The first three lessons built a chain of decisions: choose what to study, express the quantities consistently, and compare predictions with measurements. Use this checklist to carry that chain into an investigation. Record your choices before calculating, then return to them when you judge the result. The linked lessons explain each part: Physical Models, Systems, and Frames, Units, Dimensions, and Estimation, and Measurement and Model Testing.
Before choosing equations
| Check | Record | If you cannot answer |
|---|---|---|
| Question | The precise prediction or comparison sought | Narrow the question before calculating |
| Observable | What a ruler, clock, detector, or observation would report | Define a measurement procedure |
| System | Objects inside the selected boundary | Draw and label the boundary |
| Environment | Relevant objects outside it and interactions crossing it | Inspect contacts and other interactions |
| Reference | Reference objects, clock origin, coordinate origin, positive directions | Make the description reproducible |
| Idealization | Particle, rigid body, or other stated simplification | Ask which size, orientation, or deformation information matters |
| Conditions | Where and when the assumptions are expected to work | Restrict the claim or refine the model |
For numerical uncertainty comparisons in the record below, first read Uncertainty Bounds and Comparing Results.
Before trusting a number
Once the system, frame, and assumptions are clear, check how the numbers describe them. The units must preserve the meaning of each quantity, and the uncertainty must reflect the measurement procedure. These checks connect the calculation back to the question you recorded above.
| Check | Record | Warning sign |
|---|---|---|
| Quantities | Symbol meanings and units for every input and output | A number without a unit or a symbol whose meaning changes |
| Conversions | Factors equal to one, with unwanted units canceling | A squared or cubed unit converted only once |
| Dimensions | Matching dimensions for quantities equated or added | Length added to time; dimensions treated as proof of a law |
| Estimate | A plausible scale or range and its assumptions | A precise answer far outside the justified estimate |
| Measurement | Instrument, start/end events, calibration, resolution | Treating the last display digit as the entire uncertainty |
| Uncertainty | Interval or other interpretation, plus its justification | An unexplained ± value or scatter called a confidence interval |
| Arithmetic | Bounds/domains checked; intermediate digits retained | Division by an interval containing zero; early rounding |
| Evidence | Prediction and observation for the same conditions | Synthetic or simulated data presented as experimental evidence |
Choose “not applicable” only with a reason. A qualitative model may not require numerical conversions, but it still needs assumptions and an observable.
A completed falling-object record
Return to the falling-object comparison from the first lesson. Here the question is whether two compact balls have distinguishable arrival times. The record below shows how the model choices, units, and measurement checks work together to support a limited conclusion.
This is an invented practice record. It illustrates how to record a comparison; it does not establish experimental evidence or derive a free-fall law.
| Item | Practice entry |
|---|---|
| Question and observable | Do two compact balls have distinguishable release-to-arrival times? Time the ball’s bottom reaching a specified detector level |
| System | Each ball considered separately |
| Environment | Earth and air; detector contact occurs at the end of the measured interval |
| Frame and coordinates | Room frame; upward positive; detector level is height zero; each timer starts at its own release event |
| Model | Represent each ball by a particle; neglect air resistance and assume the same approximately uniform gravitational conditions |
| Supplied prediction | Equal arrival times from rest if the initial bottom heights match; its derivation belongs to later motion/dynamics lessons |
| Inputs | Bottom-to-detector release height m for each ball; common release method; no deliberate initial push |
| Practice observations | A: s; B: s |
| Meaning of bounds | Assume a prior calibration and release/detection check justify the stated enclosing intervals; sample scatter alone would not justify them |
| Comparison | A allows 0.48–0.52 s; B allows 0.49–0.53 s; overlap is 0.49–0.52 s |
| Conclusion | These observations do not distinguish the arrival times under the stated bounds. They do not prove the model or establish exact equality |
| Next test | Reduce timing limitations or change shape while retaining matched initial conditions; reconsider air resistance if a reproducible difference becomes distinguishable |
The height unit conversion is m = cm; changing the unit changes neither the drop nor its uncertainty. The height bound becomes ±1 cm. Comparing time with time passes the dimension check. There is no quantitative predicted arrival time in this record, so do not invent a calculated residual from it.
Reference routing
For unit systems and conversions: Halliday, Resnick, and Walker, Fundamentals of Physics, 10th edition, chapter 1. For dimensions, measurement, estimates, coordinates, and problem-solving checks: Serway and Vuille, College Physics, 9th edition, §§1.3–1.9. Its trigonometry section is useful later for plane geometry, but this checklist does not require it. For physical quantities and reporting precision: Verma, Concepts of Physics, part 1, chapter 1 and §§2.12–2.14. Consult the linked lessons for the conceptual explanations and cautions.