SI units
Introduced| English | Meaning |
|---|---|
| SI system/ˌes ˈaɪ ˈsɪstəm/ | SI system |
| base unit/beɪs ˈjuːnɪt/ | base unit |
| derived unit/dɪˈraɪvd ˈjuːnɪt/ | A unit formed from combinations of base units. |
| homogeneous/ˌhɒməˈdʒiːniəs/ | Describing an equation whose terms have matching physical dimensions. |
| prefix/ˈpriːfɪks/ | prefix |
One language for science
- Long ago every place used its own units — feet, cubits, pounds.
- Science and trade were a mess of conversions.
- The SI system 国际单位制 fixes this: one shared set of units for everyone.
SI unit lab
Match common quantities to the correct SI unit family.
The five base units 基本单位
- Every unit in physics is built from just five base units.
- Learn these first, then build the rest.
Select all the SI base units.
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The five SI base units are the kilogram, metre, second, ampere and kelvin. The newton and joule are derived units, built from the base units.
Which of these are SI base units? Select all that apply.
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The newton is derived: kg m s^-2, straight from F = ma. The five you need are the metre, kilogram, second, ampere and kelvin.
Fun fact: the kilogram
- Until 2019 the kilogram was a real metal cylinder kept in Paris.
- Now it is fixed by a constant of nature instead.
Build a derived unit 导出单位 from its equation
- A derived unit is base units multiplied or divided.
- Build it from the equation that defines the quantity.
- Simple ones: speed $= \dfrac{\text{m}}{\text{s}}$, acceleration $= \dfrac{\text{m}}{\text{s}^2}$.
Match each derived unit to its form in SI base units.
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Each comes from its defining equation: force gives the newton, energy the joule, power the watt, and pressure the pascal.
Put the method for finding a derived unit in base units in order.
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This is why the equation matters more than memorising: the watt comes out of P = E/t and the joule out of W = Fd, every time.
Worked example: the watt in base units
- power = energy ÷ time, so $\text{W} = \dfrac{\text{J}}{\text{s}}$.
- Put in the joule: $\dfrac{1}{\text{s}} \times \dfrac{\text{kg}\cdot\text{m}^2}{\text{s}^2}$.
- Simplify: $\dfrac{\text{kg}\cdot\text{m}^2}{\text{s}^3}$.
Checking equations: homogeneity
- An equation is homogeneous 量纲一致 when both sides have the same base units.
- In $v^{2} = u^{2} + 2as$, every term works out to $\dfrac{\text{m}^2}{\text{s}^2}$ — so it balances.
Is the equation $v = u + at$ homogeneous?
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Yes — every term is a speed. $v$ and $u$ are $\dfrac{\text{m}}{\text{s}}$, and $at = \dfrac{\text{m}}{\text{s}^2} \times \text{s} = \dfrac{\text{m}}{\text{s}}$.
An equation is homogeneous when every term has the same ____ units.
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A homogeneous equation may still be wrong, because a missing factor of one half carries no units. But a non-homogeneous equation is certainly wrong.
Matching units do not prove an equation is right — the number could still be wrong. But if the units don't match, it is wrong for sure.
Using base units, which equation is not homogeneous (so must be wrong)?
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In $v = u + a$, $a$ is $\dfrac{\text{m}}{\text{s}^2}$ but $u$ is $\dfrac{\text{m}}{\text{s}}$ — the units do not match, so it cannot be right. The other three are homogeneous.
Prefixes 词头
- A prefix scales a unit by a power of ten.
- You must know the ten in the syllabus, from pico to tera.
Put these prefixes in order, smallest factor first.
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In order of size: nano, micro, milli, then kilo, mega. Each step up this list is a larger power of ten.
A square has sides of 5.0 cm. What is its area in square metres, in units of 1e-3 m^2?
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0.050 m squared is 2.5e-3 m^2. Converting after squaring, or dividing by 100 instead of 10000, is the classic area-prefix error.
Converting a prefixed unit
- Replace each prefix with its power of ten, then simplify.
- kilo $=10^{3}$, so $2\ \text{kN} = 2 \times 10^{3}\ \text{N} = 2000\ \text{N}$.
A force is $2\ \text{kN}$. How many newtons is that?
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kilo means $\times 10^{3}$, so $2\ \text{kN} = 2 \times 10^{3}\ \text{N} = 2000\ \text{N}$.
Watch the squares
- For a squared unit like $\text{mm}^2$, square the factor too.
$(10^{-3}\ \text{m})^{2} = 10^{-6}\ \text{m}^{2}$, not $10^{-3}\ \text{m}^{2}$.
What is $(10^{-3}\ \text{m})^{2}$, written in $\text{m}^2$?
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Square the factor too: $(10^{-3})^{2} = 10^{-6}$, so $(10^{-3}\ \text{m})^{2} = 10^{-6}\ \text{m}^2$ — not $10^{-3}$.
You've got it
- every unit is built from the five base units: kg, m, s, A, K
- a derived unit comes from the equation that defines it
- check an equation with homogeneity — and when a prefix is squared, square its factor too