course Examiner is responsible for setting the weekly homework, quizzes, review tests and final exam, and for deciding your final grade, so you might view this lecture as a useful guide to the aspects of the material that he considers important!

There may be weeks when despite your best efforts and the help of all these resources, you still don't feel confident about some part of the work as the Friday morning quiz draws near. In this case you have a final line of defense: an optional two-hour tutorial session on Thursday evening. A number of class professors and graduate teaching assistants will be available to answer questions and help you with problems.

### Written Homework and Quizzes

Every week you will be asked to write up a few of the homework problems and perhaps the results of an experiment demonstrated in the lecture. These will be graded with particular attention paid to clarity and quality of the answers. In addition, your progress will be monitored by weekly quizzes held during the Friday morning class. Mostly, these will last 25 minutes and cover the work done that week. Three times in the semester there will be a 50-minute review quiz which will cover all the material since the last review quiz. The quizzes will account for as much as 55% of your final grade: see the section on Grading for more details.

## HOW TO USE A STUDY GUIDE

The key to success in this course is learning to use the study guides effectively. The material in the guides defines the course content from the point of view of the course examiner, so if you understand the contents of the guides you can be confident of a good grade. Furthermore, the structure of the guides is designed to help you organize your study so that you get through the work in as short a time as possible, while still learning the material effectively and thoroughly.

Each study guide consists of two different types of material. One type defines what you ought to know: this includes the overview, the checklists of aims and new ideas, and the summary. The second type applies this knowledge to problem solving: in this category are the questions, problems, hints, and solutions.

The two most important sections of the guide from an organizational point of view are the Aims checklist and the Summary. The Aims tell you what you are expected to know after completing the week's work: as you progress you should return to them at intervals to decide which you have already achieved and which you still need to work on.

The Summary is the heart of the guide and your main tool for organizing your study. Unless you feel you already understand all the concepts listed in the Aims checklist (in which case you can test your feeling by trying the problems), you will usually start your work by going to the Summary. Each paragraph is cross-referenced to problems in the guide related to the physics summarized in that paragraph.

If the Summary is the main tool for organizing your study, the crucial learning tool is the problem set. You haven't really understood a given topic until you can apply it in solving problems; conversely, the step-by-step process of setting up and solving a problem will often be of more help in grasping a complicated idea than reading an abstract theoretical explan-ation. For that reason, problems come in three varieties:

• S-type problems, which come with completely worked out solutions;
• H-type problems, which come with hints in the form of questions, and answers to these questions;
• problems with just the answer given.
By the time you finish the Summary, you should already have done all the problems which have no worked-out solutions. At this point you should check that you have really covered the whole of the material by going over the checklists of Aims and New Ideas. All the points in both checklists should now be familiar to you - if they aren't, go back to the Summary and try to find the bits you missed!

If you really get hung up on some particular point, try to decide exactly what is causing the trouble. If you think you understand the theory, but can't see how to apply it to a particular problem, pay particular attention to the worked examples (S-type problems). There are also examples in the textbook if the ones in the study guide don't seem to be providing much illumination. If, on the other hand, you can apply the equations mechanically to solve problems, but don't understand where they came from, make sure you have read the textbook, as the Summary itself may not provide much detail. In either case, enlist the help of your class professor, and if necessary drop in to the Thursday tutorial session.

Using this strategy (which is summarized in the flowchart on this page), you should be able to learn the material quickly and effectively. Most weeks you probably won't have to do or study the solution to every problem, though it's a good idea to do at least one problem covering a given topic.

In conclusion, the main things to remember about the study guides are that they define the content of the course, so all quizzes and exams are based on them, that you should work your way outwards from the Summary rather than trying to read the whole thing like a textbook, and that they're there to help you, not as an imposition! If they seem to contain a lot of material, it's because we were trying to ensure that you have everything you might need to help you understand and master the content of the course. Each guide has the same format, so as you proceed through the course you will be able to develop the way of using them that suits you best -- if that turns out to be different from the way suggested here, don't worry about it; you're the best judge of what works for you. For instance, if you find it easier to work from the textbook than the material in the Summary, that's just fine (but make sure you read the Aims and New Ideas checklists to confirm that you've covered everything, as the order of topics in the text is sometimes rather different).

One final note--the study guides have been specially written for this course, and are therefore quite new. We have done our best to ensure that they are as clear and accurate as possible. However, if you find any mistakes or have any comments we would greatly appreciate it if you would let us know: send e-mail to busza@mit.edu or written mail to Prof. W. Busza, room 24-510. You can also send anonymous comments and suggestions by using the feedback page.

## SUMMARY OF COURSE CONTENT

The course is divided into 13 sections or "units", each representing one week's work. Working on the principle of simplifying and idealizing situations to explore fundamental concepts, we start by dealing with objects considered as simple point particles (units 1-4) before progressing to interactions of two particles (units 5 and 6) and then to various strategies for handling systems consisting of large numbers of particles, such as solid bodies, liquids and gases (units 7-13).

```  Unit              Title                                Contents
1      Space, Time and Science           Physics and the scientific method;
properties of space and time;
calculation of velocity and
acceleration.
2      Mass, Force and Newton's Laws     Definitions of mass and force;
Newton's laws and applications;
practical and fundamental forces.
3      The Motion of a Point Particle    Review problems
4      Energy                            Kinetic and potential energy;
work; conservation of energy;
force and potential energy.
5      Systems of Particles              Momentum; conservation of
momentum; Newton's third law;
collisions; internal energy and
internal forces.
6      Energy and Momentum               Review problems
7      Practical Forces                  Friction and other dissipative
forces.
8      Rotation about an Axis            Angular velocity and acceleration;
rotational kinetic energy; moment
of inertia; torque and angular
momentum.
9      Rotation in Three Dimensions      Equilibrium for a rigid body;
statics; torque and angular
momentum as vectors; planetary
motions; gyroscopes.
10      Motion of a Rigid Body            Review problems
11      Kinetic Theory and the Ideal Gas  Model of an ideal gas; pressure;
temperature, heat and internal
energy.
12      Fluid Mechanics                   Model of an ideal liquid; buoyancy
and Archimedes' Principle;
equation of continuity and fluid
flow; surface tension.
13      Review                            Course summary and review problems

```

## CALENDAR

```Monday          Tuesday          Wednesday        Thursday          Friday

Sept 2          Sept 3           Sept 4 First     Sept 5 No         Sept 6
Labor Day       Registration     day of classes   evening class     1-hr class
Day

Sept 9          Sept 10          Sept 11          Sept 12           Sept 13
Unit 1 demo                                       Unit 1 hmw due    Unit 1 Quiz

Sept 16         Sept 17          Sept 18          Sept 19           Sept 20
Unit 2 demo                                       Unit 2 hmw due    Unit 2 Quiz

Sept 23         Sept 24          Sept 25          Sept 26           Sept 27
Vacation                                          Unit 3 hmw due    Review Quiz 1*

Sept 30         Oct 1            Oct 2            Oct 3             Oct 4 (add date)
Unit 4 demo                                       Unit 4 hmw due    Unit 4 Quiz

Oct 7           Oct 8            Oct 9            Oct 10            Oct 11
Unit 5 demo                                       Unit 5 hmw due    Unit 5 Quiz

Oct 14          Oct 15           Oct 16           Oct 17            Oct 18
Columbus Day Vacation ----->                      Unit 6 hmw due    Review Quiz 2*

Oct 21          Oct 22           Oct 23           Oct 24            Oct 25
Unit 7 demo                                       Unit 7 hmw due    Unit 7 Quiz

Oct 28          Oct 29           Oct 30           Oct 31            Nov 1
Unit 8 demo                                       Unit 8 hmw due    Unit 8 Quiz

Nov 4           Nov 5            Nov 6            Nov 7             Nov 8
Unit 9 demo                                       Unit 9 hmw due    Unit 9 Quiz

Nov 11          Nov 12           Nov 13           Nov 14            Nov 15
Veterans' Day                                     Unit 10 hmw due   Review Quiz 3*

Nov 18          Nov 19           Nov 20 (drop     Nov 21            Nov 22
Unit 11 demo                     date)            Unit 11 hmw due   Unit 11 Quiz

Nov 25          Nov 26           Nov 27           Nov 28            Nov 29
Unit 12 demo                                      Thanksgiving Vacation ---------

Dec 2           Dec 3            Dec 4            Dec 5             Dec 6
Unit 12 demo                                      Unit 12 hmw due   Unit 12 Quiz

Dec 9           Dec 10           Dec 11 Last      Dec 12 No         Dec 13
Concluding                       day of classes   evening class
lecture

```

The timetable for classes depends on your class assignment. The final exam will be scheduled sometime in the week of December 16 to December 20.

* Review Quiz 1 covers material from Units 1 through 3; Review Quiz 2 covers Units 4 through 6; Review Quiz 3 covers Units 7 through 10. The final exam includes all 13 units.

```       Test          Contribution