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1 |
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General Introduction |
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(for Lectures 1 and 2) Kleppner-Kolenkow 1.1-1.8 (but don't worry about cross-products yet); 2.1-2.3; (for Lectures 1-5) BCG 1-3. |
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Scope and limits of classical mechanics, Space model - triples of real numbers; Time model - real numbers; Position, velocity, acceleration; Vector; Mass; Newton's 0th law; mass is not weight! |
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Galileo's ship. |
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2 |
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Newton's First and Second Laws; Operations with Vectors; Units |
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(for Lectures 1 and 2) Kleppner-Kolenkow 1.1-1.8 (but don't worry about cross-products yet); 2.1-2.3; (for Lectures 1-5) BCG 1-3. |
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Addition of vectors; Multiplication of vectors by scalars; Components of vectors; F=ma (vectors!); Inertial frame; Composition of motion; Dot product; work; Balance of units; dimensional analysis. |
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Einstein's elevator; Artillery range; Uniform acceleration and circular motion using dimensional analysis. |
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3 |
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Newton's Third Law; Examples With Friction, Ropes, Pulleys |
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K+K pp. 68-75; 87-94; (for Lectures 1-5) BCG 1-3. |
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Reaction forces; Force diagrams; Constraints; Coefficients of friction; Analyzing extended objects: ropes and pulleys point-by-point. |
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Resting and sliding blocks; Skaters and trains; Jean Valjean (-> challenge problem 2); Tug-of-War; Whirling rope; 'centrifugal force'. |
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4 |
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Velocity and Acceleration in Polar Coordinates; More Examples Using Newton's Laws |
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K+K 1.9; pp. 76-86; (for Lectures 1-5) BCG 1-3. |
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Unit radius and angle vectors; Radial and angular velocity; Radial and angular acceleration; expected and 'extra'; 'Extra' pieces of the acceleration: centrifugal and Coriolis terms. |
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Whirling block; Rotating bucket; Common pendulum; Conical pendulum. |
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5 |
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More Forces: Gravity, Springs |
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K+K 1.9; pp. 95-103; (for Lectures 1-5) BCG 1-3. |
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Newton's law of gravity; Gravitational force from a shell; Hooke's 'law'. |
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Kepler's 3rd law for circular orbits; Building up the shell-force by integration; Spring gun. |
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6 |
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Spillover from 1-5 |
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After this lecture, we will have covered K+K chapters 1-2 and BCG 1-3. Now is a good time to take a deep breath and review all this.
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7 |
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Momentum; Center of Mass; Conservation of Momentum |
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K+K 3.1-3.3, Note 3.1; (for Lectures 7-8) BCG 5-6.
[Note: Our two books do not quite treat the material in the same sequence, but in total the first 4 chapters of K+K correspond pretty closely to the first 7 chapters of BCG. A good strategy might be to quickly scan BCG 1-7 and then to look up specific topics in its Table of Contents as we work through K+K systematically]
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"Quantity of motion" and the reformulation of Newton's 2nd law; 2nd law for systems; center of mass; conservation law. |
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Planetary and lunar motions; Coupled springs (push me-pull you). |
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8 |
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Applications of Momentum: Impulse; Variable Mass Problems (Recoil); Collisions; Pressure |
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K+K 3.4-3.6; (for Lectures 7-8) BCG 5-6.
[Note: Our two books do not quite treat the material in the same sequence, but in total the first 4 chapters of K+K correspond pretty closely to the first 7 chapters of BCG. A good strategy might be to quickly scan BCG 1-7 and then to look up specific topics in its Table of Contents as we work through K+K systematically]
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Impulse and momentum change; rocket equation; origin of pressure from random motion. |
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Skaters; cannon; rocket; suspended garbage can. |
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9 |
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Spillover from 7 & 8 |
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We will now have covered all the material in K+K chapters 1-3, except for vector cross-products. The quiz will be drawn from this material.
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10 |
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First Concepts in Energy |
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K+K 4.1-4.4; (for lectures 10-12) BCG 4, 7. |
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Integrating equation of motion with respect to position; work-energy theorem; potential energy; potential energy for springs and for gravity; contact forces that do no work; friction does positive work; for rigid bodies, internal forces do no work. |
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Pendulum return, loop-the-loop, escape velocity. |
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11 |
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More on Energy |
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K+K 4.5-4.13; (for lectures 10-12) BCG 4, 7. |
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Work-energy theorem for systems; for rigid bodies, internal forces do no work; energy in gravitating systems; models of internal energy; energy diagrams; equilibria and stability; small oscillations around equilibrium. |
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Ballistic pendulum, velocity converter, stability of teeter-totter. |
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12 |
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Energy Round-Up |
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K+K 4.14, browse chapter 5; (for lectures 10-12) BCG 4, 7. |
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Collisions using energy conservation, conditions for a force-field to be conservative, energy landscape. |
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Virial theorem. |
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13 |
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Planetary Motion: Clearing the Underbrush |
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K+K pages 6-8 (cross product); 9.1-9.5. You should also look at 6.2. |
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Angular momentum for particles, separation of center-of-mass and relative coordinates, effective energy diagram. |
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Angular frenzy at approach to the center; two-body "steady motion"' and three-body shenanigans in planetary simulations. |
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14 |
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Planetary Motion: Getting the Orbits |
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9.5-9.7. You should also read through the appendices, though it is certainly not necessary to memorize the details. |
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Motion of planets and comets in conic sections; Kepler's laws. |
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More simulations; Lagrange configuration. |
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15 |
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Spillover from 13-14 |
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16 |
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Relative Motion: Concepts and Equations |
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(for lectures 16-17) K+K chapter 8. Note that sections 8.1-8.4 are mostly review of things we discussed earlier.
There is a small bit of material on accelerated frames in BCG chapter 6, and some discussion of rotation kinematics in the early parts of chapters 8 and 9, including use of cross-products. |
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Fictitious force, small rotations, vector angular velocity, master formula for vectors in rotating frame, master formula for dynamics in rotating frame. |
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Einstein elevator; gyro, centrifugal, and Coriolis terms. (Lecture 17 will be entirely examples and applications!) |
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17 |
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Relative Motion: Examples and Applications |
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(for lectures 16-17) K+K chapter 8. Note that sections 8.1-8.4 are mostly review of things we discussed earlier.
There is a small bit of material on accelerated frames in BCG chapter 6, and some discussion of rotation kinematics in the early parts of chapters 8 and 9, including use of cross-products. |
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Red shift, tidal force, Foucault pendulum. |
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Gravity red shift from equivalence principle, nature of the tides, deflection of dropped ball, motion of Foucault pendulum, weather systems. |
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18 |
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Basic Angular Momentum Concepts |
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K+K 6.1-6.3, 7.5; (for lectures 18-21) BCG 8-9. |
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Angular momentum, torque, cancellation of internal torques, equations of statics. |
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Gravitational capture, rod-pendulum, lever, motorcycle lift-off. |
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19 |
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Mainly Dynamics of Fixed-Axis Rotation |
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K+K 6.4-6.6; (for lectures 18-21) BCG 8-9. |
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Conservation of angular momentum, moment of inertia, parallel axis theorem. |
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Skater, barstool shenanigans, physical pendulum, physical Atwood's machine. |
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20 |
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Combining Rotation and Translation |
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K+K 6.7. You may also enjoy reading 6.8, which is historical/cultural, and Note 6.2, which discusses the pendulum without assuming small oscillations. The result of Note 6.1 is important, but it can be derived much more simply (as I'll discuss); (for lectures 18-21) BCG 8-9. |
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Expression for angular momentum and torque separating out center-of-mass translation, energy in rotation, expression for the energy separating out center-of-mass translation. |
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Objects rolling down inclines. The next lecture is entirely devoted to two hard examples. |
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21 |
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Two Worked Examples |
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K+K problems 6.40, 6.41; (for lectures 18-21) BCG 8-9.
In this Lecture, I'll work K+K problems 6.40 and 6.41 in detail. This will give us a good work-out in most of the concepts developed in the course so far.
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22 |
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Introduction to Gyroscopic Phenomena |
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K+K chapter 7; Lecture notes points 71-76.
Note: I will only scratch the surface of a rich and difficult subject. I realize there are many pressures and demands on your time at this point in the semester. So the following might be a sensible strategy: get acquainted with the subject by browsing through the reading and relating what you saw demonstrated in class, but put off a serious confrontation until conditions are more favorable. For example, you might want to do some of the problems at the end of chapter 7 during the break between semesters. I would be happy to provide some feedback and supply further references for any of you who'd like to explore further.
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Vector nature of angular momentum, precession, conservation of vector angular momentum (its transfer between parts of a system), nutation. |
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Bicycle wheel precession, barstool shenanigans II, nutation, gyrocompass, applications to astronomy, stabilization, and inertial guidance. |
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23 |
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Guest Lecture: Chaos in the Solar System, by Jack Wisdom |
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Note: I hope you found this lecture as interesting and inspiring as I did. There is a good semi-popular account of the subject by Ivars Petersen, titled "Newton's Clock". Again, if any of you would like to explore the subject in more depth, I can supply some guidance (or you might try Professor Wisdom!).
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24 |
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Euler Disk |
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In this final lecture, I return to the demonstration given at the beginning of the course, and explain the main phenomena of the Euler disk based on what we've learned about classical mechanics.
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