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PHYS325

PHYS325 (Classical Mechanics I) is a 3-credit hour course that is required for physics majors. It is also required for the physics minor. It counts as a technical elective for both EEs and CEs. It is offered in the fall and spring semesters.

Content Covered

  • Newton’s laws
  • 1D, 2D particle dynamics
  • Conservative forces, central forces
  • Gravitation
  • Orbits
  • Simple harmonic oscillators
  • Damped oscillators, forced oscillators
  • Fourier series, Green’s functions, impulse response
  • Non-inertial reference frames
  • Calculus of variations
  • Lagrangian mechanics

This course covers many aspects of classical mechanics, including Newtonian mechanics, dynamics in three dimensions, systems of particles, orbital mechanics, oscillations, motion in rotating frames of reference, Lagrangians, and the calculus of variations. It also relates heavily to calculus, differential equations, and linear algebra.

The first part of PHYS325 is a review of PHYS211, though the material is treated much more rigorously, involving extensive application of differential equations. In this section, the course covers Newton’s laws, velocity dependent forces, stable equilibria, frequencies of small oscillations, two-dimensional dynamics, polar coordinates, and rocket motion with time-varying mass.

The course then moves on to conservative and central forces, introducing the concept of effective potential. There is a brief section on gravitation, in which students will learn to determine the gravitational potential and gravitational field due to various distributed masses. Students will then be prepared for the section on orbits, which covers energy and angular momentum in circular and non-circular orbits, as well as Kepler’s laws.

Once the course gets to oscillations, a great deal of new material will be covered in every lecture. Oscillations are a big part of the semester, taking several weeks to finish. The section begins with simple harmonic oscillators before covering damped oscillators, along with the different cases of damped oscillations. Forced oscillators are then covered, with a heavy focus on harmonic forcing. Students will learn to determine the response of a damped oscillator to a harmonic force. They will then learn to use the Fourier series to determine the steady-state solution to the equation of motion of a damped oscillator subject to any periodic force. The course then covers the Dirac delta function, impulse response, Green’s functions, and convolution, to determine the response of an oscillator to arbitrary forcing. ECE majors who take PHYS325 will find this section to mostly be a review of ECE210, though with different applications.

After that, the course covers motion in non-inertial reference frames, including rotating reference frames. This section introduces the concept of fictitious forces, focusing mainly on the Coriolis force. Towards the end of the semester, the calculus of variations is introduced. Students will learn to solve extremization problems with the Euler-Lagrange equations and Lagrange multipliers. Lagrangian mechanics is then introduced, which will provide a new perception of mechanics and make determining equations of motion generally much simpler. The course concludes with Noether’s theorem, one of the most important theorems in physics.

Prerequisites

PHYS225 and credit or concurrent registration in MATH285 are official prerequisites to PHYS325. Though PHYS325 covers classical mechanics, the sections on inertial reference frames and math applications to physics from PHYS225 will be relevant to this course. It is extremely important to take this course after or along with MATH285, as much of PHYS325 revolves around solving differential equations. It is also a good idea to review vector calculus concepts from MATH241.

When to Take It

PHYS325 is a required course for physics majors and for the physics minor. Thus, it is recommended to take this course directly after taking PHYS225.

Course Structure

PHYS325 has two lectures per week. Attendance is required and is recorded using iClickers. Before lecture, students are expected to do a prelecture reading and must explain what they learned and any questions they may have in a checkpoint on Smart Physics. Do not forget these, as they are required and you may be completely lost in lecture otherwise.

PHYS325 also has a weekly discussion section. Attendance in discussion is also required, though students do not need to submit any work. During discussion, students work through a short worksheet, with problems generally related to the homework. To be prepared for the homework and exams, it is important to work through the discussion problems deliberately and ask the TA questions.

Homework is assigned weekly. Homework is much harder than in previous physics courses, though it is essential for understanding course material. Going to office hours and working in groups to complete the homework is highly recommended. Expect to spend approximately 4 to 6 hours on the homework, or much longer if you work on it by yourself.

Finally, PHYS325 has two in-class midterm exams and one final exam. Exams focus more on testing how well you understand the concepts than on your math skills, although you still need to be good at math to do the problems. Students are allowed to write their own formula sheet.

Instructors

Recently, this course has been taught by many different professors in the physics department, including Professors Holder, Witek, Kuo, and Adshead. Instructors generally have backgrounds in astrophysics.

Course Tips

Read through and take good notes on the prelectures. You are expected to be familiar with the prelecture material before lecture, as lecture mainly focuses on going over topics that students found to be the most difficult. Though the discussion sets are not mandatory, it is a very good idea to work through them diligently. Many of the problems in discussion are similar to those on the homeworks and on exams. At the beginning of the semester, find a group to work on homework with, otherwise, homeworks can take a very long time if you are not exceedingly familiar with the course material. When studying for exams, past homework and discussion problems will be the most useful resource.

Life After

Students looking to continue study in classical mechanics should take PHYS326 - Classical Mechanics II. The next step in the physics core curriculum is PHYS435 - Electromagnetic Fields I.

Infamous Topics

  • Forced oscillators: The math for this section can be intense as this is probably the first time students will see applications of differential equations and Fourier series in a physics course.
  • Calculus of variations: The derivation of the Euler-Lagrange equations is complicated, relying on mathematics that students are unfamiliar with. Students generally find the homework problems on extremization to be among the most difficult in the course.

Resources

The optional textbook, Classical Mechanics, by John Taylor, is a good resource. The instructor provides relevant sections for students to read in addition to the prelectures for greater understanding of the material.