| Day of week and Date | Lecture Content and Homework Assignment |
|---|---|
| Fri. Aug. 19, 2016 |
Lecture: Course outline, grading, other such matters (see course
website for details). Quick Review of required mathematics. Homework #1 (due Aug. 24, 2016): Chapter 1, Problem numbers which are divisible by 10. Solutions: Solution 1-10, Solution 1-20, Solution 1-30, Solution 1-40. |
| Mon. Aug. 22, 2016 |
Newton's Laws and Inertial Frames of Reference. Some simple cases
of equations of motion: mass on an inclined plane (with and without
friction), terminal velocity of falling raindrops and other
objects. Homework #2 (due Aug. 31, 2016): Problem 2-1. |
| Wed. Aug. 24, 2016 |
Further examples of equations of motion: projectile motion with air
resistance, motion in a magnetic field. Conservation Laws. Homework #2 (due Aug. 31, 2016): Problem 2-15. *Problem 2-22. |
| Fri. Aug. 26, 2016 |
Conservative potentials, Energy conservation. Homework #2 (due Aug. 31, 2016): Problem 2-42. |
| Mon. Aug. 29, 2016 |
Simple Harmonic motion in 1- and 2-dimensions. Homework #3 (due Sep. 7, 2016): Problem 3-9. |
| Wed. Aug. 31, 2016 |
Damped oscillators, Driven oscillators. Homework #3 (due Sep. 7, 2016): Problem 3-12. *Problem 3-6. |
| Fri. Sep. 2, 2016 |
Driven oscillators, continued. Circuit analogs of mechanical
oscillators. The Fourier Transform approach for the steady-state
solution (particular integral). Homework #3 (due Sep. 7, 2016): Problem 3-26. |
| Wed. Sep. 7, 2016 |
The concept of a "Q" value. General description of methods of solving
ordinary differential equations that we commonly encounter. Homework #4 (due Sep. 14, 2016): *Problem 3-38. |
| Fri. Sep. 9, 2016 |
In-class
test #1
based on everything covered up to and including on 9/2/2016. No homework. |
| Mon. Sep. 12, 2016 |
Newtonian Gravitation: the force due to gravity and its potential. Homework #5 (due Sep. 21, 2016): Problem 5-14. |
| Wed. Sep. 14, 2016 |
The gravitational potential goes to zero at infinity, the
gravitational energy of a spherical body such as the earth (idealized
as being of uniform density), oscillation of a mass in a hole drilled
from pole to pole (again idealized as without air resistance or other
problems). Homework #5 (due Sep. 21, 2016): Problem 5-16. |
| Fri. Sep. 16, 2016 |
The divergence theorem / Gauss's Law. The Poisson equation for the
gravitational field. Fourier series, an introduction. Homework #5 (due Sep. 21, 2016): *Problem 5-11. |
| Mon. Sep. 19, 2016 |
The Lagrangian, the Action Principle and the Euler-Lagrange
equations. Generalized coordinates. Equivalence to Newton's Laws. Homework #6 (due Sep. 28, 2016): Problem 6-7. |
| Wed. Sep. 21, 2016 |
The velocity vector and its square in Cylindrical and Spherical
coordinates. Homework #6 (due Sep. 28, 2016): Problem 7-4. |
| Fri. Sep. 23, 2016 |
Textbook examples of simple Lagrangians. Homework #6 (due Sep. 28, 2016): Problem 7-5. *Problem 7-7. |
| Mon. Sep. 26, 2016 |
The Method of Lagrange Multipliers. Lagrangian mechanics with
constraints. Homework #7 (due Oct. 19, 2016): Problem 7-11. |
| Wed. Sep. 28, 2016 |
Momentum conjugate to a generalized coordinate. The Hamiltonian and
the Hamiltonian equations. Examples of simple problems solved using
the Hamiltonian. When is H = E = T + U? Homework #7 (due Oct. 19, 2016): Problem 7-22. *Problem 7-30. |
| Fri. Sep. 30, 2016 |
An Introduction to Five Theorems: Conservation of Energy, Momentum,
and Angular Momentum and the Virial and Liouville theorems. Homework #7 (due Oct. 19, 2016): Problem 7-29. |
| Mon. Oct. 3, 2016 |
Noether's Theorem: Proof and application to conservation of linear
momentum and conservation of angular momentum. Proof of Liouville's
Theorem. Homework #8 (due Oct. 19, 2016): Problem 7-40. |
| Wed. Oct. 5, 2016 |
Class canceled due to high atmospheric angular momentum. Homework #8 (due Oct. 19, 2016): No homework. |
| Fri. Oct. 7, 2016 |
Class canceled due to high atmospheric angular momentum. Homework #8 (due Oct. 19, 2016): No homework. |
| Mon. Oct. 10, 2016 |
Kepler's Laws of Planetary Motion. Conclusions about central force
motion based on simple considerations: the motion is planar and
conserves energy and angular momentum. Reduction of the problem to
effectively one-dimensional motion: the reduced mass and variation of
the distance between the masses as a function of time. Recitation session will focus on a test review. Homework #9 (due Oct. 19, 2016): No homework. |
| Wed. Oct. 12, 2016 |
In-class
test #2
based on everything covered up to and including on
9/30/2016. Homework #9 (due Oct. 19, 2016): No homework. |
| Mon. Oct. 17, 2016 |
Recap of previous lecture on central force motion, followed by: Equation of motion: solving for t in terms of r. Equation of orbit: an equation for u (= 1/r) in terms of θ. Homework #10 (due Oct. 26, 2016): Problem 8-9. |
| Wed. Oct. 19, 2016 |
Elliptical orbits for planetary motion. Homework #10 (due Oct. 26, 2016): Problem 8-24. *Problem 8-23. |
| Fri. Oct. 21, 2016 |
Completion of Kepler's Law proofs. Problem solved in class: 8-10. Homework #10 (due Oct. 26, 2016): Problem 8-25. |
| Mon. Oct. 24, 2016 |
Hohmann transfers from one circular orbit to another. Tennis walls,
tennis balls, and the gravity assisted flyby. Problem 8-39. Homework #11 (due Nov. 2, 2016): Problem 8-40. |
| Wed. Oct. 26, 2016 |
Center-of-Mass, Position, Momentum, Angular Momentum, and Kinetic
Energy of a system of particles. Elastic and inelastic collisions. Homework #11 (due Nov. 2, 2016): Problem 9-23. |
| Fri. Oct. 28, 2016 |
Scattering theory. Important variables are the impact parameter b, the
scattering angle θ, and the initial kinetic energy T0
in the reduced one-dimensional motion. Dependence of b on θ, and
the differential scattering cross-section. The total scattering
cross-section. Scattering cross-sections from a hard sphere. Homework #11 (due Nov. 2, 2016): For a certain scattering problem the relation between b and θ is given by b = a cos3/2θ, where a = 1 micron. (a) Find the differential and total scattering cross-sections. (b) For a uniform incoming beam of particles, a million are scattered. How many go into a solid angle of 5° × 5° surrounding a direction directly upwards (from the beam's point of view) and with polar angle θ = 30°? |
| Mon. Oct. 31, 2016 |
Rutherford scattering: derivation of the differential and total
scattering cross-section. We solved (or began solving) problems 9-42
and 9-51 in class. Homework #12 (due Nov. 9, 2016): Problem 9-51. |
| Wed. Nov. 2, 2016 |
Relating position, velocity and acceleration in inertial and rotating
frames of reference. The "fictitious" Coriolis and Centrifugal
forces. The formation of hurricanes. Homework #12 (due Nov. 9, 2016): Problem 10-9. *Problem 10-10. |
| Fri. Nov. 4, 2016 |
The Inertia tensor obtained from the expression for rotational kinetic
energy. Homework #12 (due Nov. 9, 2016): Consider a uniform hemispherical mass M of radius R. (a) find the position of the center-of-mass. (b) Using the CM location as the origin of the body frame coordinate system, and the symmetry axis as the z-axis, find the components of the inertia tensor. |
| Mon. Nov. 7, 2016 |
The relation between angular momentum and angular velocity in the
general case: no longer a simple proportionality. Discussion of
properties of the inertia tensor based on linear algebra: converting
to the principal axes using similarity transformations, and the
meaning of the eigenvalues and eigenvectors. Steiner's parallel-axis
theorem in the general case of an inertia tensor. Homework #13 (due Nov. 16, 2016): Problem 11-13. |
| Wed. Nov. 9, 2016 |
Finite rotations do not commute. Rotation requires 3 parameters: a
unit vector and rotation angle, or 3 angles. The Euler angles and
rotation matrices. Relation between the angular velocity vector and
time derivatives of Euler angles. Homework #13 (due Nov. 16, 2016): No homework. |
| Fri. Nov. 11, 2016 |
The Euler equations for rotation. The hemisphere moment of inertia
tensor. Homework #13 (due Nov. 16, 2016): No homework. |
| Mon. Nov. 14, 2016 |
Review of Chapters 8, 9, 10, and 11 up to the inertia tensor.
No homework. |
| Wed. Nov. 16, 2016 |
In-class
test #3
based on everything covered up to and including on
11/7/2016. No homework. |
| Fri. Nov. 18, 2016 |
Force-free motion of an azimuthally symmetric object. Homework #14 (due Monday, Nov. 21, 2016): Problem 11-26. |
| Mon. Nov. 21, 2016 |
Motion of a Symmetric Top: the three constants of motion and the
effective potential V(θ). Homework #15 (due Monday, Nov. 28, 2016): Problem 11-8. |
| Mon. Nov. 28, 2016 |
Motion of a Symmetric Top, concluded: the minimum value of θ,
precessional motion. Homework #16 (due Friday, Dec. 2, 2016): Problem 11-25. |
| Wed. Nov. 30, 2016 |
Coupled oscillations, an introduction via two coupled masses on
springs. The Lagrangian for the general case, and the Euler_Lagrange
equations. Suggested Problem (not required homework): Problem 12-1. |
| Fri. Dec. 2, 2016 |
The simple problem of two masses on springs and connected by a third
spring solved using the Lagrangian method and matrices. Homework #16: No homework assigned today! |
| Wed. Dec. 7, 2016 9:00 AM - 11:30 AM | FINAL EXAM: Covers ALL material! |