CORE 006: Newtonian Mechanics
Syllabus

The topic list for this project is: kinematics, Newton's laws, dimensional analysis, one-dimensional problems, conservation of energy, central forces, conservation of momentum and scattering theory, noninertial frames, and conservation of angular momentum and rotational dynamics.

Prerequisite: CORE 003 or the equivalent. I recommend taking CORE 004 simultaneously with this course.

Instructor: George E. Hrabovsky, george@madscitech.org, 608-276-6832.

Task #1: Start and keep a notebook for your study. This should be bound and have at least 300 sheets. You may need more than one notebook of this size. Smaller notebooks than 300-sheets can be used, but the total number of sheets should be at least 300. Each set of 300 pages started and completed is worth a point towards your final total of 4. To begin your notebook you will need a list of topics. The one listed below is only one possible choice. This choice is the default. Any choice other than this one must be approved by your instructor.

Procedure for the Course

If a topic from the list below is underscored that means there is some resource material for it. If there is no resource material for it then you must develop that for yourself.

It is expected that you will develop one or more questions for each topic. Questions can be of the form who, what, when, where, why, and how.

Once you have written down a set of questions for a topic, you either answer each of these qurestions or you explain how you attempted to answer the question and failed. Don't be alarmed; even some elementary questions resist answering. You can learn a lot just by making the effort.

The next step is to ask a set of new questions based on your previous attempts at answering your first set of questions (this can include those questions you were unable to answer before). Answer each of those questions as best you can and create another set of questions for each answer. Answer each of those to the best of your ability and ask another set of questios for each, but do not answer them right away. If you are really interested in one or more of these questions attempt to answer them in a, "topic of personal interest," session; or you may answer them in a personal research project.

Wherever possible give at least three examples of any definition, principle, or procedure.

This course will require a little less than three pages of notes for each topic to fill a 300 page notebook.

  1. The nature of physics
  2. Experimental physics
  3. Theoretical physics
  4. Computational physics
  5. Abstraction
  6. Modeling
  7. Position
  8. Displacement
  9. Time and frames of reference
  10. Velocity
  11. Acceleration
  12. The kinematical equations of motion
  13. Kinematics of rotation
  14. Kinematics in Mathematica
  15. Topic of personal interest (including, but not limited to, 5 practice problems, motion under constant acceleration, falling bodies, projectile motions)
  16. Topic of personal interest.
  17. Topic of personal interest.
  18. Review of topics 16-20
  19. Review of topics to date.
  20. Forces
  21. Mass and inertia
  22. Momentum and Newton's first law
  23. Newton's second law
  24. Newton's third law
  25. Newtonian dynamics in Mathematica
  26. Topic of personal interest (including, but not limited to, 5 practice problems, simple machines, circular motion, friction, normal force, tension, static equilibrium, electric forces, Atwood's machine)
  27. Topic of personal interest.
  28. Topic of personal interest.
  29. Review of topics 23-30
  30. Review of topics to date.
  31. Dimensional analysis
  32. Deriving force principles by dimensional analysis
  33. Dimensional analysis in Mathematica
  34. Topic of personal interest (including, but not limited to, 5 practice problems, scaling, order of magnitude, Fermi problems)
  35. Topic of personal interest.
  36. Topic of personal interest.
  37. Review of topics 33-37
  38. Review of topics to date.
  39. Time-dependent forces
  40. Velocity-dependent forces
  41. Falling bodies
  42. Linear restoring forces
  43. Harmonic oscillators
  44. Damped oscillators
  45. Forced oscillators and resonance
  46. One-dimensional motion in Mathematica
  47. Topic of personal interest (including, but not limited to, 5 practice problems, systems of oscillators, nonlinear oscillations, chaotic oscillations)
  48. Topic of personal interest.
  49. Topic of personal interest.
  50. Review of topics 40-50
  51. Review of topics to date.
  52. Work and kinetic energy
  53. Position-dependent forces and potential energy
  54. Conservation of energy
  55. Conservation of energy in Mathematica
  56. Topic of personal interest (including, but not limited to, 5 practice problems, chaotic dynamical systems, conservative forces, projectile motion, dynamic equilibrium, power, energy diagrams, work-energy theorem)
  57. Topic of personal interest.
  58. Topic of personal interest.
  59. Review of topics 53-59
  60. Review of topics to date.
  61. Newton's law of gravitation
  62. Gravitational potential
  63. Gravitational fields
  64. Kepler's laws
  65. The two-body problem
  66. Gravitation in Mathematica
  67. Topic of personal interest (including, but not limited to, 5 practice problems, central forces, central orbits, bound orbits, unbound orbits, the Cavendish experiment, work done by gravitation, inverse square forces, planetary orbits, the Bohr atom, the ratio between electric and gravitational forces)
  68. Topic of personal interest.
  69. Topic of personal interest.
  70. Review of topics 62-69
  71. Review of topics to date.
  72. Momentum and impulse
  73. Systems of particles
  74. Conservation of momentum
  75. Scattering, accretion, and decay
  76. Conservation of momentum in Mathematica
  77. Topic of personal interest (including, but not limited to, 5 practice problems, systems of interacting particles, invariance under translations, exploding projectiles, elastic collisions, center of mass, center of mass frame, rockets, reduced mass)
  78. Topic of personal interest.
  79. Topic of personal interest.
  80. Review of topics 72-79
  81. Review of topics to date.
  82. Noninertial frames
  83. Motion in noninertial frames
  84. Fictitious forces
  85. Noninertial frames in Mathematica
  86. Topic of personal interest (including, but not limited to, 5 practice problems, the galilean transformation, relative motion, Foucault's pendulum, Coriolis force)
  87. Topic of personal interest.
  88. Topic of personal interest.
  89. Review of topics 82-88
  90. Review of topics to date.
  91. Torque and angular momentum
  92. Conservation of angular momentum
  93. Kinematics of rigid bodies
  94. Dynamics of rigid bodies
  95. Rigid bodies in Mathematica
  96. Topic of personal interest (including, but not limited to, 5 practice problems, invariance under rotations, center of mass, moment of inertia, static equilibrium, fixed axis rotations, mass density, parallel axis theorem, perpendicular axis theorem, the pendulum, the physical pendulum, rotational kinetic energy, gyroscopes)
  97. Topic of personal interest.
  98. Topic of personal interest.
  99. Review of topics 91-98
  100. Review of topics to date.

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