Practical Skills II: Implementation & Measurements

• Evaluating experiments: reduce systematic errors, repeat readings, use extra apparatus (fiducial markers, set squares, plumb lines) to improve accuracy.
• Number of readings: take 3–5 repeats of every reading; record to the resolution of the instrument.
• Range of measurements: use 5–10 values, evenly spaced (steps of 1, 2, 5, or a multiple of 10), spanning as wide a range as the apparatus safely allows.
• Significant figures: know the rules for identifying them, and keep every column in a results table to the same number of s.f.
• Correcting units: every physical quantity has one correct SI-derived unit — learn them, and be able to derive them from an equation.
• Anomalous readings: spot the outlier (differs from the mean by more than ~10%, or doesn't sit near the line of best fit), ignore it in your mean, and repeat that measurement.

Think of an experiment as a chain of possible weak links. Every measurement you take has some built-in wobble to it — maybe your reaction time when you click a stopwatch, maybe your eye judging where a shadow falls on a ruler. Evaluating an experiment means hunting down those weak links and tightening them before you even start collecting data, and also reflecting on them afterwards.

There are two big levers you can pull to make an experiment better:

1. Repeat measurements and average them. Random errors (small, unpredictable wobbles) tend to cancel out when you average several readings — this boosts accuracy.
2. Reduce systematic errors. A systematic error shifts every single reading in the same direction by roughly the same amount (e.g. a ruler that's been chipped at the zero end, or a consistent parallax habit). No amount of averaging fixes this — you need a smarter method or better apparatus.

A Worked Case: Timing a Pendulum

This is the classic example examiners love, so let's really dig into why each trick works.

If you time one oscillation of a pendulum with a stopwatch, your reaction time (roughly ±0.2–0.3 s at the start and the same again at the end) is a huge chunk of a swing that might only last 1–2 seconds. That's a massive percentage error.

Fix #1 — Time over many oscillations, not one. If you time 10, 20, or more full swings and then divide the total time by the number of oscillations, your one fixed reaction-time error gets "diluted" across many swings instead of dominating a single one. The absolute error in your stopwatch reading stays the same, but the error per oscillation shrinks enormously.

Fix #2 — Use a fiducial marker. fastest slowest

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set square