Class Diary for Physics 4222-Spring 2002

 

Date Notes
W 1/9 Introductions, course policies.
F 1/11 Review of vectors. Adding vectors, dot (scalar) product. Class photos.
M 1/14 Cross product. Differentiation of vectors. Started cylindrical coordinates. See lecture notes.
W 1/16 Finished cylindrical coordinates. Briefly discussed spherical coordinates. Started discussion of Newton's Second Law, using the example of a block sliding off a frictionless cylinder.
F 1/18 Finished discussion of block sliding off of the cylinder.
M 1/21 MLK Day (no classes)
W 1/23 Started calculus of variations. Set up brachistochrone problem, catenary problem, soap film problem.
F 1/25 Discussed stability analysis briefly. Other problems which require the calculus of variations. Review of calculus of a single and several variables. Started minimization of a functional. Problem Set 2 due.
M 1/28 AD at U Chicago-class to be rescheduled.
W 1/30 Derived Euler's equation. Examples: shortest distance between points on the plane, started brachistochrone.
F 2/1 Derive the "second" form of Euler's equation. Finished brachistochrone problem (solution is a cycloid). Started soap film problem.
M 2/4 Solved soap film problem. Discussed surface tension, soap films and bubbles, (Young)-Laplace law. Motorway problem. Problem Set 3 due.
W 2/6 Motivation for Lagrangian mechanics. Hamilton's Principle. Lagrange's equations.
F 2/8 Constraints. Generalized coordinates. Example: plane pendulum. Problem Set 4 due.
M 2/11 Lagrange's equations in generalized coordinates. Holonomic constraints. Kinetic energy in cylindrical and spherical coordinates.
W 2/13 Examples: particle moving inside cone; block sliding down moving incline.
F 2/15 More examples: swinging Atwood's machine, block on moving incline.
M 2/18 Numerical solution of the equations of motion for the swinging Atwood's machine. Started discussing conservation of energy.
W 2/20 Conservation of energy, linear momentum, and angular momentum. Connection between symmetries and conservation laws.
F 2/22 First quiz (in class).
M 2/25 Central force motion. Reduction of the two body problem using relative and center of mass coordinates. Conservation laws.
W 2/27 Angular momentum conservation, Kepler's Second Law. Started discussing qualitative aspects of orbital motion.
F 3/1 Derivation of the orbit equation.
3/4-3/8 Spring break.
M 3/11 Orbits in an inverse-square force field (Kepler problem).
W 3/13 Examples from M&T on central force motion.
F 3/15 Started dynamics of many-particle systems. Center of mass. Problem Set 7 due.
M 3/18 Lecture by Filippos Klironomos: AD at March meeting of APS. Conservation of linear and angular momentum.
W 3/20 Lecture by Filippos Klironomos: conservation of energy for many-particle systems.
F 3/22 Lecture by Filippos Klironomos: discussion of homework assignment. Problem Set 8 due.
M 3/25 Scattering geometry. CM vs. LAB frames.
W 3/27 More on elastic collisions. Applications to finding the optimal moderator for a nuclear reactor.
F 3/29 Scattering cross sections. Scattering from an impenetrable sphere. Problem Set 9 due.
M 4/1 Rutherford scattering.
W 4/3 Kinematics of rigid rotations. Velocity and acceleration in noninertial frames. Fictitious forces: Coriolis and centrifugal forces.
F 4/5 Second quiz (in class).
M 4/8 Unsuccessfully tried to watch the "Frames of Reference" video. Simple examples of the use of the centrifugal and Coriolis forces.
W 4/10 Bead on a rotating wire example solved in the rotating frame. Starting discussing motion near the Earth's surface and deflection due to the Coriolis force.
F 4/12 Finished discussion of deflection of a falling body. Started rigid body motion (Chapter 11 material).
M 4/15 Kinetic energy-separation into translation and rotational pieces. Inertia tensor, moments and products of inertia. Problem Set 10 due.
W 4/17 Examples. Center of percussion.
F 4/19 Angular momentum. Principal axes of inertia. Parallel axis theorem.
M 4/22 Course evaluations. Euler angles. Started discussion of the motion of a heavy symmetric top.
W 4/24 Finished discussion of the heavy symmetric top. Brief discussion of Euler's equations. Problem Set 11 due.
W 5/1 Final exam, 5:30-7:30 p.m.