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Kowalski, Stanley, 8.01 Physics I, Fall 2003. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed 09 Jul, 2010). License: Creative Commons BY-NC-SA

8.01 Physics I

Fall 2003

Conic sections for gravitational orbits.
Gravity is one of the fundamental forces in nature.  Applying conservation laws for energy and angular momentum results in well defined orbits for systems of two masses.  These orbits may be represented by conic sections:  circles, ellipses, parabolas, and hyperbolas depending on the total energy of the system.  (Figure by Prof. Stanley Kowalski.)

Course Highlights

This undergraduate level introductory physics course includes lecture notesproblem sets with solutions, and exams with solutions.

Course Description

Physics I is a first-year physics course which introduces students to classical mechanics. Topics include: space and time; straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics.


General Information

8.01 is the mid-level first-year physics course, aimed at the majority of MIT students. It is paced faster than 8.01L, it is less rigorous that 8.012, and it does not have the emphasis on take-home experiments that characterizes 8.01X.

Our goal is to convey the excitement of the physicist's quest to understand nature at its deepest level, and at the same time to provide the knowledge and tools that you will need to continue your studies in science or engineering. We hope you will enjoy the course.


Lectures will be given by Prof. Stanley Kowalski thrice a week, for 1 hour each. We expect you to attend the lectures. The lectures will explain the concepts that you are expected to understand, and in addition there will be live demonstrations that are important to your understanding of the material.

Recitation Classes

You will be assigned to a recitation class that meets twice a week, for 50 minutes each meeting. These classes will give you an opportunity to ask questions about the material, and to practice the art of problem solving. There will be five 25-minute quizzes given during recitation. If you need to change your recitation class, ask at the Physics Education Office.

Tutoring and Instructors’ Office Hours

Graduate student tutors will be available throughout the term, and you are strongly encouraged to seek their help. Tutoring sessions last 25 minutes. Initially they will be on a drop-in basis, but we may switch to a sign-up system if there is a problem with overcrowded sessions.


Young and Freedman. University Physics. 11th ed. 2003.

The textbook is a required purchase. When the material in the Study Guide is too concise for your taste, you can turn to the textbook, which provides more detailed derivations and explanations of the results and formulas. It also has more worked examples and problems, problem-solving hints, etc. Homework problems will be assigned from the textbook.

Study Guide

Busza, Wit, Susan Cartwright, and Alan H. Guth. Essentials of Introductory Classical Mechanics. 6th ed.

The Study Guide is not a required purchase, but is recommended. It was written especially for this course and will be your main resource for the course's material. It defines the content of the course, provides a concise discussion of the relevant principles of physics, and includes a large collection of physics problems, some with full solutions and some without. If by the end of the term you understand and know how to use the material in the Study Guide, you will deserve an A for the course. Since the Study Guide is still under development, it may contain some errors. If you discover any errors, we would very much appreciate your sending an e-mail message about them. No error is too small to be worth correcting.

Problem Sets

Problem sets will be assigned about once a week; the exact schedule of hand-out dates and due dates is included on the Course Calendar, attached to this handout. Normally, written homework will be posted on the web on Wednesdays. It will be due the following week on Thursdays by 4 pm. There are exceptions. Check the web. Normally, Mastering Physics assignments will be posted on the web on Tuesdays. They will be due the following week on Tuesdays by 10 pm. Check the course calendar for exceptions. The two lowest homework scores will be excluded from the homework grade.

We believe that working out the problems on the homework is absolutely essential to learning the material of this course. Trying to learn physics without doing problems is like trying to learn how to ride a bicycle by reading a book. We strongly encourage students to get together in groups to discuss the homework, but of course the mere copying of solutions written by your friends will not help you learn physics. Solutions to each problem set will be made available immediately after they are due.

Mastering Physics

Registered students will be given access to Mastering Physics, an on-line tutorial and homework system. We will be using the access kit that comes with Young and Freedman's eleventh edition. Note: OCW Users will not be able to access this material.


Recitation Quizzes

On five selected weeks, 25-minute quizzes will be given in the Wednesday and Thursday recitation sections. The dates of the recitation quizzes are shown on the course calendar.

50-minute Exams

Three lecture periods during the term -- session #17, session #35, and session #53 -- will be used for 50-minute exams. Each exam will focus on all the material since the previous exam, and will include at least one problem that is at most a slight modification of a previously assigned homework problem. Students will be assigned to exam rooms according to their family names.

Target Scores

The material in this course is tightly interconnected, so it is very difficult to understand the contents of Chapter N if you are not comfortable with the ideas in Chapters 1 . . . N -1. For that reason, we want to do everything that we can to encourage you to stay on top of the subject, avoiding any gaps in your understanding. As part of this encouragement, after each exam Prof. Kowalski will announce a target score -- a level that is comfortably above the passing line, which we would like all students to attain. Students who fall below the target score will have the opportunity to improve their grades (and their understanding) by taking a Make-Up Exam.

Make-Up Exams

The Make-up Exams will be given on Tuesday evenings at 7:30 p.m., at least one week after the original 50-minute Exam. Make-up Exam #1 will be held during session #23; #2 will be held during session #42 at 7:30 pm; #3 will be held session #58 at 7:30 pm. The dates for the 50-minute Exams and the Make-up Exams are shown on the course calendar. Students electing to take the Make-up Exam will have a grade recorded as their exam grade which is the average of the Make-Up Exam and the regular 50-minute Exam, if any, up to a maximum of the target score.

Final Examination

The 3-hour final exam, which will cover the material from the entire course, will be held five days after the last lecture (lec 36), 9 am - noon. There will be no make-up final.


Problem Sets 9%
Mastering Physics 9%
Recitation 10%
50-minute Exams 36%
Final Exam 36%

Academic Behavior and Honesty

During quizzes and exams, exchange of information with others is unacceptable. So is the use of notes or other materials, unless explicitly authorized. You will not be allowed to use calculators (they will not be needed). Anyone suspected of violating these guidelines will be charged with academic dishonesty and subject to MIT’s disciplinary procedures. However, you are strongly encouraged to get together in groups to discuss the problem sets and the material presented in the course.

MIT's academic honesty policy can be found at MIT Policies and Procedures.


Y&F* = Young and Freedman. University Physics. 11th ed. 2003.
MP** = Mastering Physics
PS*** = Problem Set

1 Introduction
Classical Mechanics
Coordinate Systems
Units of Measurement
Changing Units
Dimensional Analysis
Y&F*: pp. 1-13  
2 Kinematics
Speed and Velocity
Constant Velocity Motion
Y&F: pp. 40-47  
3 Acceleration
Constant Acceleration Problems
Acceleration of Gravity
Y&F: pp. 47-62 MP** 1 due
(a day after ses #3)
4 Vectors
Vector Addition
Vector Components
Unit Vectors
Vector Multiplication
Scalar Product
Y&F: pp. 14-27 PS*** 1 due
(a day after ses #4)
5 Vector Product
Kinematics in 3D
3D Velocity
3D Acceleration
Acceleration: Perpendicular
Acceleration: Parallel
Y&F: pp. 27-30, 78-87  
6  Projectile Motion Y&F: pp. 87-97 MP 2 due
(a day after ses #6)
7 Uniform Circular Motion
Non-uniform Circular Motion
Galilean Relativity
Coordinate Transformations
Velocity Transformations
Acceleration Transformation
Relative Velocity Problems
Y&F: pp. 98-106 Recitation Quiz 1

PS 2 due
(a day after ses #7)
8 Newton's Laws
Fundamental Forces in Nature
Newton's First Law
Newton's Second Law
Superposition of Forces
Y&F: pp. 119-138 MP 3 due
(4 days after ses #8)
9 Newton's Third Law
Gravitational Force
Gravitational/Inertial Mass
Hooke's Law/Springs
Motion with a Constant Force
Y&F: pp. 138-146 PS 3 due
(a day after ses #9)
10 Motion Examples
Y&F: pp. 153-171 Exam 1
Lectures: 1-8
-Homework: 1-3 due
(3 days after ses #10)

MP 4 due
(4 days after ses #10)
11 Friction
Kinetic Friction
Static Friction
Drag Force and Terminal Speed
Resistive Force Proportional to Velocity
Y&F: pp. 171-181 PS 4 due
(a day after ses #11)
12 Dynamics of Uniform Circular Motion
Motion in a Vertical Circle
Conical Pendulum
Work and Energy
Work/Variable Force
Y&F: pp. 181-189, 207-213  
13 Kinetic Energy
Gravitational Potential Energy
Gravity and Other Forces
Y&F: pp. 213-229, 241-253 Makeup Exam 1
(a day after ses #13)

MP 5 due
(a day after ses #13)
14 Conservation of Energy
Conservative Forces
Potential Energy of Conservative Forces
  Recitation Quiz 2

PS 5 due
(a day after ses #14)
15 Spring Potential Energy
Gravitational Potential Energy
Non-conservative Forces
Force and Potential Energy
Y&F: pp. 253-268 MP 6 due
(4 days after ses #15)
16 Potential Energy Curves
Equilibrium and Stability
Forms of Energy
Y&F: pp. 268-270 PS 6 due
(a day after ses #16)
17 Particle Momentum
Conservation of Momentum
Newton's Laws and Momentum
Momentum for a System
Momentum and Forces
Y&F: pp. 282-292  
18 Center-of-Mass Motion
Energy of a System of Particles
Rocket Motion
Y&F: pp. 309-313 MP 7 due
(a day after ses #18)
19 Variable Mass Problems
Inelastic Collisions
Elastic Collisions
Y&F: pp. 295-305 PS 7 due
(a day after ses #19)

Exam 2
Lectures: 1-18
-Homework: 1-7 due
(2 days after ses #19)
20 2D-Elastic Collisions
Ballistic Pendulum
Center-of-Mass Collisions
Y&F: pp. 305-308 MP 8 due
(a day after ses #20)
21 Rigid Body Kinematics
Right Hand Rule
Constant Angular Acceleration
Relation between Angular and Linear Motion
Rotational Kinetic Energy
Moment of Inertia
Y&F: pp. 327-345 Recitation Quiz 3

PS 8 due
(a day after ses #21)
22 Parallel Axis Theorem
Perpendicular Axis Theorem
Particle Angular Momentum
Straight Line Angular Momentum
Circular Motion Angular Momentum
Angular Momentum and Forces
Conservation of Angular Momentum
Angular Momentum and Central Forces
Y&F: pp. 345-349  
23 Dynamics of a Rigid Body
Angular Momentum and Torque
Conical Pendulum: Torque and Angular Momentum
Torque and Angular Acceleration
Torque and Gravity
Rigid Body Angular Momentum
Conservation of Angular Momentum
Y&F: pp. 361-370 Makeup Exam 2
(a day after ses #23)

MP 9 due
(a day after ses #23)
24 Work and Energy in Rotational Motion
Angular Impulse
Translation and Rotation
Rolling Motion of a Rigid Body
Y&F: pp. 370-386 PS 9 due
(a day after ses #24)
25 Rolling Cylinders/Spheres
Angular Momentum and Collisions
Y&F: pp. 386-389 MP 10 due
(4 days after ses #25)
26 Forces in Equilibrium Y&F: pp. 406-421 Recitation Quiz 4

PS 10 due
(a day after ses #26)
27 Law of Universal Gravitation
Newton's Law of Gravity
Gravitational Potential Energy
Potential Energy of a Spherical Shell
Cavendish Experiment
Y&F: pp. 436-451  
28 Potential Energy of a Sphere and Particle
Gravitational Forces and Extended Bodies
Force between Two Spheres
Tidal Forces
Weight and Gravitational Force
Planetary Motion
Circular Orbits
Y&F: pp. 456-464 MP 11 due
(a day after ses #28)
29 General Planetary Motion
Generalized Orbits
Kepler's Laws
Y&F: pp. 452-456 Exam 3
Lectures: 1-28
-Homework: 1-11 due
(2 days after ses #29)
30 Oscillations
Simple Harmonic Motion
Mass-Spring Systems
Energy in SHM
Y&F: pp. 476-494 PS 11 due (by 11 am)

MP 12 due
(a day after ses #30)
31 Simple Pendulum
Physical Pendulum
Torsional Pendulum
Damped Oscillations
Y&F: pp. 495-502 PS 12 due
32 Special Relativity
Galilean Transformations
Light/Theory of Waves
Stellar Aberration
  Makeup Exam 3
(a day after ses #32)

MP 13 due
(a day after ses #32)
33 Paradox; Light Spheres
Einstein's Special Relativity
Postulates of Special Relativity
Relativity and Measurements
Space-Time Coordinates
Relativity of Simultaneity
Lorentz Transformations
Y&F: pp. 1403-1411 Recitation Quiz 5

PS 13 due
(a day after ses #33)
34 Time Dilation
Length Contraction
Perpendicular Lengths
Orientation; Moving Rod
Paradox: Pole-Vaulter
Headlight Effect
Y&F: pp. 1412-1419  
35 Relativistic Velocity Transformation
Doppler Effect
Transverse Doppler Effect
Twin Paradox
Shape of Moving Objects
Relativity and Forces
 Y&F: pp. 1420-1425  
36 Relativistic Momentum
Relativistic Energy
Massless Particles
Space-Time Invariant
General Relativity
Y&F: pp. 1426-1434   Tell A Friend