Physics H7a:
Honors Mechanics
Key Ideas by Lecture
This is a summary of some of the main ideas. The links point
to sites that might be of interest: some are more detailed explanation of
what we did in lecture, others are more advanced material than we'll cover
in lecture
 Lectures 1,2 (K&K 1.11.8):

 Generalities
 Vectors: Properties (magnitude and direction) and
Operations (including dot and cross product)
 Position, Velocity, Acceleration
 Some links for further reading (also see general
links):
 Lecture 3 (K&K 1.9, Note 1.1):

 Plane Polar Coordinates
 Mathematical Approximations
 Units
 links for further reading

Mechanics Textbook, by D. Morin, Chap. 14 (Appendix), B&C,
section on approximations/limits and units
 Lectures 4,5 (K&K 2.12.4):

 Newton's Laws
 Some applications
 links for further reading
 Lectures 6,7,8 (K&K 2.5, Note 2.1)

 Types of Forces
 Gravity
 Contact ForcesTension, Friction, Normal, Viscosity
 Hooke's Law
 links for further reading
 Lectures 9,10,11 (K&K 3.13.6, Note 3.1)

 Definition of Momentum
 Momentum of a compound system
 Center of mass
 formal definition
 use in simplifying problems
 center of mass coordinates
 conservation of momentum
 impulse
 momentum and mass transport
 links for further reading
 Lectures 12, 13, 14 (K&K 4.14.14)

 Definition of work, evaluation of line
integrals
 kinetic energy
 conservative and nonconservative forces
 potential energy
 stability, energy diagrams
 small oscillations and harmonic oscillator
 energy conservation
 collisions and conservation laws
 links for further reading
 Lecture 15 (K&K 5)

 partial derivatives
 gradient, definition and physical meaning
 curl
 links for further reading
 Lectures 16, 17, 18 (K&K 6)

 Angular momentum and torque
 dependence on position
 consequences of angular momentum conservation: equal area law for orbits
 moment of inertia
 dynamics, kinetic energy of angular motion, solving general problems
with both rotations and translations
 pendulums
 impulse, "sweet spot"
 links for further reading
 Lectures 19,20,21 (K&K 7)

 Commuting infinitesimal rotations: angular momentum and velocities as vectors
 gyroscope precession: horizontal and at an angle
 energy conservation, nutation
 rotational stability
 inertia tensor, principal axes, stability around principal axes
 links for further reading
 Lectures 22, 23,24 (K&K 8, note 8.1)

 Galilean transformations
 Accelerating Frames
 Tides
 Principle of equivalence, grav. red shift
 fictitious forces in a rotating frame
 Centrifugal force
 Coriolis force
 examples: vertical motion, weather, foucault pendulum
 Mach's principle
 links for further reading
 Lectures 25,26,27 (K&K 9)

 Definition of central forces
 Reduced mass
 conservation laws and complete solution
 effective potential
 energy diagrams
 perturbed 2 body interactions
 solution of 1/r potential problem
 1/r problem orbits
 Kepler's laws
 links for further reading
 Lectures 28, 29, 30 (K&K 10, Note 10.1, 10.2, and/or French 1,4345,7789,
6270, 9296)

 harmonic oscillator, complex number solution
 damped harmonic oscillator: underdamped, overdamped, critical
 Q
 forced harmonic oscillator
 linearity, transients
 resonance
 links for further reading
 Lectures 31,32

 superposition
 fourier series, orthogonality of cosines and sines in a period
 beats
 coupled oscillations
 normal modes
 matrices and normal modes
 normal modes for simple systems
 links for further reading
 Lectures 33,34,35

 Many coupled oscillators
 Symmetries and normal mode frequencies for infinite chain
 use of boundary conditions: fixed, free
 transverse oscillations
 continuum limit: waves
 wave equation
 compare to large number of oscillators
 general wave equation solution plus boundary conditions:free, fixed
 initial conditions and fourier transforms
 2 and 3 dimensions
 driven oscillations

 links for further reading
 Lectures 36,37,38

 air columns/ sound velocity
 travelling waves
 reflections
 pulses
 group and phase velocities
 cutoff
 energy
 links for further reading
 Lectures 39,40,41

 Doppler effect
 shock waves
 static fluids
 mass conservation
 energy conservation
 links for further reading
