A Physics Toolkit

A Physics Toolkit — American System Physics Revision Notes & Topical Questions

5 min read 7 parts Lesson 1 of 5 1 quiz

📚 American System Physics Hub / Topical Revision

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Lesson summary

A Physics Toolkit: Measurement, Mathematics and Graphs — AMERICAN SYSTEM PHYSICS notes: Use SI units, significant figures, error analysis and graphs to carry out and interpret quantitative physics work.The SI (International System of Units) is built on seven base units (m, kg, s,…

scientific theory
Dimensional analysis
Reliable (repeatable)
Zero error
slope (gradient)
Extrapolation

Part 1 of 5SI units, estimation and unit conversion

The SI (International System of Units) is built on seven base units (m, kg, s, A, K, mol, cd) from which all other units are derived.

Estimate answers (order of magnitude) to check they are reasonable.

Scientific theory

A scientific theory is a well-tested explanation, supported by a large body of evidence, of why things happen; it can be changed if new evidence contradicts it.

Speed is distance divided by time

v = d / t, with distance in m, time in s and speed in m/s. Dimensional analysis treats units as algebraic quantities that can be multiplied, divided and cancelled;
- both sides of a valid equation must have the same units.
For example d = vt gives (m/s)(s) = m, which checks.

Converting units, in this order

write the given quantity with its unit (72 km/h);
- multiply by a factor with the unwanted unit on the bottom (× 1000 m / 1 km);
- multiply by a second factor to replace the time unit (× 1 h / 3600 s);
- cancel matching units, leaving m/s;
- calculate 72 × 1000 ÷ 3600 = 20 m/s.

Part 2 of 5A method for solving problems and significant figures

Read the problem and list every known quantity with its symbol and unit; identify the unknown.

Convert all values into SI base units (km to m, g to kg, min to s).

Choose the equation linking knowns to the unknown and rearrange algebraically before substituting.

Do a dimensional analysis check: the units alone must simplify to the unit of the unknown.

Substitute, calculate, and round to the correct number of significant figures (the fewest in the data for multiplication and division).

State the answer with its unit and judge whether its size is reasonable.

Numbers that are counted or defined (for example 1 km = 1000 m exactly) have unlimited significant figures and do not limit the answer. In exam command words, Calculate means show setup, substitution and the answer with units, and Predict means state the expected outcome, adding a reason only if asked to justify.

Part 3 of 5Measurement quality: accuracy, precision and error

Accuracy

Accuracy how close a measured value is to the true or accepted value.

Precision

Precision the degree of exactness of a measurement; precise readings are close together.

Reliable (repeatable)

Reliable (repeatable) consistent values when the same person repeats the measurement with the same method and equipment.

Zero error

Zero error a systematic error in which an instrument does not read zero when the quantity is zero; correct it by subtracting the zero reading from every result.

Systematic errors shift every reading the same way, so averaging repeat readings does not remove them.

Random errors (reaction time, estimating between scale marks, draughts) can be reduced by averaging.

Timing many swings of a pendulum and dividing reduces the relative effect of reaction time.

The resolution of a typical metre rule is 1 mm.

Readings of 5.62, 5.61 and 5.63 cm when the true value is 5.90 cm are precise but not accurate.

Part 4 of 5Graphing data

Plot the independent variable on the x-axis and the dependent variable (measured, responding) on the y-axis.

Label each axis with quantity and unit (for example "time / s").

Choose a linear scale so the data fill at least half the grid in each direction (steps of 1, 2 or 5 per square).

Plot points accurately with a small cross or dot and draw a single thin line of best fit (straight or smooth curve), with roughly equal numbers of points above and below it.

Do not join dot-to-dot and ignore anomalies.

The slope (gradient) is rise over run, m = Δy/Δx, with units y-unit per x-unit.

Graphing data

To find it, draw the best-fit line, choose two points on the line (not data points) far apart, draw a large right-angled triangle covering more than half the line, read the rise and run with units, and divide.

The slope of a distance-time graph is the speed in m/s.

The y-intercept completes the equation y = mx + b, and slope and intercept should be interpreted physically.

Relationship	Graph	Behaviour
y = kx	straight line through the origin	direct proportion
y = a/x	hyperbola	inverse; xy = a, doubling x halves y
y ∝ x²	curve	tripling x makes y nine times larger

Extrapolation extends the line beyond the measured range to predict a value and is less reliable than interpolation within the range.

Part 5 of 5Worked examples

Convert 72 km/h to m/s. [2]2 marks
A balance reads 0.3 g with nothing on it. What type of error is this? [1]1 mark
A stack of 250 sheets is 2.5 cm thick. Find the thickness of one sheet. [2]2 marks
Which error cannot be reduced by averaging repeat readings: reaction time, air draughts, a miscalibrated meter or estimating between scale marks? [2]2 marks
A line passes through (2, 5) and (6, 17). Find its slope. [2]2 marks
If y ∝ x² and x is tripled, what happens to y? Which graph shape does y = a/x give? [2]2 marks

Key terms

Term	Meaning
SI (International System of Units)	The internationally agreed system of measurement built on seven base units from which all other units are derived.
Dimensional analysis	Checking an equation or converting units by treating units as algebraic quantities that cancel; both sides must have the same units.
Scientific theory	A well-tested, evidence-supported explanation of why things happen that can be changed if new evidence contradicts it.
Accuracy	How close a measured value is to the true or accepted value.
Precision	The degree of exactness of a measurement.
Zero error	A systematic error where an instrument does not read zero when the quantity is zero.
Slope (gradient)	The rise divided by the run between two points on a line, with units of y-unit per x-unit.
Extrapolation	Extending the line of best fit beyond the measured data to predict a value; less reliable than interpolation.

Avoid these mistakes

Averaging readings to remove a zero error — it is systematic, so subtract the zero reading instead.

Confusing precision with accuracy — precise readings cluster together; accurate readings are close to the true value.

Joining plotted points dot-to-dot — draw a single best-fit line or smooth curve.

Choosing data points for the slope triangle — use two widely spaced points on the line.

Giving the answer without units or with too many significant figures — round to the fewest in the data.

Last updated: 18 October 2026

Part 1 of 5SI units, estimation and unit conversion

Part 2 of 5A method for solving problems and significant figures

Part 3 of 5Measurement quality: accuracy, precision and error

Part 4 of 5Graphing data

Part 5 of 5Worked examples

Convert 72 km/h to m/s. [2]2 marks

A balance reads 0.3 g with nothing on it. What type of error is this? [1]1 mark

A stack of 250 sheets is 2.5 cm thick. Find the thickness of one sheet. [2]2 marks

Which error cannot be reduced by averaging repeat readings: reaction time, air draughts, a miscalibrated meter or estimating between scale marks? [2]2 marks

A line passes through (2, 5) and (6, 17). Find its slope. [2]2 marks

If y ∝ x2 and x is tripled, what happens to y? Which graph shape does y = a/x give? [2]2 marks

Key terms

Avoid these mistakes

Marked practiceQuizzes for this lesson

If y ∝ x² and x is tripled, what happens to y? Which graph shape does y = a/x give? [2]2 marks