Every time I teach the undergraduate physics course on classical mechanics, I change things just a little bit. However, after this latest semester I think I have some material that works fairly well. What follows below are the topics I cover in the course along with any worksheets and videos I created for my students.
Feel free to use this for your own learning or your own course, it’s here for you (and for me when I forget what I did).
Course Details
This I an undergraduate physics course covering classical mechanics. The assigned text book is Classical Mechanics by John R. Taylor (University Science Books). I think it’s a fine book, but no textbook is perfect. As for the course goals, my only real main objective was to get through Lagrangian Mechanics. Yes, this is often a topic for the second semester of classical mechanics–but it’s possible that our students only take the first semester so I put that topic in the first semester.
Oh, python. You know I’m going to include using numerical calculations to solve problems. I like to use Web VPython because the students don’t have to install anything. Here is my syllabus.
OK, let’s get into it. I’m going to post links to my video lectures, worksheets, and tests.
Newtonian Mechanics and Coordinate Systems
This is mostly from chapter 1 in Taylor. The key ideas are to look at solving problems (and differential equations) using Newton’s second law and to write Newton’s second law in polar coordinates. I mean, I guess you could do spherical coordinates too–but that gets very messy.
- Newtonian mechanics practice problems (pdf)
- Mass on a Spring (video)
- Pulling a block with friction (video)
- Newton’s 2nd law in polar coordinates to solve for the motion of a pendulum (derivation include) (video) Note: this includes coding a solution in python
- Solving for the motion of a pendulum with Jupyter notebooks (video)
- Polar coordinates worksheet (pdf)
- Example: mass on a vertical cylinder (video)
- Test 1: Newtonian and Coordinates (pdf)
Velocity Dependent Forces
This is from chapter 2 in Taylor. Really, it’s just more practice using Newton’s second law to solve some differential equations.
- Velocity dependent forces worksheet (pdf)
- Modeling motion with drag in python (pdf)
- Linear drag and horizontal motion (video)
- Falling with linear drag (video)
- 2D projectile motion with linear drag (video)
- Horizontal motion with quadratic drag (video)
- Falling with quadratic drag (video)
- Physics question: two balls are tossed up. Which one reaches the highest point first, the one with or the one without air resistance? (video)
- Which ball hits the ground first – a horizontal launched ball or a dropped ball? (video)
- Test 2: Velocity dependent forces (pdf)
Work Energy Principle
Chapter 4 from the Taylor textbook. I skipped chapter 3 on momentum and angular momentum. Maybe that was a bad idea, but it just seems like it focused mainly on the rocket equation (which is actually just kind of silly). Oh, there’s also the center of mass and stuff–but we will get to that in the second semester of Classical Mechanics.
- Worksheet: Intro to work energy and line integrals (pdf)
- Tutorial: Line integrals in python (pdf)
- Intro to the work energy principle (video)
- Work energy and line integrals (video)
- Numerical line integrals with python (video)
- Vector fields and line integrals around closed paths (video)
- Conservative forces and the vector curl (video)
- Calculating the work done by the normal force (video)
- Physics problem: when does a block of ice lose contact with an inverted sphere-work energy method (video)
- Physics problem: block sliding down a movable wedge (energy method) (video)
- Demonstration of the Virial Theroem (video)
- Using potential energy to determine stable equilibrium (video)
- Test 3: Work Energy and Line Integrals (pdf)
Non Inertial Reference Frames
Chapter 9 from Taylor. Yes, I know I took a large jump forward. I wanted to go over this now rather than in the second semester for a few reasons. First, this is a great place to reuse our ideas about acceleration in polar coordinates (for rotating reference frames). Second, fake forces are cool and students think about them anyway. Finally, I like talking about the tides. Students rarely understand the tides before this sections.
- Worksheet: Non Inertial Reference Frames (linear and rotational) (pdf)
- Python tutorial: modeling motion in a rotating reference frame (pdf)
- Practice problems: non inertial reference frames (pdf)
- Derivation of centrifugal and coriolis forces (video)
- What causes the Earth’s tides? (video)
- Physics problem: Object dropped from a tower with Coriolis force (video)
- Python physics: modeling the motion of a rock kicked on a rotating asteroid (video)
- Python physics: ball thrown in a rotating space station (video)
- Modeling the Foucault pendulum (video)
- Test 4: Non Inertial Reference Frames (pdf)
Lagrangian Mechanics
This is what we have been waiting for. OK, maybe it’s just me. This is from chapter 7 of Taylor. I skipped chapter 6 on the variational principle. Yes, you need that for Lagrangian mechanics but I’ve found that students don’t really get that part too well. If we just accept the Euler-Lagrange equation, we can move on – so that’s what I do.
- Worksheet: Lagrangian Mechanics (pdf)
- Tutorial Example: Chain sliding off a table – python included (pdf)
- Intro to Lagrangian mechanics (video)
- Not my video, but this Veritasium video on the variational principle is legit (video)
- Example: motion along three different paths (video)
- Example: jiggle pendulum – pendulum on an oscillating mount (video)
- Python physics: using Sympy to solve Lagrangian problems (video)
- Example: bead on a rotating hoop (video)
- Example: mass on a table with a hole (video)
- Example: chain sliding off a table (video)
- Lagrangian multipliers and force of constraint – mass sliding off a sphere (again) (video)
- Force of constraint: would a mass fall off a parabolic path? (video)
- Example: bead on a rotating wire – and what happens when it leaves? (video)
- Test 4: Lagrangian Mechanics (pdf)
Course Summary
Maybe I should have put this at the beginning.
That’s it.