S Skills in Physics HL

Move from hazard to control

Identify the specific hazard, who or what could be harmed, and how exposure could occur. Then choose a control that removes the hazard or reduces probability or severity—for example shielding and distance for ionizing radiation, insulation for hot equipment, or containment for pollutants.

Protect self, others and the environment

Check the investigator, nearby people, organisms, equipment and surroundings. After applying controls, state any residual risk and whether the investigation should proceed, be redesigned or not be performed.

Frame an ethical choice

Compare benefits and harms for the affected people. For a medical isotope, balance possible treatment benefit against side effects and the consequence of not treating; do not present a medical choice as risk-free.

Discuss rather than list

A discussion needs more than one perspective or consequence and a reasoned comparison. For environmental questions, consider extraction, use, disposal and long-term effects.

Common trap

Do not write a vague claim such as “it is dangerous.” Name the mechanism and the consequence, then connect it to the decision.

Choose and prepare the instrument

Match range and resolution to the expected value and required precision. Check calibration, zero, units and viewing geometry before measuring mass, time, length, volume, temperature, force, current, potential difference, angle, sound intensity or light intensity.

Read the value

Record enough digits to reflect the instrument’s resolution and include the unit. For a corrected reading, apply the zero offset with the correct sign; a displayed value is not automatically the true value.

Worked example — signed zero correction

A caliper shows $20.60\,\mathrm{mm}$ around a sphere but reads $-0.30\,\mathrm{mm}$ when closed. True diameter $=20.60-(-0.30)=20.90\,\mathrm{mm}$. Subtract the zero reading algebraically; do not guess the correction direction.

Improve reliability

Repeat measurements, average them, and measure at different positions or orientations when geometry permits. This reveals random variation and reduces its effect on the mean.

Common trap

Do not increase precision by writing extra decimal places that the instrument cannot resolve, and do not correct a zero error in the wrong direction.

Choose technology for the data needed

Name the variable, required range, resolution and sampling interval before choosing a tool. The technology must produce data that can answer the investigation question; a convenient output is not automatically suitable.

Example — image sensing

A CCD converts light arriving at pixels into electrical signals and then numerical pixel values. Smaller pixels can improve spatial resolution, while quantum efficiency limits the fraction of incident photons detected. Record these limits before interpreting intensity or position.

Keep observation and model separate

Sensors, databases and images record or encode observations; simulations generate consequences of assumptions. Either can be useful, but they are not interchangeable evidence.

Use a spreadsheet deliberately

Keep raw data separate from calculated columns. Use formulas to transform variables, propagate units and uncertainties, and make the calculation reproducible rather than replacing the reasoning with a cell output.

Choose a graph that tests the model

Plot the variables suggested by the relationship. A straight line, its gradient and intercept can reveal the constant, proportionality or systematic offset.

Worked processing route — test a nonlinear model

If a model predicts $y=kx^2$, keep the raw $x$ and $y$ columns, create a spreadsheet column for $x^2$, then plot $y$ against $x^2$. A straight-line model with intercept consistent with the physical expectation supports the proposed form; the gradient estimates $k$ with the plotted units.

State model assumptions

A simulation explores consequences of chosen assumptions; it does not independently validate them. Compare simulated and measured outputs and identify which parameters were held fixed.

Keep the process reproducible

Label axes and units, preserve formulas rather than pasted answers, and state model settings. A graph or trendline does not explain itself: connect its gradient, intercept and deviations to the physical relationship being tested.

Choose the mathematics from the relationship

First identify what changes, what is held constant and whether the model is additive, proportional, exponential or geometric. Rearrange symbols before substituting numbers; this exposes the dependence and reduces calculator-entry errors.

Worked check — rearrangement and proportion

From $E=\tfrac12mv^2$, $v=\sqrt{2E/m}$. If $m$ is unchanged and $E$ becomes four times larger, $v$ becomes $\sqrt4=2$ times larger. This scale check should agree with the calculated value.

Estimate before accepting a result

Keep guard digits until the end, compare the answer with the nearest order of magnitude and neglect an effect only when you can explain why it is small. A proportionality is not an equation until its constant is included.

A vector needs magnitude and direction

Draw its arrow to scale when a scale diagram is required, label its magnitude, direction and point of application, and choose axes before resolving it. Scalars such as mass and energy have magnitude only; force, velocity and momentum are vectors.

Worked resolution

For a $10.0\,\text{N}$ force at $30^\circ$ above the positive horizontal, $F_x=10.0\cos30^\circ=8.66\,\text{N}$ and $F_y=10.0\sin30^\circ=5.00\,\text{N}$. The signs change if the chosen directions change; the physical vector does not.

Free-body diagram method

Choose one object, draw only forces acting on it at the required point of application or centre of mass, then add up to three coplanar vectors head-to-tail or by components. Subtraction means adding the reversed vector; multiplying by a negative scalar reverses direction.

Do not mix an interaction pair

The force exerted by the object on its surroundings belongs on the surroundings' diagram, not on the object's own free-body diagram.

Make every number carry a compatible unit

Convert prefixes before substitution and use the symbols defined in the guide/data booklet. The SI base units most often used in physics are metre (m), kilogram (kg), second (s), ampere (A) and kelvin (K); mole (mol) and candela (cd) complete the SI base set.

Use units as an equation check

For $E=\tfrac12mv^2$, the right side has units $\text{kg}\,\text{m}^2\,\text{s}^{-2}=\text{J}$, so it can represent energy. This unit check can reject an expression, but matching units alone do not prove that its numerical factor or physics is correct.

Round once, at the end

Keep guard digits during working. Report the final value and its uncertainty to compatible decimal places, with the uncertainty usually at one significant figure (or two when needed to avoid misleading rounding). Units such as eV, ly, pc, hour, day and year may be used where the syllabus context makes them appropriate.

Uncertainty states a range, not a mistake

Write a measured result as $x\pm\Delta x$ in matching units. The absolute uncertainty is $\Delta x$; fractional uncertainty is $\Delta x/x$; percentage uncertainty is $(\Delta x/x)\times100\%$.

Worked propagation

For $L=(2.00\pm0.01)\,\text{m}$ and $W=(1.00\pm0.01)\,\text{m}$, $A=LW=2.00\,\text{m}^2$. The fractional uncertainty is $0.01/2.00+0.01/1.00=0.015$, or $1.5\%$. Therefore $\Delta A=0.015\times2.00=0.03\,\text{m}^2$, so $A=(2.00\pm0.03)\,\text{m}^2$.

Powers multiply fractional uncertainty

If $V\propto r^3$ and $r$ has $2\%$ uncertainty, $V$ has $3\times2\%=6\%$ uncertainty under the syllabus propagation rule. For addition or subtraction, add absolute uncertainties instead—never percentage uncertainties.

Report sensible precision

Round the uncertainty first, then round the measured value to the same decimal place. A small difference between two measured values can have a large percentage uncertainty even when both original measurements look precise.

Build a graph that exposes the relationship

Put the independent variable on the horizontal axis, label both axes with quantity and unit, choose scales that use the plotting area, and show uncertainty bars where available. Use a line or curve of best fit for the trend; do not join each point.

Extract meaning from the fit

Calculate gradient from two well-separated points on the best-fit line and include its units. Use maximum- and minimum-gradient acceptable lines through the uncertainty bars to estimate gradient uncertainty; apply the same idea to intercepts. Interpolate within the measured range cautiously; extrapolation relies on the model continuing beyond the evidence.

Example — test an exponential claim

For exponential decay, equal time intervals should give approximately the same multiplicative factor (or a constant half-life). Alternatively, a suitable logarithmic transformation should be linear. Agreement must be judged with the uncertainty bars, not from visual closeness alone.

Interpret, do not merely describe

A gradient is a rate of change; a changing gradient shows a changing rate; an intercept is the predicted value at zero input; maxima/minima are turning points; and an area under a graph is an accumulated quantity only when the product of the axis units represents that quantity.

Start with evidence, then narrow the question

Consult varied sources, select information that is relevant and sufficient, and note the conditions under which each claim applies. Use that background to identify a measurable relationship or comparison—not merely a broad topic.

Explain the prediction

Connect the expected change to scientific understanding and state the assumptions that make the model useful. Independent thinking means using sources to justify and refine the question, not copying a source's conclusion.

Keep the three stages distinct

A question asks what will be investigated; a hypothesis proposes a relationship; a prediction states what the measurements should show. Each must remain testable by the proposed evidence.

Design backwards from the evidence needed

Choose whether a hands-on experiment, database, simulation or model can answer the research question. Then specify how the independent variable will be changed, the dependent variable measured and relevant control variables held constant.

Pilot before fixing the method

A short pilot checks whether the range produces measurable changes, whether the apparatus resolution is adequate and whether the sequence is practical. Use its observations to revise the method; do not invent or discard results to fit the hypothesis.

A valid method changes one intended cause at a time

Give enough procedural detail for another student to reproduce the investigation. A larger range, more readings or different technology is an improvement only when it strengthens the evidence for the stated relationship.

Control an effect because it could change the outcome

For every control, state the unwanted influence, the practical action and how that action protects the dependent measurement. A variable name alone does not show that the investigation is controlled.

Example — pendulum timing

If length is the independent variable and period is measured, keep a measurable release condition such as the initial angle constant; bob mass, diameter or material may also matter to the chosen setup. Explain how the same value is reproduced for every trial.

Control the system, not merely the equipment name

Saying “use the same stopwatch” or “keep gravity constant” does not identify a controllable influence in this design. Name a measurable feature and the method used to maintain it.

Record what happened, not what was expected

Capture relevant qualitative observations alongside sufficient quantitative readings. Qualitative evidence may explain a change, threshold or anomaly; quantitative evidence establishes the size and spread of the relationship.

Address issues while preserving the evidence

If a sensor saturates, a timing event is missed or the setup changes, pause and check the method. Repeat the affected measurement under the stated conditions when possible, but keep the original entry identified rather than silently replacing or adjusting it.

Use consistent precision

Record to the precision supported by the instrument and keep units explicit. Enough data means sufficient range, spacing and repeats to reveal the relationship—not a large table of duplicated or invented values.

Process only what the research question needs

Show calculations from raw to processed values, then interpret the appropriate table, chart, diagram or graph. Separate what the representation displays from the physical explanation proposed for the pattern.

Justify inclusion or removal

Do not remove a point merely because it weakens the trend. Keep it unless there is a documented measurement or procedural reason to exclude it; where the cause is uncertain, compare the analysis with and without the point and state how the conclusion changes.

Worked data decision

For diameter readings $0.18, 0.20, 0.21, 0.22, 0.26, 0.18\,\text{mm}$, $0.26\,\text{mm}$ is visibly separated from the cluster. If a documented reason supports exclusion, the mean of the remaining five is $0.198\,\text{mm}\approx0.20\,\text{mm}$. Without that justification, report the alternative mean or discuss the point rather than hiding it.

Data can be precise without being accurate—and accurate-looking data can come from an invalid test

Assess each quality separately against the intended measurement and research question.

Repeats target random variation

Repeating a drop-time measurement under the same conditions can reveal spread and improve precision of a representative result. Saying only “find an average” is incomplete: the reason is to reduce the influence of random variation, not to guarantee accuracy.

Systematic effects need a changed method

A zero offset can shift every reading together, so tightly clustered repeats may still be inaccurate. Calibration or correction can address the offset; averaging the same biased method cannot. Validity can also fail even when readings are precise and reliable if another variable causes the observed change.

A conclusion is a bounded answer to the research question

State the measured relationship or result, cite the processed evidence that supports it and say whether the stated hypothesis is supported, contradicted or remains unresolved. Do not repeat the procedure.

Example — evaluating an inverse model

If a hypothesis predicts $y\propto1/x$, values of $xy$ that clearly vary beyond their uncertainties contradict that prediction. Values that are approximately constant are consistent with the model, but they do not prove it: another relationship may also fit the limited range.

Uncertainty controls confidence, not truth

Agreement within stated uncertainty supports consistency with an accepted value; disagreement outside it flags tension, underestimated uncertainty or systematic effects. Neither result alone proves the model or identifies the cause.

Evaluate by tracing cause → measurement → result → conclusion

Name a specific random or systematic effect, explain which measurement it changes and in what direction when known, then state how the processed result and conclusion are affected. A label such as “human error” is not an evaluation.

Evaluate the hypothesis, not just the apparatus

Use trend, intercept, uncertainty bars and alternative explanations to state whether the evidence supports or contradicts the hypothesis. A best-fit line missing some uncertainty bars weakens the proposed model; an approximately constant transformed quantity is compatible with a model but cannot prove it.

Make improvements specific and realistic

For each weakness, name the physical change, how it reduces or measures the stated effect and why the conclusion becomes stronger. “Be more careful” and unrelated extra repeats do not correct a systematic bias or an unrealistic assumption.