S.I. units — OCR A-Level Physics

This row continues the list of S.I. base quantities: mass has the base unit kilogram (kg), and length is the next base quantity, with the base unit metre (m). Length measures the separation between two points and underpins derived quantities such as area (m²) and volume (m³). In calculations, convert centimetres or millimetres to metres before substituting: 25 cm = 0.25 m and 250 mm = 0.250 m. Prefixes scale the metre, for example 1 km = 10³ m and 1 nm = 10⁻⁹ m, but the base unit itself remains the metre.

This row completes the base-unit list: length has the base unit metre (m), and time is the next S.I. base quantity, with the base unit second (s). Time measures duration and appears in derived quantities such as speed (m s⁻¹), acceleration (m s⁻²) and frequency (s⁻¹ or Hz). In calculations, convert minutes to seconds by multiplying by 60, so 2.5 min = 150 s, and convert milliseconds by multiplying by 10⁻³, so 50 ms = 0.050 s. The second is defined from atomic transitions, but for A Level you simply treat it as the base unit of time.

This row lists four S.I. base quantities and their units: time in seconds (s), electric current in amperes (A), thermodynamic temperature in kelvin (K), and amount of substance in moles (mol). A base unit is defined independently, not derived from other units. In calculations, convert to these units before substituting: for example, 25 °C becomes 298 K by adding 273, and 250 mA becomes 0.250 A by dividing by 1000. The kelvin scale starts at absolute zero, so 0 K is the lowest possible temperature. Amount of substance counts particles in moles, where one mole contains the Avogadro constant of entities. Recognising each quantity's unit helps you check equations for consistency.

The symbol (mol) is the S.I. unit for amount of substance. One mole contains the Avogadro constant, approximately 6.02 × 10²³, of specified particles such as atoms, molecules or ions. Amount of substance is not mass: the mass of one mole depends on the substance's molar mass. For example, 1 mol of carbon-12 has a mass of 12 g, while 1 mol of oxygen molecules (O₂) has a mass of about 32 g. To find the number of moles, divide mass in grams by molar mass in g mol⁻¹, or divide number of particles by the Avogadro constant. In equations, the mole allows you to count particles by weighing.

Derived units are combinations of S.I. base units. For example, the newton (N) is kg m s⁻², the joule (J) is kg m² s⁻², and the watt (W) is kg m² s⁻³. You can check whether an equation is dimensionally consistent by replacing each quantity with its base units and seeing whether both sides match. For instance, in F = ma, the right-hand side has units kg × m s⁻² = kg m s⁻², which is the newton. Derived units may have special names, but they can always be broken down into base units. This skill helps you identify errors in equations and convert between units.

The specification lists units that you must recognise and use, including S.I. base units and derived units with special names. You should be able to state the physical quantity for each unit and convert between units where necessary. For example, the pascal (Pa) is the unit of pressure and equals N m⁻², which is kg m⁻¹ s⁻². The coulomb (C) is the unit of charge and equals A s. The volt (V) is the unit of potential difference and equals J C⁻¹, or kg m² s⁻³ A⁻¹. The ohm (Ω) is the unit of resistance and equals V A⁻¹. Knowing these relationships helps you check equations and solve problems accurately.

Homogeneity checking tests whether every term in a physical equation reduces to the same S.I. base units. Write each quantity as its base-unit combination: for example speed is m s⁻¹, acceleration is m s⁻², force is kg m s⁻² and energy is kg m² s⁻². Substitute these into the equation and simplify powers. If both sides match, the equation is homogeneous; if they do not, it cannot be correct. This catches errors such as writing v = u + at², where at² has units m and v has m s⁻¹. It cannot prove an equation is correct, because dimensionless factors such as ½ or 2π are invisible to the check.

The prefix pico, symbol p, means 10⁻¹² of the base unit. It is used for very small quantities, such as a picosecond (1 ps = 1 × 10⁻¹² s) or a picometre (1 pm = 1 × 10⁻¹² m). To convert a value in picometres to metres, multiply by 10⁻¹²; to convert metres to picometres, divide by 10⁻¹², which is the same as multiplying by 10¹². For example, 250 pm = 250 × 10⁻¹² m = 2.5 × 10⁻¹⁰ m. In calculations, replace the prefix with its power of ten before substituting into an equation.

The prefix nano, symbol n, means 10⁻⁹ of the base unit. It is used for small quantities such as a nanometre (1 nm = 1 × 10⁻⁹ m) or a nanosecond (1 ns = 1 × 10⁻⁹ s). To convert a value in nanometres to metres, multiply by 10⁻⁹; to convert metres to nanometres, multiply by 10⁹. For example, 450 nm = 450 × 10⁻⁹ m = 4.5 × 10⁻⁷ m. The symbol n must not be confused with the prefix p for pico or μ for micro. In calculations, replace nano with 10⁻⁹ before substituting into an equation.

The prefixes micro, symbol μ, and milli, symbol m, represent 10⁻⁶ and 10⁻³ respectively. A micrometre (1 μm) is 1 × 10⁻⁶ m and a millimetre (1 mm) is 1 × 10⁻³ m. To convert to metres, multiply by the prefix factor: 25 μm = 25 × 10⁻⁶ m = 2.5 × 10⁻⁵ m, and 25 mm = 25 × 10⁻³ m = 2.5 × 10⁻² m. To convert from metres, multiply by 10⁶ for micrometres or 10³ for millimetres. The symbol m for milli must not be confused with the unit symbol m for metre; context and spacing show which is meant.

The metre (symbol m) is the S.I. base unit of length. The prefix centi (symbol c) means one hundredth, so it multiplies a unit by 10⁻². Combining them gives the centimetre (cm), where 1 cm = 10⁻² m = 0.01 m, and conversely 1 m = 100 cm. To convert a length from centimetres to metres, divide by 100, or equivalently multiply by 10⁻²; to convert metres to centimetres, multiply by 100. For example, 250 cm = 250 × 10⁻² m = 2.5 m. In calculations you should normally convert all lengths to metres before substituting into equations, because derived units such as the newton and joule are defined in terms of the metre. A multiple-choice question may ask you to identify the correct prefix value, the correct symbol, or the result of a conversion.

The metre (symbol m) is the S.I. base unit of length. The prefix deci (symbol d) means one tenth, so it multiplies a unit by 10⁻¹. Combining them gives the decimetre (dm), where 1 dm = 10⁻¹ m = 0.1 m, and conversely 1 m = 10 dm. To convert a length from decimetres to metres, divide by 10, or equivalently multiply by 10⁻¹; to convert metres to decimetres, multiply by 10. For example, 35 dm = 35 × 10⁻¹ m = 3.5 m. Although the decimetre is uncommon in A Level work, you should still recognise the prefix and its value. In calculations, convert all lengths to metres before substituting into equations, because derived units such as the newton and joule are defined in terms of the metre. A multiple-choice question may ask you to identify the correct prefix value, the correct symbol, or the result of a conversion.

The metre (symbol m) is the S.I. base unit of length. The prefix kilo (symbol k) means one thousand, so it multiplies a unit by 10³. Combining them gives the kilometre (km), where 1 km = 10³ m = 1000 m, and conversely 1 m = 10⁻³ km. To convert a length from kilometres to metres, multiply by 1000, or equivalently multiply by 10³; to convert metres to kilometres, divide by 1000. For example, 2.4 km = 2.4 × 10³ m = 2400 m. In calculations you should normally convert all lengths to metres before substituting into equations, because derived units such as the newton and joule are defined in terms of the metre. A multiple-choice question may ask you to identify the correct prefix value, the correct symbol, or the result of a conversion.

The metre (symbol m) is the S.I. base unit of length. The prefixes kilo (k), mega (M), giga (G) and tera (T) mean 10³, 10⁶, 10⁹ and 10¹² respectively. Combining them with the metre gives the kilometre (km), megametre (Mm), gigametre (Gm) and terametre (Tm), where 1 km = 10³ m, 1 Mm = 10⁶ m, 1 Gm = 10⁹ m and 1 Tm = 10¹² m. To convert from a prefixed unit to metres, multiply by the corresponding power of ten; to convert from metres to a prefixed unit, divide. For example, 3.5 Mm = 3.5 × 10⁶ m = 3.5 × 10⁶ m. Note that the symbols are case-sensitive: k is lower case, while M, G and T are upper case. In calculations, convert all lengths to metres before substituting into equations.

Graph axes and table columns must be labelled with the quantity name or symbol followed by a forward slash and its unit, for example time $t$ / s or current $I$ / A. The slash means 'divided by', so the numerical scale shows the value of the quantity divided by its unit. A column heading such as mass $m$ / kg tells the reader that entries are in kilograms. If a quantity is a ratio or has no unit, write 'no unit' or leave the space after the slash empty only when the quantity is dimensionless. For logarithmic axes, label with the quantity and state that the scale is logarithmic. Always include units on both axes and every column, and use the same convention throughout a table or graph to ensure clear communication of experimental data.