Physics route · lesson 1 of 5
- 01Measurement and uncertaintyUnseen
- 02Motion and interactionUnseen
- 03Energy and conservationUnseen
- 04Waves and informationUnseen
- 05Fields, models, and limitsUnseen
Physics / Field trial lesson 01
Measurement and uncertainty
Turn an instrument reading into an honest claim by naming the method, separating scatter from offset, and reporting only the precision the evidence supports.
- Study time
- Awaiting learner observation
- Evidence
- Unseen
- Candidate
- 0.1-foundations-candidate
- Review
- Named human reviews pending
A reading becomes evidence only when the procedure travels with it
“The period is 2.4” is not yet a physical result. Which event started the timer? Which event stopped it? Was one swing or ten swings timed? What unit did the display use? What was the instrument's smallest step? Could another observer repeat the same procedure?
Measurement connects a phenomenon to a comparison standard through an operation. The reported number is therefore a claim about the phenomenon, the instrument, and the method together. Leaving out the unit or uncertainty does not make the measurement cleaner; it hides part of what is known.
Repetition shows scatter; a reference exposes offset
Repeated trials can reveal how much a procedure varies. A tight cluster is precise; a broad cluster is less precise. But the cluster's centre may still be displaced from an accepted reference. That displacement is a discrepancy and can arise from a shared calibration offset or another systematic effect.
Repetition alone cannot diagnose every shared offset because the same shift can affect every trial. To test accuracy, compare with a defensible reference, reverse the method when possible, or use an independent instrument or calibration procedure.
Read the figure description
Plot A has closely packed measurements centred on 10.0 centimetres and is both precise and accurate. Plot B has measurements spread from 9.6 to 10.4 centimetres but centred near 10.0, so it is less precise while its centre is accurate. Plot C has closely packed measurements near 10.5 centimetres, so it is precise but discrepant from the 10.0-centimetre reference.
| Diagnostic | Evidence it provides | Blind spot |
|---|---|---|
| Read the smallest display or scale step | Instrument resolution | Does not expose calibration offset |
| Repeat the same procedure | Trial-to-trial scatter and repeatability | A shared shift may remain hidden |
| Measure a trusted reference | Discrepancy from the reference | Reference itself has uncertainty |
| Change observer or method | Sensitivity to procedural choices | New method may add different effects |
Compute a summary without pretending it is the whole experiment
Worked example
Worked example — report repeated timing trials
Five period measurements are 2.38 s, 2.42 s, 2.39 s, 2.41 s, and 2.40 s. Use the mean as the best estimate and half the range as a simple uncertainty convention.
- Add the five values to obtain 12.00 s, then divide by 5. The mean is 2.400 s.
- Find the range: 2.42 s minus 2.38 s equals 0.04 s.
- Half the range is 0.02 s. State explicitly that half-range, not a standard deviation or confidence interval, is the chosen convention.
- Round the best estimate to the same decimal place as the uncertainty.
- Report 2.40 plus or minus 0.02 s using the stated repeated-timing procedure.
ConclusionThe result is 2.40 ± 0.02 s, where 0.02 s is half the observed range. It summarizes repeatability but does not rule out a shared timer offset.
Worked example
Worked example — decide whether a stopwatch can separate two results
A stopwatch has stated uncertainty ±0.05 s. Two sprint times are 12.04 s and 12.07 s. Can the display alone support the claim that the second runner was 0.03 s slower?
- Compute the displayed difference: 12.07 s minus 12.04 s equals 0.03 s.
- Compare that difference with the stated uncertainty scale of 0.05 s for each timing.
- The difference is smaller than even one timing's stated uncertainty, so the intervals overlap substantially.
- Extra decimal places in the display do not reduce the stated uncertainty.
ConclusionThese readings do not support a confident ordering at a 0.03 s separation with this uncertainty. The limitation belongs in the conclusion.
Hide an offset inside a convincing cluster
Prediction before motion
Hold scatter fixed and increase the hidden zero offset. Predict what happens to the cluster width, cluster centre, precision, and accuracy before revealing the reference.
- Invariant
- Repetition changes the estimate of the cluster and its scatter; a constant zero offset shifts every trial and is only identifiable against a reference or independent calibration.
- Observe
- Run repeated trials, then reveal the reference. Which feature diagnosed scatter and which comparison exposed the shared offset?
- Static account
- For a true value of 10.0 cm, low scatter with zero offset produces a tight cluster near 10.0 cm. The same scatter with a +0.5 cm offset produces an equally tight cluster near 10.5 cm. Precision is similar; accuracy is not.
Design a comparison that can fail honestly
The transfer task asks you to compare two pendulum periods. A useful design identifies the start and stop events, times multiple cycles to reduce reaction-time influence, repeats trials, states a summary and uncertainty convention, and checks for at least one systematic effect such as timer calibration or inconsistent release angle.
A strong conclusion is conditional. It says what the measurements distinguish at the achieved uncertainty and what remains unresolved. That is not weakness; it is the boundary that makes the claim trustworthy.
The frozen 0.1-preview release record retains the earlier sketch and manifest.