Office Hours:

Office hours are 12:30pm-2pm on Tuesday, 1:30-2:30pm on Wednesday, or schedule an appointment.

Grader

Patrick McArdle.

Online grades

Grades are posted into the web grades book. Make sure that posted grades coincide with their paper one.

For the first time login use your WM official email as “login” and hit the reset password button. You will get a password shortly via email.

If you have any suggestions or comments, please, let me know.

Lecture 01

• Angular momentum of many body system
• Transformation of angular momentum between inertial frames
• Center of mass reference frame for the two-body problem

Lecture 02

• Two-body system
  • kinetic energy expression
  • angular momentum expression
  • Lagrangian
  • conservation laws
  • converting to 1D problem with effective potential energy
  • 2nd Kepler’s law and angular momentum conservation
  • bounded and unbounded orbits

Lecture 03

• Two-body system in attractive 1/r potential
  • orbits types
    • ellipse
    • parabola
    • hyperbola
  • no go zone
• Two-body system in repulsive 1/r potential
  • orbits types
    • hyperbola

Lecture 04

• Two-body system in attractive 1/r potential
  • 3rd Kepler’s law
  • same semimajor axes different eccentricities cases
  • masses of the stellar objects from orbits parameters
• Simple case of the Virial theorem

Lecture 05

• Two-body system in attractive 1/r potential
  • speed along the orbit
  • orbits transfer
    • relative change of orbit parameters and what it leads too (all about alpha)

Lecture 06

• Two-body system in attractive 1/r potential
  • feather and the stone paradox revisited
  • orbits transfer continued
    • time to Mars travel
    • Hohmann transfer

Lecture 07

• Collisions and cross sections
  • simple definitions
  • probability of scatter
  • mean free path
  • diffusive motion and travel time
  • “immeasurable” cross section and how to connect it to scattering angles

Lecture 08

• Collisions and cross sections
  • differential cross section

Lecture 09

• General theory of scattering
  • Rutherford scattering
• Moving from CM to the lab reference frame

Lecture 10

• Scattering angle in the lab reference frame
  • special cases light, heavy, and equal masses
  • transformation of differential cross section
• Non-inertial reference frames

Lecture 11

• Non-inertial reference frames
  • moving with V(t) and rotating
  • fictitious forces

Lecture 12

• Non-inertial reference frames
  • Examples of problems with fictional forces

Lecture 13

• Midterm review

Lecture 14

• Non-inertial reference frames
  • Tidal forces

Lecture 15

• Rigid bodies

Lecture 16

• Rigid bodies
  • angular momentum
  • moments of inertia

Lecture 17

• Rigid bodies
  • kinetic energy and angular momentum with tensor of inertia
  • principal axes
  • example: tensor of inertia for a cylinder

Lecture 18

• Rigid bodies
  • Period of rolling cylinder
  • rotational speed with respect to different points of the body
  • spinning top and precession

Lecture 19

• Rigid bodies
  • Euler equations
  • Chandler wobble

Lecture 20

• Rigid bodies
  • discussion of various demo movies
    • wobble of the top
    • “anti-gravity” wheel
    • gyro compass
    • top precession
    • the tennis racket theorem or intermediate axis theorem or the Dzhanibekov Effect (Эффект Джанибекова)

Lecture 21

• 1D wave equation
  • derivation of the wave equation for a string with tension
  • general solution with forward and backward moving waves
  • solution for known excitation at time 0 and zero initial speed

Lecture 22

• 1D wave equation
  • Matlab’s demos
    • various possible propagating functions
    • superposition
    • standing wave
  • physical demo with rods
    • reflection from fixed and free end
  • separation of variables techniques

Lecture 23

• 1D wave equation
  • derivation of sound (pressure) wave
  • full derivation of wave (sound) speed for gases

Lecture 24

• Chaos

Lecture 25

• Special relativity
  • Lorentz transformation via Voigt transformation preserving wave equation

HW 01

See assignment in the hw01.pdf. Submission deadline is Thursday 09/08 at 11am.

HW 02

See assignment in the hw02.pdf. Submission deadline is Thursday 09/14 at 11am.

HW 03

See assignment in the hw03.pdf. Submission deadline is Thursday 09/21 at 11am.

HW 04

Read chapter 14. Get ready for the first midterm on Thursday 09/28

HW 05

Read chapter 14. Pay attention to the differential cross section definition and derivation.

HW 06

Read chapter 14.

See assignment in the hw06.pdf. Submission deadline is Thursday 10/12 at 11am.

HW 07

See assignment in the hw07.pdf. Submission deadline is Thursday 10/19 at 11am.

HW 08

Read chapter 9. Get ready for the first midterm on Tuesday 11/24

HW 09

See assignment in the hw09.pdf. Submission deadline is Thursday 11/02 at 11am.

Read chapter 9 about tides, we will go over it on Tuesday. Come with questions.

HW 10

See assignment in the hw10.pdf. Submission deadline is Thursday 11/09 at 11am.

HW 11

The problem 3 is reworded. Hopefully it is easier to read now.

See assignment in the hw11.pdf. Submission deadline is Thursday 11/16 at 11am.

optional bonus HW

In class I distributed a certain toy. Explain why it prefers a certain spinning direction and refuses to spin in the opposite direction.

Submission deadline is Tuesday 11/28 at 11am.

HW 12

Update for the problem 2. The top is precessing in the Earth gravitational field.

See assignment in the hw12.pdf. Submission deadline is Thursday 11/30 at 11am.

HW 13

See assignment in the hw13.pdf. Submission deadline is Thursday 12/07 at 11am.