IB Physics IA: linearising data and handling uncertainty

What each criterion looks for in physics

The investigation may be a hands-on experiment, a database analysis or a simulation. Teachers' guidance says tables, graphs, equations, calculations, headings and references do not count towards the 3,000 words.

Choosing a relationship to test

Physics IAs work best when theory predicts a relationship you can test: the period of a pendulum and its length, the resistance of a wire and its length or temperature, the terminal velocity of a sphere in a liquid and its radius, the intensity of light and distance from the source, the damping of an oscillation over time. The best questions add a twist that makes the investigation yours, such as testing where a simple model stops working.

Plan the range and number of values before you start. Five or more values of the independent variable, spread over as wide a range as the apparatus allows, with repeats at each value, give a graph that can show a real trend and a credible gradient uncertainty. A narrow range makes every line fit and proves nothing.

Worked example: finding g from a pendulum

Invented results, to show the analysis. For small swings, theory gives T = 2π sqrt(L/g), where T is the period and L the length.

1. Linearise: square both sides to get T^2 = (4π^2/g) × L. A graph of T^2 against L should be a straight line through the origin with gradient 4π^2/g.
2. Measure: time 10 swings for each length and divide by 10, which reduces the reaction-time uncertainty in each period by a factor of 10. Square each period and carry its uncertainty: the percentage uncertainty in T^2 is twice the percentage uncertainty in T.
3. Plot T^2 against L with error bars. Suppose the best-fit gradient is 4.02 s^2 m^-1, and the steepest and shallowest lines that still pass through all the error bars have gradients 4.12 and 3.92.
4. Gradient uncertainty = (4.12 - 3.92) ÷ 2 = 0.10 s^2 m^-1, which is 0.10 ÷ 4.02 = 2.5%.
5. Calculate g = 4π^2 ÷ gradient = 39.48 ÷ 4.02 = 9.82 m s^-2. The percentage uncertainty in g equals that of the gradient, 2.5%, so the absolute uncertainty is 9.82 × 0.025 = 0.25, and the result is g = 9.8 ± 0.2 m s^-2.
6. Conclude: the accepted value, about 9.81 m s^-2, lies within the range, so the data support the model. A clearly non-zero intercept would point to a systematic error, such as measuring length to the top of the bob instead of its centre.

Where Physics IA marks are lost

• Plotting the raw variables when theory predicts a curve, so the gradient means nothing.
• No error bars, or error bars drawn but no best-fit and worst-fit lines to give a gradient uncertainty.
• Uncertainties that ignore the real limitation: a stopwatch reads to 0.01 s, but human reaction time is much larger.
• Too few data points or too narrow a range for the trend to be convincing.
• Conclusions that ignore the intercept or never compare the result with theory.
• Evaluation copied from a list of generic errors instead of reasoned from the student's own graph.

How one-to-one lessons help with the Physics IA

A tutor who teaches IB Physics helps the student pick a relationship that theory predicts and the school lab can test, then work out how to linearise it and what the gradient and intercept should mean before any data is taken. With data in hand, lessons practise the analysis on the shared whiteboard: uncertainty in squared and reciprocal quantities, error bars, worst-fit lines, and propagating the gradient uncertainty into the final value.

The IA must be the student's own work, and teachers can give only limited feedback on a draft. A tutor teaches the skills and explains the criteria; the student designs, carries out and writes the investigation.