Title: InkPhysics / Measurements
On every note of this deck, unless a note says otherwise:
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Front: DEFINITION
Define: Reproducibility.
Back: A different experimenter, or a different method or equipment, still obtains consistent results.

Front: RECALL
State how to combine uncertainties when adding or subtracting.
Back: Add the absolute uncertainties of the quantities.

Front: SPOT THE ERROR
Say what is wrong with this claim: A measurement is a number.
Back: A number alone is not a measurement. A measurement is a value, a unit and an uncertainty, because every instrument has finite resolution and every method has scatter.

Front: RECALL
State the benchmark density of air.
Back: About 1.2 kg m^−3.

Front: SPOT THE ERROR
Say what is wrong with this claim: Units are labels you attach once the number is finished.
Back: Units are part of the physics, not labels added afterwards. Carry them through the calculation to check the algebra; an answer with the wrong unit is wrong.

Front: RECALL
State the conversion between electronvolts and joules.
Back: 1 eV = 1.60 × 10^−19 J, the energy an electron gains crossing a potential difference of one volt.

Front: DEFINITION
Define: Random error.
Back: Error that scatters readings unpredictably either side of the true value.

Front: RECALL
State how to check an equation for homogeneity.
Back: Replace every symbol by its SI base units, collect and cancel the powers, then compare the two sides and every term that is added to another.

Front: RECALL
State where the crossover between adjacent orders of magnitude falls.
Back: Values compare by ratio, so the boundary is √10 ≈ 3.2: anything above about 3.2 × 10^n rounds to 10^n+1.

Front: RECALL
State how to combine uncertainties when multiplying or dividing.
Back: Add the percentage uncertainties of the quantities.

Front: DEFINITION
Define: Repeatability.
Back: The same experimenter, using the same method and equipment, obtains consistent results.

Front: DEFINITION
Define: Precision.
Back: How closely repeated readings cluster together.

Front: RECALL
Explain what a failed homogeneity check proves, and what a passed one does not.
Back: A mismatch proves the equation is wrong. A match does not prove it right, because a missing pure number such as ½ or 2π leaves the base units untouched.

Front: EQUATION · NOT ON THE DATA SHEET
Percentage uncertainty:
percentage uncertainty = ?\(\text{percentage uncertainty} = \, ?\)percentage uncertainty = ?
Back: percentage uncertainty = uncertaintyvalue × 100\(\text{percentage uncertainty} = \frac{\text{uncertainty}}{\text{value}} \times 100\)percentage uncertainty = uncertainty/value × 100

Front: RECALL
State the convention for labelling a table column or a graph axis.
Back: Write the quantity divided by its unit, as in speed / m s^−1, so that the entries below it are pure numbers and no unit is repeated against them.

Front: DEFINITION
Define: Resolution.
Back: The smallest change in a quantity that an instrument can display.

Front: RECALL
State the benchmark density of water.
Back: About 1000 kg m^−3.

Front: DEFINITION
Define: Order of magnitude.
Back: A value expressed to the nearest power of ten.

Front: RECALL
State the SI base quantities.
Back: The base quantities used at A-level: mass, length, time, electric current, temperature and amount of substance. (SI has a seventh: luminous intensity.)

Front: RECALL
State the value of the prefix centi.
Back: Centi (c) multiplies a unit by 10^−2, the only required prefix that is not a power of a thousand.

Front: RECALL
State the SI base units.
Back: The units of the six base quantities: the kilogram (kg), metre (m), second (s), ampere (A), kelvin (K) and mole (mol).

Front: DEFINITION
Define: Uncertainty.
Back: The interval within which the true value can reasonably be expected to lie, quoted after a ± sign.

Front: RECALL
State how to find the uncertainty of a quantity raised to a power n.
Back: Multiply the percentage uncertainty by n.

Front: RECALL
Explain how to convert a squared unit that carries a prefix.
Back: The prefix is squared along with the unit: 1 mm^2 = (10^−3 m)^2 = 10^−6 m^2.

Front: RECALL
State what "differ by n orders of magnitude" means.
Back: One quantity is about 10^n times the other.

Front: RECALL
Explain why repeating readings does not reduce a systematic error.
Back: Repeating and averaging does not reduce a systematic error, because every reading is shifted the same way.

Front: DEFINITION
Define: Systematic error.
Back: Error that shifts every reading the same way, such as a zero error.

Front: RECALL
Explain how precision and accuracy differ.
Back: A precise result need not be accurate: readings can cluster tightly about a value offset from the true value.

Front: SPOT THE ERROR
Say what is wrong with this claim: If it came out of the calculator, it must be right.
Back: Calculators execute keystrokes; they cannot notice a slip. An order-of-magnitude estimate made first is what catches the misplaced power of ten.

Front: RECALL
State the SI base quantity whose base unit is the mole.
Back: Amount of substance, which is an SI base quantity in its own right, on the same footing as mass and length.

Front: DEFINITION
Define: Accuracy.
Back: How close a result is to the true value.

Front: RECALL
State the conversion between kilowatt hours and joules.
Back: 1 kW h = 3.6 × 10^6 J, because 1000 W is delivered for 3600 s.

Front: RECALL
Explain how random error is reduced.
Back: Random error is reduced by taking repeat readings and averaging, because the scatter partly cancels.

Front: RECALL
State how to find the uncertainty of a mean from repeated readings.
Back: Half the range: subtract the smallest reading from the largest and halve the result.

Front: DEFINITION
Define: Homogeneous equation.
Back: An equation in which every term, on both sides, has the same SI base units.