Teaching yourself physics from a textbook comes down to five moves:
- Take a curriculum off the shelf rather than inventing one. Susan Fowler’s “So You Want to Learn Physics…” is the most complete free physics syllabus we have found — nine undergraduate topics in order, the books for each, and the maths you need first. Start there, not with a plan of your own.
- Get one real textbook and stay in it. OpenStax’s University Physics is a free, openly licensed (CC BY-NC-SA 4.0) three-volume sequence, readable in a browser or as a PDF.
- Work problems from the first day, not once the chapter “makes sense.” Reading physics is not learning physics, and the gap between the two is invisible from the inside.
- Write the account before you look at the answer. Three or four sentences, in words, no equations: which principle you used, why that one, what happens to the answer if a quantity doubles, what you assumed. Then check the number.
- Bring the chapter back weeks later. Mechanics decays while you are busy with thermodynamics.
Step 4 is the step the standard self-study guides leave out, and it is what this post is about. Not because working problems is wrong — that is the whole subject. But because the check that follows a problem, in every guide that ranks for this question, is compare my number to the printed number. Physics has spent more than thirty years publishing evidence, in its own journals, that this particular check does not tell you what you think it tells you.
What the best physics self-study guides tell you to do
Fowler’s guide deserves its position. It is a genuine curriculum rather than a book list: nine undergraduate topics from introductory mechanics to thermodynamics and statistical mechanics, six graduate ones ending in quantum field theory, with the named textbooks and the required mathematics for each. If you want the sequence, take it and stop reading roadmaps — the same conclusion we came to about teaching yourself philosophy without a teacher, where the reading orders are also solved and also not the hard part.
Here is the guide’s complete advice on how you know your work is right:
“you’ll still need to solve the physics problems in each textbook. Solving problems is the only way to really understand how the laws of physics work.”
“make sure you can solve problems at the end of each chapter before continuing”
and, on where the verification comes from:
“the solutions are easy to find online”
That is the whole checking method. It is not an oversight peculiar to one guide — it is the consensus. Autodidact Society’s physics guide states it plainly: “solve the questions and then refer back to the answers to test your understanding.” Nerd Notes (21 September 2025) prescribes volume — “For each unit, set aside time to tackle around 100 problems” — and its own AI grader is scoped to its own bank, marking “300+ included questions,” not the textbook on your desk.
Strip those three pages down and you get the same instrument in all of them: you produce a number, and a number in the back of a book adjudicates. None of the three mentions conceptual self-assessment, misconceptions, or physics education research — which is odd, because that field exists, it is large, and it was built specifically to answer the question their readers are asking.
Why a right answer is weak evidence in physics
Eric Mazur, teaching an introductory physics course for engineering and science majors at Harvard, ran the experiment on that very class. Having read Halloun and Hestenes’ finding that instruction “does little to change” students’ common-sense beliefs about force and motion, the first reaction was, in Mazur’s own words, “Not my students…!” So the test went to the class.
From Mazur’s account of what happened (adapted from Peer Instruction: A User’s Manual, Prentice Hall, 1997):
“The first warning came when I gave the Halloun and Hestenes test to my class and a student asked, ‘Professor Mazur, how should I answer these questions? According to what you taught us, or by the way I think about these things?’”
Sit with that question for a second, because it is the whole problem in one sentence from a student who could clearly do the coursework. There were two separate systems in that student’s head — the one that produced correct answers on physics problems, and the one that actually predicted how the world behaves — and the student knew it.
Mazur then paired a purely conceptual question about a simple dc circuit with a harder numerical question on the same concept, and set them as the first and last problem of a midterm in the spring of 1991. The results:
“over 40% of the students believed that closing the switch doesn’t change the current through the battery but that the current splits into two at the top junction and rejoins at the bottom! In spite of this serious misconception, many still managed to correctly solve the mathematical problem.”
“39% of the students did substantially worse on the conceptual question. (Note that a number of students managed to score zero on the conceptual question and 10 on the conventional one!) Conversely, far fewer students (9%) did worse on the conventional question.”
The conclusion drawn in the paper, verbatim: “it is possible for students to do well on conventional problems by memorizing algorithms without understanding the underlying physics.” And the students were fooled too — “they believe they master the material and then are severely frustrated when they discover that their plug-and-chug recipe doesn’t work in a different problem.”
This is not one lecturer’s anecdote. It is the finding that produced an entire measurement literature. David Hestenes, writing in the American Journal of Physics in 1998, reported the number that gets quoted most:
“for a typical University Physics course we found that nearly 80% of the students could state Newton’s Third Law at the beginning of the course, while FCI data showed that less than 15% of them fully understood it at the end.”
(David Hestenes, “Who needs physics education research!?”, American Journal of Physics 66: 465–467, 1998. The FCI is the Force Concept Inventory: Hestenes, Wells and Swackhamer, The Physics Teacher 30(3), 141–158, March 1992.)
In the same paper, discussing an FCI item the test’s own authors judged defective, Hestenes names the failure mode exactly: “too many students chose the Newtonian response for nonNewtonian reasons.”
The right answer for the wrong reasons. That is a thing the back of the book cannot see. The reverse case is rarer — 9% of Mazur’s class did worse on the numerical question than the conceptual one — and more demoralising: you understood the physics, dropped a factor of two in the algebra, and the answer key tells you you were wrong about a concept you had correct.
So the self-learner’s one feedback instrument reports a bit — match, no match — about a question it was never able to answer.
The one diagnostic that would settle it is not available to you
The natural response is: fine, then test the concepts directly. There is a well-validated instrument for exactly that, the Force Concept Inventory — thirty multiple-choice questions, no calculations, in wide use since 1992.
You cannot have it. PhysPort’s FCI page states the policy in one line:
“Downloads are restricted to high school and college faculty.”
The restriction is defensible — a concept inventory stops working the moment its answers circulate. But look at the position it leaves you in. The instrument that established that your answer-checking is unreliable is behind an instructor login.
The textbooks work the same way. OpenStax University Physics is free and openly licensed, and the preface to Volume 1 tells you that “odd-numbered answers to Conceptual Questions, Problems, Additional Problems, and Challenge Problems are also provided in the Answer Key” — while the even-numbered answers are “provided only to instructors in the Instructor Answer Guide,” reachable only by verified instructor accounts. Half the problems in OpenStax have no answer you can see, and the half that do give you a number.
This is a different shape of hole from the ones we have found in other subjects. In linear algebra the answer key mostly doesn’t exist. In economics the keys exist and are excellent, and cannot read a sentence. In Kant the misreading happens silently while you read, and the difficulty at least announces itself. In physics the key exists, it is free, it is instant — and it is a number, and a number cannot tell correct reasoning from a lucky recipe.
How do you check your physics when you’re studying alone?
Here is the procedure. It costs nothing and you can start it on the next problem you do.
Write the account before you look at the answer. After you have a numerical result and before you turn to the back, write three or four sentences in plain words with no equations in them:
- Which principle or law did this problem turn on, and why that one rather than a neighbouring one?
- What is the answer doing physically — which direction, which sign, on what?
- If I doubled one given quantity, what happens to the result, and why?
- What did I assume that the problem didn’t state? Frictionless, massless, quasi-static, non-relativistic, small angle?
Then check the number. You now have two verdicts instead of one, and the interesting cases are where they disagree. Right number, incoherent account — that is Mazur’s 40%, and it is the case the answer key silently passes. Wrong number, sound account — an arithmetic slip, and you should not spend the evening re-reading the chapter over it.
Two further habits genuinely help:
- Do the Conceptual Questions, not just the Problems. Most intro textbooks separate them, and most self-learners skip the qualitative ones because they don’t feel like real work. They are the closest thing to a concept inventory you can actually get, and in OpenStax the odd-numbered ones have published answers.
- Predict before you compute. Say out loud what the answer should look like — order of magnitude, sign, limiting behaviour as a variable goes to zero or infinity — and commit to it before doing the algebra. A prediction is falsifiable in a way a worked solution is not.
Neither closes the loop. Both still end with you judging your own account, which is the documented weak point of studying alone. And notice what the free stack marks:
| What you produce | What checks it, free |
|---|---|
| A number | The answer key — odd-numbered problems only |
| A conceptual multiple-choice answer | Textbook Conceptual Questions, odd-numbered |
| Your written account of why | Nothing |
| A whole solution, at your own pace, repeatedly | A forum thread, when someone has time |
That third row is the gap, and it is the row that Mazur’s experiment says matters most.
The one genuinely good answer available today is a human. Physics Forums has people who will read your reasoning and tell you where it broke, and a physicist reading your work beats every automated option in this article. It is also unscheduled, unrepeatable, and not there at eleven on a Tuesday when you are stuck on rotational dynamics. Among the automated tools, Nerd Notes’ Phy does grade submissions, inside its own question bank; Physics AI explains solutions well for $6 a month and is explicit that it is “designed to support understanding, practice, and self-study — not to replace your own work.” What none of them does is read the account you wrote about the chapter you are working through.
Studying physics with Study Junkie
That last row is the thing Study Junkie is built for. You upload the textbook — the actual PDF you are working from — and it becomes a chaptered course generated from the full text, never a summary of it. The tutor chat is grounded in that book, so when you ask why the normal force does no work, the answer comes from your source’s treatment rather than from the internet’s average opinion. The course sets problems from the chapter you just read, you submit written work, and the feedback addresses what you wrote. Then it schedules the material to come back, because misconceptions are exactly the thing that returns quietly once you have moved on.
We would rather show it than assert it. The recorded run we have is on mathematics rather than physics — Study Junkie working through Jim Hefferon’s open Linear Algebra: the book becomes a course, the course sets a linear-systems problem, a written solution goes in, and the feedback locates the exact sign error and shows where it happened. Then one-, three- and seven-day recall. The loop is identical on a physics chapter — the recorded run we happen to have is mathematics.
Honest limits. An AI reading your physics textbook is not a physicist, and it will be more useful on your reasoning about a chapter’s own material than on a research-level question. A textbook’s worked solutions beat us on the problems they actually cover — use them. Fowler’s curriculum is better than any sequence we would generate, and it is free. If you have access to a person who knows mechanics and will read what you wrote, use the person.
If you want to try it on the chapter you are stuck in now: signing up gives you 1,500 free Study Credits, no card. After that it is one-time credit packs — $10, $25 or $50 — that never expire and only spend when you generate something. No subscription, which matters when you read a textbook in bursts rather than on a term schedule. You can see how the read, practise and recall loop fits together before signing up for anything.
FAQ
How do I know if I actually understand physics? Separate the two verdicts. Solving a numerical problem correctly and explaining the physics in words are different skills, and physics education research has measured the gap directly: in Eric Mazur’s spring 1991 midterm, 39% of students did substantially worse on a conceptual circuits question than on a harder numerical one on the same concept, and some scored zero on the conceptual question and 10 on the numerical one. If you have never written the qualitative explanation, you have never tested the half that fails first.
Should I do every problem in the physics textbook? Fowler’s guide says to work through “every single problem in the book,” and Nerd Notes suggests around 100 per unit. Both are defensible if you have the time. If you don’t, the higher-yield trade is fewer problems with a written account attached to each than more problems checked against the key alone — the account is where a misconception becomes visible.
What’s the best physics textbook for self-study? The one whose problems have answers you can reach and whose level matches your maths. OpenStax’s University Physics is free, openly licensed and covers the full introductory sequence across three volumes, with odd-numbered answers published. Fowler’s guide names harder canonical texts topic by topic, with the required mathematics for each — worth following once you have finished a first pass on mechanics.
Can I learn physics without the maths? You can learn about physics without it. Doing physics is applying principles quantitatively, and the mathematics is the medium, not a barrier in front of the subject. The honest sequence is to fix the maths gap first: our post on self-studying linear algebra when there’s no answer key covers the same checking problem one level down, and the bridge from popular science to real science covers why the prerequisite hierarchy is the path rather than the obstacle.
How do I stop forgetting mechanics while I’m doing thermodynamics? Schedule the return rather than trusting that you’ll notice the decay — you won’t, because recognising a chapter feels identical to knowing it. Spaced repetition for books, without making flashcards walks through doing this from the source material rather than by hand-building a deck.