# How to Take Physics Notes for Problem Solving

> Make physics notes that help you choose a model, explain each equation, solve a new problem, and check whether the result makes physical sense.

- Canonical page: https://brainden.app/blog/how-to-take-physics-notes-for-problem-solving
- Published: 2026-10-15
- Author: BrainDen Team
- Category: Study Methods
- Reading time: 9 min read

To take physics notes for problem solving, record the *reasoning* that connects a physical situation to an equation. For each concept, keep a small sketch, the system and assumptions, the meaning of each symbol, a worked example, and a new problem to solve without the answer visible. End with checks for units, direction, and physical plausibility. A formula list alone cannot tell you when a model applies.

Use your course materials as the authority for notation and assessment rules. Your notes should help you reconstruct a solution, not replace practice problems or your instructor's explanation.

## Why a physics formula sheet is not enough

A formula may be correct while your choice of formula is wrong. For example, an equation for constant acceleration does not apply to every motion problem. A free-body diagram can expose forces that a copied calculation hides. The important question is often what physical model fits the situation.

[MIT OpenCourseWare explains](https://www.ocw.mit.edu/courses/res-8-005-vibrations-and-waves-problem-solving-fall-2012/pages/instructor-insights/articulating-the-two-parts-of-physics-problems/) that turning a word problem into a physical picture and then into mathematics is a central difficulty. [OpenStax University Physics](https://openstax.org/books/university-physics-volume-1/pages/1-7-solving-problems-in-physics) likewise separates strategy, solution, and checking the result. Build those stages into the note itself.

A useful physics note answers four questions: What is happening? Which principle explains it? What calculation follows? How can I tell whether the answer is sensible? If you cannot answer one, mark the gap rather than filling it with a guessed step.

## What belongs in one problem-solving note?

Make a note for a concept you can use to solve a family of problems, such as conservation of energy on an incline. Do not make one giant page called “mechanics.” Keep the original lecture, textbook section, or worksheet reference near the top.

Use this compact structure:

```text
Topic and source: course, lecture, reading section, problem number
Physical situation: one sentence and a small sketch
System: the object or objects being analyzed
Known and wanted: quantities, symbols, units, and direction
Principle: why it applies here
Assumptions: what the model ignores or holds constant
Worked example: setup, algebra, substitution, result
Checks: units, sign or direction, size, limiting case
New prompt: a changed problem to solve with this note closed
Unclear point: the exact question to ask or verify
```

You do not need every field for every concept. A conceptual question may need a diagram and explanation, with no calculation. A multi-step calculation may need several equations. Keep each assumption explicit because the same symbols can describe different physical situations.

[Stanford's Physics 41 study guidance](https://ctl.stanford.edu/students/study-tips-physics-41) asks students to take active notes, explain ideas in their own words, and keep questions visible. It also recommends a routine for identifying the target quantity and given information before solving. The template above makes that routine easy to repeat.

## How to take notes during a physics lecture

### Before class: prepare the problem frame

Read the learning objective and skim any assigned example. Write the concept name and two questions. For an incline lesson, you might ask, “Which forces act along the slope?” and “When can I use energy instead of forces?” Leave room for a diagram and the instructor's reasoning.

If the lecturer provides slides, keep a slide reference. You can avoid copying a formula that already appears on the slide. Make room for what the slide may omit: why the formula applies, what changes if a condition changes, and which common mistake the instructor flags.

### During class: capture decisions, not every word

When the instructor starts an example, note the first *decision*. Did they choose the moving object as the system? Did they set a positive direction? Did they ignore friction because the problem explicitly says to? Draw a rough sketch as they speak. Record the exact symbols, units, and sign convention.

If you miss a step, write the question beside that point. For example: `Why is friction absent in the second line?` Do not silently copy the next line and assume the missing reasoning is obvious. Stanford recommends recording unfinished in-class problems and returning to them later.

If you use a lecture recording or an AI-created note, check symbols and equations against the original lecture. Speech recognition can confuse a sign, subscript, or unit. Use the recording only when your course permits it. A polished transcript is a source to review, not proof that the physics is correct.

### After class: rebuild one example without looking

Cover the worked solution and start from the problem statement. Identify the system, draw the diagram, list the givens and target, and state the principle before using numbers. Compare your setup with the instructor's. A different valid route can be useful, but verify that its assumptions and final result agree.

Then change one condition. Add friction, reverse the direction, or ask for a different unknown. You do not need to solve every variation immediately. Ask whether the original method still applies. This reveals whether you learned a reusable model or memorized one set of steps.

## A worked note: a cart on a smooth incline

Suppose a cart starts from rest on a smooth incline. It moves 2.0 m along the slope in 1.0 s. You want its acceleration along the slope. The word *smooth* means the exercise intends you to ignore friction. The simple kinematics model also assumes constant acceleration. Check those conditions in your actual course problem.

Your study note could read:

> **Situation:** A cart starts at rest and moves down a straight incline. Sketch the cart and mark down-slope as positive.
>
> **Known:** Initial speed `u = 0 m/s`, displacement `s = +2.0 m`, time `t = 1.0 s`.
>
> **Wanted:** Acceleration `a` along the slope.
>
> **Model:** For constant acceleration, `s = ut + 1/2 at²`. This equation connects the known displacement and time to the wanted acceleration.
>
> **Solve:** `a = 2(s - ut)/t² = 2(2.0 m)/(1.0 s)² = +4.0 m/s²`.
>
> **Check:** Meters divided by seconds squared gives the correct unit. The positive sign matches the chosen down-slope direction.
>
> **Next question:** If the cart starts with an up-slope speed, which sign does `u` have under the same convention?

This is a *kinematics* example, not a complete force analysis. It does not calculate the incline angle or explain what produces the acceleration. If your question asks for the angle or a friction force, add a suitable force diagram and another principle. [OpenStax's problem-solving guide](https://openstax.org/books/college-physics/pages/2-6-problem-solving-basics-for-one-dimensional-kinematics) stresses identifying knowns, unknowns, units, and a reasonable final result.

Notice what the note preserves beyond the final number: the chosen direction, the model's condition, and the reason for selecting the equation. Those details let you approach a new problem with different values. They also help you find the first error if your answer differs from the solution key.

## How to write useful equations and diagrams

### Give symbols a meaning and a direction

Write what each symbol measures in this problem. The letter `a` can mean acceleration, while an angle may be written with another symbol. A minus sign can describe a direction under your chosen axis. It does not always mean the magnitude is wrong. Include units with values and carry them through the calculation.

A formula entry should state its use condition. For example: `s = ut + 1/2 at²` belongs to a constant-acceleration model. Beside it, write a problem clue that supports the model and one clue that would make you question it. Do not attach an equation to a topic just because the same variable appears in both.

### Draw the smallest diagram that answers a question

For motion, show positions, direction, and an axis. For forces, isolate the chosen object and show the forces acting *on it*. For circuits, show components and connections. A diagram does not need to look polished. It needs to make the system and relationships unambiguous.

[OpenStax's free-body diagram guide](https://openstax.org/books/university-physics-volume-1/pages/5-7-drawing-free-body-diagrams) explains why the diagram is part of the analysis. If your sketch changes after feedback, keep a note about *why*. That correction is more useful than quietly replacing the original image.

### Check beyond the unit

Correct units are necessary but do not prove a numerical answer is correct. Compare the sign with your direction convention. Ask whether the size is plausible. Test a simple limiting case when the model allows one. For example, if a force is set to zero, does your result change in the expected way? OpenStax recommends checking units, magnitude, and sign after solving.

## How to organize physics notes for later problem sets

Keep course and unit folders stable. Give each concept note a title that names the model, such as `PHYS 101 | Motion | Constant acceleration`. Keep worksheet names and problem numbers so you can find the official question and solution. The original problem set remains the source of truth.

Connect notes when one model depends on another. A note about work and energy might link to a note about forces with a reason such as `use forces when the problem asks for acceleration`. BrainDen's [linked-notes feature](/features/linked-notes) shows how you can connect related notes without putting every topic in one file. Link selectively. A link with no reason can become another distraction.

If your notes and problem sheets are already scattered, use the broader guide to [organizing lecture notes and practice problems](/blog/how-to-organize-lecture-notes-and-practice-problems). This physics workflow adds the model, representation, and plausibility checks that each physics example needs.

After a problem set, keep a brief record of the first point where a solution failed. Use labels such as `wrong system`, `diagram`, `model choice`, `sign`, `units`, or `algebra`. Keep your first attempt and the correction distinguishable. Our [mistake-log guide](/blog/how-to-make-a-mistake-log-for-studying) explains how to turn that record into a later test.

## How to study from physics notes before an exam

Choose one problem with no method named in its title. Close the note and write a prediction: which principle applies, and why? Draw the diagram before you look up an equation. Solve with units. Then inspect the answer key and your note for the *first* point where your reasoning differs.

Repeat with a problem that looks similar but needs a different method. A force question and an energy question may share a cart and an incline, but ask for different quantities. Explain the clue that changes your choice. Stanford advises students to explain why each step works rather than only reading a solution key.

Use short recall prompts for facts or decisions: `When does constant acceleration apply?` or `Which forces belong on this diagram?` Use full problems to test multi-step reasoning. A quiz can help you identify a weak definition or method choice, but it cannot replace writing and checking a physical solution.

Start with one upcoming topic. Make one note with a checked diagram, a reasoned example, and one fresh problem. Solve the fresh problem with the note closed. If you cannot justify a step, return to the lecture, textbook, or instructor before you treat the note as complete.

If your course permits you to use your checked notes in a study tool, BrainDen can make practice questions from them. Try the [physics quiz workflow](/tools/physics-quiz-generator), then verify each question, symbol, and answer against your course material.

## Use BrainDen

Apply this workflow to your own material in the [BrainDen web app](https://learn.brainden.app), or install BrainDen for [iPhone and iPad](https://apps.apple.com/us/app/brainden-ai-study-companion/id6757434859) or [Android](https://play.google.com/store/apps/details?id=com.brainden.app).