📚 Fundamental and Derived SI Units | 基本与导出国际单位制单位
The International System of Units (SI) is the globally adopted modern metric system, used in virtually every field of science, engineering and daily life. In IB Physics, a thorough grasp of SI units is not just about memorising names and symbols – it is about understanding how physical quantities are measured, defined and related to one another. The system is built upon seven fundamental base units that are defined in terms of unchanging natural constants, and from these, an infinite number of derived units can be constructed. This article will walk you through the base units, their modern definitions, how derived units are formed, and how to use dimensional analysis to check equations and perform unit conversions – all essential skills for success in IB Physics.
国际单位制（SI）是当今全球通用的公制系统，几乎用于科学、工程和日常生活的所有领域。在 IB 物理中，深入掌握 SI 单位不仅在于记住名称和符号，更在于理解物理量是如何测量、定义和相互关联的。该体系建立在七个由不变的自然常数定义的基本单位之上，并由此可以构造出无数个导出单位。本文将带你逐一了解基本单位及其现代定义，导出单位如何形成，以及如何运用量纲分析检验方程并进行单位换算——这些都是 IB 物理取得优异成绩所必需的技能。
1. The Seven Base Quantities and Their Units | 七个基本量及其单位
The SI is founded upon seven carefully chosen base quantities. Each base quantity is linked to a base unit, a unique symbol, and a dimension symbol used in dimensional analysis. In the 2019 revision of the SI, all base units are defined by fixing the numerical values of seven defining constants, such as the speed of light and the Planck constant. This guarantees long-term stability and universal reproducibility, free from the limitations of physical artefacts.
SI 建立在七个精心挑选的基本量之上。每个基本量都有一个对应的基本单位、唯一的符号，以及在量纲分析中使用的维度符号。在 2019 年的 SI 修订中，所有基本单位都通过固定七个定义常数的数值来定义，例如光速和普朗克常数。这保证了长期稳定性和全球可复现性，摆脱了实物制品的限制。
The table below summarises the seven base quantities, their English and Chinese names, base units and symbols.
下表总结了七个基本量、其中英文名称、基本单位和符号。
| Base Quantity (English) | 基本量 (中文) | SI Base Unit | Unit Symbol |
|---|---|---|---|
| Length | 长度 | metre | m |
| Mass | 质量 | kilogram | kg |
| Time | 时间 | second | s |
| Electric current | 电流 | ampere | A |
| Thermodynamic temperature | 热力学温度 | kelvin | K |
| Amount of substance | 物质的量 | mole | mol |
| Luminous intensity | 光强度 | candela | cd |
In IB Physics, you will use these base units daily – from writing down quantities with correct symbols to checking whether a formula is dimensionally consistent.
在 IB 物理中，你每天都会用到这些基本单位——从用正确的符号写下物理量，到检查某个公式是否在量纲上一致。
2. The Metre – Redefined by the Speed of Light | 米——由光速重新定义
The metre (m) is no longer a platinum‑ a second. This ties the metre to the second and the exact constant c = 299 792 458 m s⁻¹.
米（m）不再是一根铂铱棒；自 1983 年起，它由真空中的光速来定义。定义指出，一米等于光在真空中于 1/299 792 458 秒的时间间隔内所行经的路径长度。这使米与秒以及精确常数 c = 299 792 458 m s⁻¹ 相联系。
In practice, the metre can be realised by interferometry using lasers with known frequencies. This ensures incredibly high precision, enabling measurements at atomic scales. The dimension of length is denoted by L in dimensional analysis.
在实践中，米可以通过使用已知频率的激光进行干涉测量来实现。这确保了极高的精度，使得在原子尺度的测量成为可能。在量纲分析中，长度的维度用 L 表示。
3. The Kilogram – From a Physical Artefact to the Planck Constant | 千克——从实物制品到普朗克常数
²). This means the kilogram is derived from the metre, the second and the Planck constant.
一个多世纪以来，千克一直由存放在巴黎附近的一个金属圆柱体定义。2019 年，这一定义发生了革命性变化：千克（kg）现在通过将普朗克常数 h 固定为 6.626 070 15 × 10⁻³⁴ J s（其中 J = kg m² s⁻²）来定义。这意味着千克由米、秒和普朗克常数导出。
The dimension of mass is M. The new definition allows mass to be realised anywhere using a Kibble balance, without relying on a physical artefact. For IB students, the key point is that the kilogram remains the base unit of mass, but its definition now rests on unchanging quantum‑mechanical constants.
质量的维度是 M。新的定义使得质量可以在任何地方使用基布尔秤来实现，而不再依赖实物制品。对于 IB 学生来说，关键点在于千克仍然是质量的基本单位，但其定义现在基于不变的量子力学常数。
4. The Second – Tied to Atomic Transitions | 秒——与原子的跃迁相联系
ding to the transition between the two hyperfine levels of the ground state of the caesium‑133 atom. This number is exact and links the second to the unperturbed ground‑state hyperfine transition frequency Δν_Cs.
自 1967 年以来，秒（s）一直由原子性质定义。它是铯‑133 原子基态的两个超精细能级之间跃迁所对应的辐射周期的 9 192 631 770 倍的持续时间。这一数字是精确的，并将秒与未受扰动的基态超精细跃迁频率 Δν_Cs 联系起来。
problems, you will often express other units, such as hertz (Hz = s⁻¹), using the second.
时间的维度是 T。秒的原子定义为 GPS、通信和科学实验提供了基础。在力学问题中，你经常会用秒来表示其他单位，例如赫兹（Hz = s⁻¹）。
5. The Ampere – Defined by the Elementary Charge | 安培——由基本电荷定义
rent corresponding to the flow of 1/(1.602 176 634 × 10⁻¹⁹) elementary charges per second.
安培（A）是电流的基本单位。自 2019 年起，它通过将基本电荷 e 固定为 1.602 176 634 × 10⁻¹⁹ C（其中 C = A s）来定义。因此，一安培对应于每秒流过 1/(1.602 176 634 × 10⁻¹⁹) 个基本电荷的电流。
gnetic fields, always remember that charge in coulombs (C) is a derived unit: 1 C = 1 A s.
电流的维度是 I。这一定义将安培与秒和基本电荷直接联系起来。在 IB 物理中，当分析电路或磁场时，要始终记住电荷库仑（C）是导出单位：1 C = 1 A s。
6. The Kelvin – No Longer Based on Water | 开尔文——不再基于水的性质
the kelvin to the joule, which itself is derived from kg, m and s. The change means that the triple point of water is no longer the defining reference, though it remains a valuable calibration point.
开尔文（K）是热力学温度的基本单位。它现在通过将玻尔兹曼常数 k 固定为 1.380 649 × 10⁻²³ J K⁻¹ 来定义。这使得开尔文与焦耳联系起来，而焦耳本身由 kg、m 和 s 导出。这一变化意味着水的三相点不再是定义参考，尽管它仍是一个有价值的校准点。
The dimension of temperature is Θ (theta). For everyday use, temperature differences are often expressed in kelvin, and the Celsius scale is offset by exactly 273.15 K. In thermal physics problems, always be prepared to convert between temperature scales and use absolute temperatures when applying gas laws.
温度的维度是 Θ。在日常使用中，温度差通常以开尔文表示，摄氏温标则偏移了精确的 273.15 K。在热物理问题中，要随时准备在温标之间进行转换，并在应用气体定律时使用绝对温度。
7. The Mole and Candela – Amount of Substance and Light Measurement | 摩尔与坎德拉——物质的量和光的测量
The mole (mol) is the unit for amount of substance. It is defined by fixing the Avogadro constant NA ly 6.022 140 76 × 10²³ mol⁻¹. One mole contains exactly this number of elementary entities – s definition links the mole to a pure number, disconnecting it from the kilogram of carbon‑12.
摩尔（mol）是物质的量的单位。它通过将阿伏伽德罗常数 NA 固定为 6.022 140 76 × 10²³ mol⁻¹ 来定义。一摩尔恰好含有这个数目的基本实体——原子、分子、离子、电子等。这一定义将摩尔与一个纯数字联系起来，使其不再与碳‑12 的千克挂钩。
² Hz to be 683 lm W⁻¹. Its dimension is J. Although the candela is less common in core IB mechanics, it completes the set of seven base units.
物质的量的维度是 N。坎德拉（cd）用于测量发光强度，它通过将频率为 540 × 10¹² Hz 的单色辐射的光视效能固定为 683 lm W⁻¹ 来定义。其维度是 J。虽然坎德拉在 IB 核心力学中不太常见，但它完善了七个基本单位的集合。
8. Derived Units: The Building Blocks of Physics | 导出单位：物理学的基石
its unit is m²; volume is m³; speed is distance/time, giving m s⁻¹; acceleration is m s⁻².
任何非基本单位的 SI 单位都是导出单位。导出单位是通过根据相应物理量的代数关系组合基本单位而形成的。例如，面积是长度 × 宽度，因此其单位是 m²；体积是 m³；速度是距离/时间，单位为 m s⁻¹；加速度为 m s⁻²。
Many derived units have special names and symbols for convenience. The table below lists some of the most frequently encountered derived units in IB Physics, along with their expressions in base units.
为方便起见，许多导出单位具有专门的名称和符号。下表列出了 IB 物理中最常遇到的一些导出单位及其用基本单位表示的形式。
| Physical Quantity (English) | 物理量 (中文) | Unit Name & Symbol | Expression in Base Units |
|---|---|---|---|
| Force | 力 | newton (N) | kg m s⁻² |
| Energy, work, heat | 能量、功、热量 | joule (J) | kg m² s⁻² |
| Power | 功率 | watt (W) | kg m² s⁻³ |
| Pressure | 压强 | pascal (Pa) | kg m⁻¹ s⁻² |
| Electric charge | 电荷 | coulomb (C) | A s |
| Potential difference | 电势差 | volt (V) | kg m² s⁻³ A⁻¹ |
| Resistance | 电阻 | ohm (Ω) | kg m² s⁻³ A⁻² |
| Frequency | 频率 | hertz (Hz) | s⁻¹ |
Notice that each derived unit can be expressed as a product of powers of base units. This is the key to dimensional analysis, which you will use to verify whether an equation is physically meaningful.
请注意，每个导出单位都可以表示为基本单位幂次的乘积。这是量纲分析的关键，你将利用它来验证某个方程在物理上是否有意义。
9. Dimensional Analysis: Unlocking the Checks and Balances of Equations | 量纲分析：方程检验的核心工具
In IB Physics, you are expected to use dimensional analysis to check the consistency of equations. Each physical quantity is assigned a dimension – a combination of the base dimensions M (mass), L (length),
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