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Spec mapping: OCR H556 Module 2.1 — Physical quantities and units. This lesson establishes the seven SI base quantities, the (number × unit) grammar of every physical statement, and the conventions OCR mark schemes police. (Refer to the official OCR H556 specification document for exact wording.)
Physics is a quantitative science. Every statement worth making — every claim about the universe, every prediction, every experimental result — ultimately reduces to a measurement: a number paired with a unit. The OCR A-Level Physics A course (H556) places Module 2 (Foundations of Physics) at the very start of the specification for exactly this reason. Without a watertight understanding of units, quantities, and the algebra of their manipulation, no meaningful mechanics, electricity, waves, or quantum work can follow. This lesson is therefore deceptively important: nine of the ten common categories of mark loss in OCR numerical questions trace, in the end, back to a sloppy treatment of the foundational ideas in these pages.
The principle at the centre of the lesson is one short equation that we will return to over and over:
physical quantity=numerical value×unit
Everything else — homogeneity, unit conversion, dimensional checking, base-unit derivation — flows from taking that equation seriously.
Key definition: An SI base quantity is one of the seven physical quantities chosen by the International System of Units as conceptually independent. Their base units (kilogram, metre, second, ampere, kelvin, mole, candela) form the foundation from which every other unit in physics is built.
Before the SI was formalised in 1960, scientists and engineers worked in a bewildering variety of unit systems — imperial pounds, dynes, ergs, calories, horsepower, atmospheres, mmHg, fathoms, BTUs, foot-poundals, electrostatic units, electromagnetic units. Communication across borders and disciplines was painful, and the cost of conversion errors compounded over years. The most cited modern illustration is the 1999 NASA Mars Climate Orbiter loss: one engineering team supplied thrust data in pound-seconds while the mission's navigation software assumed newton-seconds. The factor-of-4.45 mismatch in impulse meant that the spacecraft entered the Martian atmosphere far lower than intended and disintegrated. Years of work and the better part of $300 million were destroyed by a unit error.
The Système International d'Unités (SI) is the agreed remedy. It is:
The 2019 redefinition is the most important upgrade to the SI in your lifetime: until then, the kilogram was defined as the mass of an actual platinum-iridium cylinder (the IPK or "Le Grand K") sitting in a vault in Sèvres. The cylinder drifted in mass by ≈50 µg over 130 years — a tiny but measurable amount — meaning that the kilogram itself was changing. From May 2019 the kilogram is fixed via an exact value of the Planck constant and the metre and second, an arrangement that cannot drift.
There are exactly seven base quantities. Every other physical quantity you meet in A-Level — speed, force, energy, pressure, voltage, magnetic flux density — can be built up from these seven via multiplication, division, and integer powers.
| Base quantity | Symbol for quantity | SI base unit | Unit symbol |
|---|---|---|---|
| Mass | m | kilogram | kg |
| Length | l | metre | m |
| Time | t | second | s |
| Electric current | I | ampere | A |
| Thermodynamic temperature | T | kelvin | K |
| Amount of substance | n | mole | mol |
| Luminous intensity | Iv | candela | cd |
At A-Level Physics you will routinely use the first six. The candela appears in lighting and photometric contexts but is essentially never the answer to a Module-2 calculation; you should know it exists and that it measures the power of light weighted by the eye's spectral response.
Exam tip: OCR expects instant recall of base units for mass, length, time, current, temperature and amount of substance. A typical 1-mark question is "State the SI base unit of mass". The correct answer is kilogram (kg) — never "gram", never "kilo".
A genuine curiosity of the SI is that the base unit of mass is the kilogram, not the gram. The seven base units include exactly one with a built-in prefix. The reason is historical: when the metric system was conceived during the French Revolution (1795), the practical reference standard was a litre of water at 4 °C, which weighs about a kilogram. The gram was too small to serve as a convenient artefact; the kilogram fits in the hand.
This produces two operational consequences that often trip up A-Level students:
Take the equation physical quantity=number×unit seriously and most of the algebra of physics drops out. If a rod has a measured length of 2.5 metres we write l=2.5m. The "2.5" is dimensionless — a pure real number. The "m" is the unit. Together they specify the physical quantity "length of the rod".
Units multiply, divide, cancel and raise to powers exactly as algebraic symbols would. If you multiply length by length you get an area:
l×l=2.5m×2.5m=6.25m2
If you divide a distance by a time you get a speed:
20s100m=5m s−1
The unit that comes out of any calculation is itself a check on the calculation — a topic we return to in the next lesson under the heading "homogeneity".
The single most prolific source of numerical mark-loss at A-Level is substituting a quantity into an equation while it is still in a non-base unit. Consider Newton's second law F=ma with m=500g and a=2m s−2. The correct procedure is:
F=(0.500kg)×(2m s−2)=1.00N
A student who writes F=500×2=1000N has not made an arithmetic error — they have substituted a non-base quantity (grams) into an equation that demands base units (kilograms). The answer is wrong by exactly a factor of 103.
Common exam mistake: Substituting cm where m is required, g where kg is required, or minutes where s is required. The factor-of-100, factor-of-1000, or factor-of-60 error this introduces is rarely caught by a re-check because it does not flag as obviously wrong in the calculator.
"F=20" is not a physical statement. Twenty what? Newtons? Kilonewtons? Pound-force? Dynes? Every numerical answer in an OCR exam carries its unit, and at A-Level the unit should normally be SI unless the question explicitly asks for another (such as "express your answer in km h⁻¹").
A student records the mass of a trolley as 1.2 kilograms and its velocity as 3.0 metres per second. Write each as (number × unit) and identify the base quantities involved.
Solution. m=1.2kg — mass, an SI base quantity, unit kg. v=3.0m s−1 — speed, a derived quantity, built from the base quantities length (m) and time (s). The numerical part 3.0 is dimensionless; the unit m s⁻¹ encodes that "we covered one metre in each second".
A 250 g apple falls from a tree. Taking g=9.81m s−2, calculate its weight.
Solution. Weight W=mg. First convert mass to the base unit kg:
m=250g=0.250kg
Then substitute:
W=0.250×9.81=2.4525N≈2.45N(3 s.f.)
A student who substitutes m=250 directly obtains W=2452.5N — the weight of a small car, applied through a stalk. The discrepancy with intuition is so large that the error becomes obvious on inspection. Many real exam errors are subtler: a factor of 100 from cm-to-m never flags as absurd, which is precisely what makes it dangerous.
A current of 2.0 A flows through a wire for 5.0 minutes. Calculate the total charge transferred.
Solution. Q=It. Convert time to seconds: t=5.0×60=300s. Then Q=2.0×300=600C. The coulomb is a derived unit; in base units the answer reads 6.0×102A s.
Classify each of the following as base or derived: mass, density, force, ampere, mole, frequency, pressure, kelvin.
Solution. Mass = base (kg); density = derived (kg m⁻³); force = derived (newton, kg m s⁻²); ampere = base (current); mole = base (amount of substance); frequency = derived (Hz, s⁻¹); pressure = derived (pascal, kg m⁻¹ s⁻²); kelvin = base (temperature). Five of the eight are derived; only mass, ampere, mole and kelvin are base. The trick at A-Level is to spot that "ampere" is the unit whereas "current" is the quantity — OCR sometimes phrases the question one way, sometimes the other.
Since 20 May 2019, the seven SI base units have been defined by assigning exact numerical values to seven fundamental physical constants:
| Constant | Symbol | Exact value | Defines |
|---|---|---|---|
| Speed of light in vacuum | c | 299792458m s−1 | metre |
| Caesium-133 hyperfine transition frequency | ΔνCs | 9192631770Hz | second |
| Planck constant | h | 6.62607015×10−34J s | kilogram |
| Elementary charge | e | 1.602176634×10−19C | ampere |
| Boltzmann constant | k | 1.380649×10−23J K−1 | kelvin |
| Avogadro constant | NA | 6.02214076×1023mol−1 | mole |
| Luminous efficacy | Kcd | 683lm W−1 | candela |
You do not need to memorise these exact figures; they appear on the H556 data sheet. What you must appreciate is the philosophical shift. The metre used to be the length of a platinum-iridium bar; now the metre is "however far light travels in 1/299792458 of a second". Every base unit is now anchored to an unchanging physical constant. This makes the SI extraordinarily precise — modern atomic clocks are accurate to one part in 1018, equivalent to losing one second every 30 billion years — and immune to drift in any physical artefact.
Examiner reports repeatedly identify sloppy notation as a source of avoidable mark loss. Internalise the conventions early.
Discriminator mark: Examiners draw a tier line through candidates who write "300 °K" or "5 ms⁻¹". Both are wrong: the kelvin takes no degree symbol (Lord Kelvin took the degree sign out when he abolished the zero offset relative to Celsius), and "ms⁻¹" reads as "per millisecond", which is a thousand times faster than the intended speed.
Question (6 marks). A student writes the relationship "force equals mass times acceleration" but works the example "a 500 g object accelerated at 2 m s⁻²" by computing F=500×2=1000N.
(a) State the SI base units of mass, length, time and current. (2) (b) Using the (number × unit) framework, identify the student's error and give the correct value of F, justifying each conversion step. (3) (c) Explain why the OCR mark scheme would award zero marks for an answer of "F=1000" without an associated unit. (1)
| Mark | AO | Awarded for |
|---|---|---|
| 1 | AO1 | Stating mass = kg, length = m (1 mark for any two correct) |
| 2 | AO1 | Stating time = s, current = A (1 mark for the remaining two correct) |
| 3 | AO2 | Identifying that 500 g must be converted to 0.500 kg before substitution |
| 4 | AO2 | Computing F=0.500×2=1.00N |
| 5 | AO2 | Stating the correct unit (newton, N) on the answer |
| 6 | AO3 | Explaining that a bare number is not a physical quantity — quantity = number × unit |
AO split: AO1 = 2, AO2 = 3, AO3 = 1.
Mid-band response (4/6). (a) Mass is in kg, length in m, time in s and current is in amps. (b) The student forgot to convert grams to kilograms. 500 g = 0.5 kg. So F=0.5×2=1N. The answer 1000 is wrong by a factor of 1000. (c) Because a number on its own does not say what unit it is in.
Examiner commentary: To lift this to top-band, the candidate would need to (i) explicitly justify the conversion using the (number × unit) framework rather than just saying "forgot to convert", (ii) give the answer to sensible significant figures with units placed correctly ("F=1.00N" not "1 N"), and (iii) frame the AO3 mark in OCR-friendly language ("a physical quantity is a number multiplied by a unit; without the unit no physical content is conveyed"). The candidate scores M1 (part a, two correct units), M1 (part a, remaining two units), M1 (conversion 500 g → 0.500 kg), M1 (computing F = 1 N) — four marks. M5 lost on significant-figure presentation and M6 lost on the bare AO3 justification.
Top-band response (6/6). (a) The SI base unit of mass is the kilogram (kg), of length the metre (m), of time the second (s) and of current the ampere (A). (b) Newton's second law F=ma is a coherent SI equation: substituting m in any unit other than kilograms gives the wrong numerical value. The student supplied mass as 500g, which must be converted using the prefix relation 1g=10−3kg, giving m=0.500kg. Substitution then gives
F=0.500kg×2m s−2=1.00N(3 s.f.)
so the correct value is 1.00 N, three orders of magnitude smaller than the student's 1000. (c) A physical quantity is defined as a numerical value multiplied by a unit: quantity=number×unit. The bare number 1000 conveys no physical information — it could refer to newtons, dynes, kilonewtons or pound-force, which differ by up to five orders of magnitude. The unit is therefore load-bearing for the meaning of the answer, not decoration.
Examiner commentary: Full 6/6. M1 + M2 (all four base units correct), M3 (explicit conversion using 1g=10−3kg), M4 (numerical evaluation), M5 (unit and significant figures), M6 (AO3 phrased in the language of the (number × unit) framework). The OCR discriminators that lift this from Stronger to top-band are the explicit conversion factor cited (not just "convert grams"), the inclusion of significant figures, and the AO3 explanation framed in OCR vocabulary rather than colloquial English.
Many candidates lose marks here by confusing "gram" with "kilogram" as the base unit of mass. The base unit is the kilogram. Grams are a sub-multiple, and substituting g where kg is required produces a factor-of-1000 error.
A typical pitfall is writing "Kg" instead of "kg". Symbols for units named after people take a capital letter (newton → N, kelvin → K) but the kilogram is named for the metric system, not a person, so it stays lower-case. The K is reserved for kelvin.
Many candidates write "sec" or "min" or "hr" in place of the SI symbols. The SI symbol for second is s, for minute is min and for hour is h — but the latter two are not even base units. In a physics calculation you must convert to seconds.
A common slip is pluralising unit symbols: "5 Ns" is not "five newtons" — it is "five newton-seconds", a unit of impulse. The correct form is "5 N".
Many candidates forget to convert. cm-to-m, g-to-kg, min-to-s, mA-to-A — every one of these is a factor of 10ⁿ that destroys the numerical answer if missed. The mantra is convert first, substitute second.
Some candidates omit the unit from a numerical answer. A unit-less "5" is not a physics answer. OCR mark schemes typically award the unit as a separate mark, and "5" loses it.
A subtle mark-loss is writing "°K". Kelvin takes no degree symbol — write "300 K", not "300 °K". Lord Kelvin abolished the degree sign when he set the absolute zero offset.
Many candidates confuse "amount of substance" (a base quantity, unit mol) with "mass" (also a base quantity, unit kg). Avogadro's constant is the bridge; conflating them is a Module 2 → Module 5 error that lasts the whole course.
At undergraduate level the seven-base-unit system is generalised under the umbrella of dimensional analysis — the formal study of the algebra of physical dimensions, developed largely by Edgar Buckingham (the famous Pi theorem is his) and Lord Rayleigh in the early twentieth century. Buckingham's theorem says that any physically meaningful equation involving n variables can be written as a relation between n−k dimensionless groups, where k is the number of fundamental dimensions involved. This is the principle behind Reynolds number in fluid mechanics, Mach number in aerodynamics, and the cosmological density parameter Ω.
A first-year mechanics course revisits Newton's second law in a more careful way: F=ma is the form valid in inertial frames in flat spacetime, but the broader expression F=dp/dt remains correct when masses are changing (rockets) or when velocities approach c (relativistic mechanics). The momentum p=γmv in special relativity has the same base units (kg m s⁻¹) but the γ factor is dimensionless — exactly the kind of dimensionless multiplier that homogeneity can never detect.
A first-year metrology course develops the SI redefinition in depth. The Kibble balance (or watt balance) that defines the kilogram is itself a beautiful piece of physics: it measures the electromagnetic force needed to lift a mass against gravity and relates that force to electrical units, which in turn are anchored via the Josephson and quantum-Hall effects to h and e. The fact that the kilogram is now defined via a fundamental constant of quantum mechanics, rather than a lump of metal, is one of the great achievements of late-twentieth-century physics.
Two Oxbridge-interview-style prompts to chew on. "Why do you think the metre, second and kilogram were the units chosen as 'base' rather than, say, the joule and watt?" — the answer involves the historical accident of which quantities were easy to measure precisely in 1795, plus the modern observation that any coherent system needs a minimal independent basis (you cannot define both length and area as base because area is derived from length). "What would change if humanity adopted Planck units (where ℏ=c=G=k=1)?" — almost nothing, except that all the numerical factors in physics equations would shift; the physics is invariant, and base units are a human bookkeeping convenience.
In the next lesson we build derived units systematically from these seven base units and develop the homogeneity test for any equation.