SI units and dimensional analysis – base units, prefixes and checking equations
PhysicsMeasurement & UncertaintyAges 15–16
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Build any SI unit from powers of the seven base units and see how derived units such as the newton, joule, watt, pascal and volt follow from their defining equations. Convert between prefixes from nano to giga on a powers-of-ten scale, test whether an equation is dimensionally consistent, and derive the form of the pendulum period from dimensions before measuring the constant 2π.
Lesson: SI units, prefixes and dimensional analysis
What it shows
The International System of Units (SI) has seven base units: metre, kilogram, second, ampere, kelvin, mole and candela. Every other unit is a product of their powers, so the newton is kg·m·s⁻² because F = ma. Prefixes such as kilo (10³) and micro (10⁻⁶) scale a unit by powers of ten. Dimensions [M L T I Θ] show what a quantity is made of. Terms that are added or equated must have the same dimensions, which lets you reject wrong equations and predict how a quantity depends on others. Pure numbers such as ½ or 2π have no dimensions, so they must come from theory or experiment.
How to use
On Units, choose a Quantity to see its defining equation, then build units with the steppers. On Prefixes, set a Value and two prefixes. On Check equations, pick an Equation, make your prediction and press Check. On Derive a formula, change the powers until M, L and T match, then press Time 10 oscillations several times and find k from the table.
Parameters you can change
- Screen Units, Prefixes, Check equations, Derive a formula
- Quantity (Units) velocity, acceleration, force, momentum, energy (work), power, pressure, density, frequency, electric charge, potential difference, resistance
- Value (Prefixes) 0.001–1000000000
- From prefix giga (G), mega (M), kilo (k), no prefix, centi (c), milli (m), micro (µ), nano (n)
- To prefix giga (G), mega (M), kilo (k), no prefix, centi (c), milli (m), micro (µ), nano (n)
- Unit (Prefixes) metre, gram, second, watt, hertz, volt, ampere
- Equation to check Displacement with constant acceleration (A), Final velocity squared, Final velocity, Displacement with constant acceleration (B), Centripetal force, Mass–energy equivalence, Kinetic energy, Pressure in a liquid, Power and velocity, Period of a pendulum (A), Period of a pendulum (B), Newton's law of gravitation, Heating a substance, Ohm's law
- Formula to derive Pendulum period, Mass–spring period, Wave speed on a string
- Pendulum length 0.1–2 m
- Mass 0.05–1 kg
- Spring constant 5–100 N/m
- String tension 1–100 N
- Mass per unit length of the string 0.001–0.05 kg/m
Questions to explore
- Why must every term of a physics equation have the same dimensions?
- Which pure number in the pendulum formula can dimensional analysis not find, and how can you find it?
- Why does a dimensionally consistent equation not have to be correct?
