How I Self-Studied MIT OCW 8.01, Classical Mechanics, in 297 hours

I took 297 hours to complete 8.01.

I have also completed 18.01SC (single variable calculus), 18.02SC (multivariable calculus), and 18.03SC (differential equations), and have written about my experience completing18.01SC. That post has more details about my overall approach to completing these courses. This post details what I thought of 8.01SC specifically.

I’d like to point you to a Github repository where I have uploaded my lecture notes, problem set solutions, notes from readings, etc.

How the 8.01SC is Organized

On MIT OCW, certain courses are called “scholar” courses. The materials are all from the original MIT courses, but MIT OCW took steps to organize the material in a specific way that can be helpful for online learning.

In the case of 8.01SC, the material is organized in twelve weeks. Each week is about a specific topic, e.g. kinematics in week 1, continuous mass transfer in week 6, or angular momentum in week 11.

The courses I have done so far have been based on full length lectures of between 40 and 60 minutes. In 8.01SC, the lectures are broken up into snippets of between roughly 2 and 15 minutes.

What I loved about this structure is that each video is absolutely straight to the point. Sometimes a concept is introduced, sometimes the lecturer works through a specific problem (aka “worked example”). There is absolutely no wasted time in each video lecture.

Normally in a full length lecture the lecturer is pausing between ideas and concepts, making a joke, perhaps pacing to and fro, looking through his/her notes, etc.

Nothing wrong with any of this, but if instead the lecturer were to make a video for each part of a lecture where he develops an idea, concept, or calculation from start to finish, he’d probably end up with a shorter total time of recording. This is what 8.01’s video lectures are like: straight to the point and not as long as regular lectures. Some people might say “well, I like the interaction, the jokes, etc”.

For me, I’m great with the efficiency of 8.01 and I prefer this style.

Problem Sets

There are twelve problem sets, each with about five problems. Each problem usually requires a lot of thinking. They are pretty hard, especially if you are interested in understanding every aspect of the problem.

Important to note that the MIT OCW site does not contain solutions to the problems. I found solutions scattered on the internet and also on this website called Chegg. However, now my repository contains my solutions to all the problems, so hopefully if anyone takes this course they can use my solutions for comparison (and let me know if any of my solutions are incorrect!).

For example, there was one problem in the final problem set involving a ball rolling inside of a circular ring that was moving with a constant velocity. The problem was actually pretty simple: it just asked what the velocity of the center of mass of the ball was under certain conditions (that the ball wasn’t slipping on the surface of the ring).

I actually spent about a day and a half exploring different scenarios

• How would a ball actually reach that state of no slipping if it started at rest on one side of the ring and rolled down?
• As this proved difficult to reason about at first, I considered simpler cases: a ball on a horizontal surface; then the horizontal surface moving at a constant velocity; then I inclined the surface, but still a straight surface
• As I consider each case, I am asking questions and expressing them in equations. “Is the ball initially slipping?”, “Does the ball even rotate if there is no friction with the ring?”, “What if there is no gravity?”, “Is the friction kinetic or static”, “What is the velocity of the contact point of the ball with the ring from the perspective of the ring, ie the reference frame of the ring?”, “How long does it take for no slipping to occur?”, “What happens after that?”, etc, etc, etc.
• This sort of tinkering can take hours and hours, but I think it is essential. It is more worthwhile, in my opinion, to go through one of these sessions of just asking questions and answering them in with mathematical equations than solving fifty end-of-chapter exercises from University Physics.
• The reason is that you not only have to use all the concepts you are learning (and not just the one specific one perhaps being used in a simple problem), but you also have to use the mathematical tools you learned to deal with the physics. In the case of 8.01, this is basically vector calculus, integration, and differentiation. You get lots of practice with these topics.
• By the way, this sort of tinkering is why I spent 297 hours on the course and not, say 197 hours.

Exams

There are no exams in this course.

This is actually pretty nice and interesting. Usually problem sets contain the hardest problems that take the longest and require the most thinking. Such problems aren’t placed on an exam because of the time constraint. This makes exams a strange entity, in the sense that they aren’t as technically challenging as problem sets, yet they can be more challenging simply because of the pressure (to do well, or to not fail, or because there is a time constraint). Exams are one of these things that are made as a one size fits all thing meant to suffice in the face of the reality that we are all different from one another. Academia and learning is so antiquated, so old-fashioned. This is all ripe for disruption.

Materials and Tools I Used

Textbook

The course is based on course notes, which if we were to print them out I believe they would constitute a book with several hundred pages. The notes are very, very good and heavily based on Calculus. The latter fact makes the notes more challenging than certain widely used college-level introductory physics textbooks such as “University Physics”.

Not that you can’t use a book like that one. I used University Physics in addition to the notes for basically three topics: work, energy, rotational motion and angular momentum.

• Week 7: Kinetic Energy and Work
• Week 8: Potential Energy and Energy Conservation
• Week 10: Rotational Motion
• Week 11: Angular Momentum

Maple

I really took my fluency and skills in Maple to another level during this course. I am not an expert by any means, but I can quickly use Maple to speed up my work, check my results, or explore scenarios that interest me.

For example, if I have a system of equations, I may use Maple to solve it for me. If I find an expression containing certain variables, I may use Maple to plot one variable against another variable given values of the remaining ones.

I also use Maple to solve differential equations, though these were very few in 8.01 and not really necessary. I just used them in particular cases in my “tinkering” mode.

I would highly, highly recommend using a program like Maple.

Physics StackExchange

As I mentioned previously, many times I really start asking “what if” questions about a problem. I can go hours thinking about such questions, but at some point I ask for help if I can’t figure it out. As I mentioned in a section in a previous article about 18.01, different communities on StackExchange have different “personalities”. Math has so far been the most friendly. Physics is also a relatively friendly community, though I had some “incidents”.

PhysicsForums

Towards the end of 8.01, I discovered the forums at physicsforums.com.

This is my go to for posting my questions now. I tend to spend a lot of time, whether on physicsforums or physics stackexchange, writing out the latex equations in full, and making sure my questions are well-written. It can take me an hour to think a question through and write out the equations. Ultimately, this isn’t lost time in my opinion: it forces me to have to think through what I have been mulling over and sometimes in the process I either find the answer or find a mistake in my reasoning.

Why Did I Take So Long?

8.01 is a twelve credit course from MIT, which takes an estimated 168 hours to complete. In my original post on completing 18.01SC, I wrote a few paragraphs about how this estimation is calculated.

I took a very long time to complete this course because I really spent a lot of time on each problem in the problem sets, and I just spent a lot of time thinking. Really thinking about things in my head. Usually I would get up from the desk and go lie down, and jus think about a particular problem or concept. I would try and go through equations in my head, and think about particular aspects of a problem that I was trying to solve.

Bottom Line

It feels very rewarding to complete 8.01SC. Physics is hard, and it is hard in a way that is very different from mathematics. It is quite different solving a difficult math problem than solving a difficult physics problem, at least a classical mechanics problem.

You can usually directly visualize the problem, and it can be something relatively mundane like a ball rolling down an incline, or something as spectacular as a rocket taking off from a planet, or a satellite on a fly-by of the Earth. The thing is, even something as mundane as a ball rolling down an incline has multiple aspects to it: friction, rotation, type of ball, is the surface moving, etc.

Coming from recent courses in Calculus, the opportunity to apply the skills acquired there was great, especially if you decide to “tinker” around with the problems.

I feel very ready to push on and continue with 8.02, Electromagnetism.