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. A fiducial marker is just a fixed reference point (a pin, a piece of tape, a pointer) placed exactly where the pendulum passes through its equilibrium (centre) position. Why does this help? Because the pendulum moves fastest at the bottom of its swing and slowest at the top (where it momentarily stops to change direction). If you tried to time the pendulum at the top of its swing, it would be really hard to judge exactly when it "turns around" — it's barely moving, so your eye can't pin down the exact instant. But at the bottom, sighting against a fixed marker as the bob whips past gives you a much sharper, more precise moment to start/stop your stopwatch.

B Apparatus for Alignment: Set Squares & Plumb Lines

A set square is just a right-angled triangular plate. In practical physics it's a cheap, precise way to check that two things are truly perpendicular or parallel — far more reliable than eyeballing it.

• Checking a ruler is vertical to measure spring extension — align the set square's right-angle edge with the ruler and the base of the spring, so ruler ∥ spring's line of action.
• A plumb line (string with a weight) always hangs perfectly vertically due to gravity — use it alongside a set square to confirm a rig is truly upright.
• Measuring the diameter of a cylinder: place two set squares against either side of the cylinder, flush against a ruler. This guarantees the ruler reads the true diameter perpendicular to the cylinder's edges, instead of a slightly-off diagonal measurement made "by eye."

Every measurement you take has some uncertainty baked into it. Take it just once, and you have no way of knowing whether that single number was a fluke — too high, too low, or bang on. Take it several times, and patterns emerge: you can average out the noise and get a genuine sense of how reliable your data actually is.

Here's an example results table with the right number of readings for measuring how time falls for an object dropped from different heights:

Why does repeating readings actually help? Three separate reasons, and it's worth knowing all three because exam mark schemes reward you for naming the right one for the context:

• Increases precision — averaging multiple readings smooths out the small random scatter in each individual measurement.
• Increases confidence / reliability — it shows the result isn't just a one-off fluke; if your three repeats are all close together, you can trust the value more.
• Lets you quantify uncertainty — the spread of your repeats gives you a number for how uncertain your measurement is.

You also need to record data to a sensible, consistent number of decimal places — this should match the resolution of whatever instrument you used.

Number of readings tells you how many times to measure at each point. Range is a different question entirely: how far apart should your data points be spread out? A cluster of values crammed into a tiny range can completely hide the true shape of a relationship — you might think a graph is a straight line when actually it curves sharply just outside the range you tested.

8 values, step of 0.25 m — a good, evenly-spaced range ✓

A Two things limit your range

• The measuring instrument's own limits. A standard ruler is 1 m long — asking for a range up to 5 m using one ruler is impractical and error-prone (you'd need to reposition it multiple times, introducing extra error). Likewise, the smallest reading should stay comfortably above the instrument's resolution — for a ruler with 1 mm divisions, don't try to read down to 0.1 mm.
• The apparatus's physical limits. Stretch a spring too far and it passes its elastic limit — permanently deforming it and ruining the experiment. Push current/voltage too high in a circuit and components can overheat, fuse, or catch fire. Your range's maximum must sit safely below any such limit.

B Why a wide range actually matters (not just "more data")

This is the part students often gloss over — a wide range isn't just "nice to have," it's often the only way to discover the true relationship between two variables.

Significant figures (s.f.) are the digits in a number that actually carry meaning about how precisely you know that value. Get the rules solid — they come up constantly, both for rounding answers and for spotting errors in given data tables.

A The Five Rules

B How to Round to N Significant Figures

1. Identify the significant figures using the rules above.
2. Count from the first significant figure up to your target number.
3. Look at the next digit along — this is your "rounder decider."
4. If the decider is 5 or more, round the previous digit up by 1. If less than 5, leave it as is.

C Consistency in Results Tables

Every value in a given column of a results table should be recorded to the same number of significant figures — usually matching the resolution of the instrument used (often this ends up being 3 s.f., since that's generally the level of precision we can confidently read off a graph).

A number without a unit is meaningless in physics — "5" tells you nothing, but "5 mm" and "5 km" describe wildly different things. You need to know the correct SI-derived unit for every common quantity, and be able to derive a unit from an equation when you're not sure.

A Deriving a Unit From an Equation

Sometimes you're not given the unit — you have to work it out from the formula that defines the quantity. The trick is to substitute in the known base units for every quantity on the right-hand side, and simplify.

Even with a great method, sometimes a single reading just... doesn't fit. Maybe you fumbled the stopwatch, misread a scale, or a stray gust of wind nudged the pendulum. These are called experimental errors (or "operator errors" / "one-off errors"), and the resulting bad data point is an anomaly.

Anomalies matter because they can seriously distort your mean and mislead your conclusions — so they need to be identified during the evaluation of results, before you draw any final conclusions from the data.