OCR A Level Physics: Development of Practical Skills — Revision Notes

Condensed for the final weeks. For the full explanation, use the Development of Practical Skills study guide.

Variables and design

Independent — what you change. Dependent — what you measure. Control — kept constant.

A control variable is not the same as a control experiment: the latter is a parallel run with the independent variable absent, showing the observed effect is caused by the factor being tested.

Choose instruments with resolution appropriate to the quantity — a micrometer, not a ruler, for a wire’s diameter — and state a sensible range and interval, typically at least six values spread across the range. A risk assessment must be specific: the hazard, the risk it creates, and the control measure — a generic “wear safety goggles” with no link to the actual experiment earns nothing.

The four words that decide marks

Term	Meaning
Accurate	Close to the true value
Precise	Repeat readings agree with each other
Repeatable	Same result, same method, same person
Reproducible	Same result, different method or person

Precise but not accurate is the case examiners test: a miscalibrated instrument gives tightly grouped readings that are all consistently wrong.

More repeats improve reliability, reveal anomalies, and improve the accuracy of the mean by reducing the effect of random error — but they do nothing for a systematic error. Removing a systematic error needs better-calibrated or more sensitive apparatus.

Errors

Random — unpredictable scatter; reduced by repeating and averaging. Systematic — a consistent offset; repeating does not help, only recalibration or zeroing. Zero error — the instrument does not read zero when it should.

An additive systematic error (e.g. a zero error) appears on a graph as the correct gradient with an unexpected intercept — a line that should pass through the origin but doesn’t is the giveaway. A proportional (calibration) systematic error instead changes the gradient, leaving the intercept at the origin.

Uncertainty

single reading:  half the smallest scale division
two readings:    double it
percentage uncertainty = (uncertainty / value) x 100

Operation	Rule
Add or subtract	Add absolute uncertainties
Multiply or divide	Add percentage uncertainties
Power n	Multiply percentage by n

The power rule matters most: a radius measured to 2% gives a volume uncertain to 6%.

Reduce percentage uncertainty by measuring a larger quantity — time 20 oscillations rather than one, then divide. The absolute uncertainty is fixed by the instrument, so it becomes a smaller share of a larger reading.

Graphs and analysis

• Independent on x, dependent on y; linear scales using over half the grid; axes labelled with quantity and unit.
• Line of best fit; identify anomalies and exclude them.
• Rearrange into y = mx + c form so the gradient and intercept give the physical quantities — identifying what to plot against what is usually the first mark.

Error bars and gradient uncertainty:

uncertainty in gradient = (max gradient - min gradient) / 2

Draw the steepest and shallowest lines that still pass through all the error bars. Where two data sets’ error bars overlap, the difference may not be significant.

Finding the gradient itself: use a large triangle spanning most of the plotted line, taking coordinates from the line, not from individual data points.

Linearising relationships

Rearrange a relationship into y = mx + c form so a straight-line graph gives the gradient a physical meaning.

T = 2 pi sqrt(l / g)      ->      T^2 = (4 pi^2 / g) l

Plotting T² against l gives a straight line through the origin with gradient 4π²/g, so g = 4π² ÷ gradient. “What to plot, and what the gradient represents” is the single most common form of practical question.

Improving an experiment

Generic answers score nothing. Name a specific change and its reason:

• Use a micrometer rather than a ruler, because the smaller scale division reduces percentage uncertainty.
• Use light gates rather than a stopwatch, to eliminate the uncertainty from human reaction time.
• Repeat and average, to reduce random error.
• Measure a larger quantity, to reduce percentage uncertainty.
• Use a fiducial marker at the equilibrium position, because that is where the object moves fastest and timing is most consistent.

Worked example: which measurement limits accuracy

A pendulum of length 0.800 m ± 0.005 m gives a period of 1.79 s ± 0.02 s, testing g via T = 2π√(l/g).

% uncertainty in l = (0.005 / 0.800) x 100 = 0.63%
% uncertainty in T = (0.02 / 1.79) x 100  = 1.12%
g depends on T^2, so T contributes 2 x 1.12% = 2.24%
Total = 0.63% + 2.24% = 2.87%

Timing dominates. Timing 20 oscillations and dividing by 20 cuts this far more than a better ruler would — the same principle as reducing percentage uncertainty by measuring a larger quantity.

Exam traps

• Swapping accuracy and precision.
• Saying repeats reduce systematic error.
• Forgetting to double uncertainty for two-reading measurements.
• Forgetting the power rule.
• Suggesting improvements without reasons.
• Quoting more significant figures than the data justifies.
• Taking the gradient from two data points instead of a large triangle on the line.
• Giving a generic risk assessment not linked to the specific experiment.

Self-test

1. Distinguish accuracy from precision with an example.
2. Which error type does averaging reduce, and which does it not?
3. A radius is known to 2%. What is the uncertainty in a volume proportional to r³?
4. How is gradient uncertainty found from error bars?
5. Why use light gates instead of a stopwatch?
6. For a simple pendulum, what should be plotted to find g from a straight-line graph, and what does the gradient represent?
7. A pendulum’s length is known to 0.63% and its period to 1.12%. Which measurement limits the accuracy of g, and what single change would best reduce it?

Answers: 1. Accuracy is closeness to the true value, precision is agreement between repeats; a balance with a zero error gives precise but inaccurate readings. 2. Averaging reduces random error but not systematic error, which requires recalibration. 3. 6% — the percentage uncertainty is multiplied by the power. 4. Draw the steepest and shallowest lines that pass through all error bars and take half the difference between their gradients. 5. They eliminate the uncertainty from human reaction time, which a stopwatch cannot avoid. 6. Plot T² against l; the gradient equals 4π²/g, so g = 4π² divided by the gradient. 7. The period, since it is squared in the relationship for g, doubling its percentage contribution to 2.24% against length’s 0.63%; timing many oscillations and dividing by the number of oscillations would reduce this far more effectively than a more precise length measurement.