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 1.1-1.8):
-
- 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 2.1-2.4):
-
- 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 Forces-Tension, Friction, Normal, Viscosity
- Hooke's Law
- links for further reading
- Lectures 9,10,11 (K&K 3.1-3.6, 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 4.1-4.14)
-
- Definition of work, evaluation of line
integrals
- kinetic energy
- conservative and non-conservative 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 1,43-45,77-89,
62-70, 92-96)
-
- 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
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