Core Concepts of the SI System | SI单位制的核心概念

📚 Core Concepts of the SI System | SI单位制的核心概念

The International System of Units (SI) is the globally accepted framework for measurement in science and everyday life. In CIE A-Level Physics, a firm grasp of SI units is not just a starting point but a recurring skill tested across mechanics, electricity, thermal physics, and beyond.

国际单位制（SI）是全球科学界和日常生活中普遍接受的计量体系。在 CIE A-Level 物理中，牢固掌握 SI 单位不仅是学习的起点，更是贯穿力学、电学、热学等各章节的反复考查技能。

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1. What Is the SI System | 什么是 SI 单位制

The SI system, established by international treaty, defines seven base units from which all other physical quantities are derived. It replaced older, inconsistent systems (such as the cgs system) to ensure that scientists and engineers worldwide communicate measurements unambiguously.

SI 单位制由国际条约确立，定义了七个基本单位，所有其他物理量均由这些基本单位导出。它取代了旧有的、不一致的单位体系（如 cgs 制），确保全球科学家和工程师能够无歧义地交流测量结果。

Every physical quantity in A-Level Physics — force, energy, pressure, resistance — can ultimately be expressed in terms of the seven base units. This structural simplicity is why SI is the standard for all scientific work.

A-Level 物理中的每一个物理量——力、能量、压强、电阻——最终都可以用七个基本单位来表示。这种结构上的简洁性正是 SI 成为所有科学工作标准的原因。

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2. The Seven Base Units | 七个基本单位

There are exactly seven base quantities in the SI system, each with its own unit symbol. Memorising these is essential for CIE examinations.

SI 单位制中有七个基本量，每个都有对应的单位符号。牢记这些是 CIE 考试的基本要求。

Base Quantity 基本量	Base Unit 基本单位	Symbol 符号
Mass 质量	kilogram 千克	kg
Length 长度	metre 米	m
Time 时间	second 秒	s
Electric current 电流	ampere 安培	A
Temperature 热力学温度	kelvin 开尔文	K
Amount of substance 物质的量	mole 摩尔	mol
Luminous intensity 发光强度	candela 坎德拉	cd

Notice that the kilogram is the only base unit whose name contains an SI prefix. This historical quirk means that when converting between base and derived units, you must never “strip the prefix” from kg when working in base units — the kg itself is the base unit.

注意，千克是唯一一个名称中含有 SI 词头的基本单位。这个历史遗留问题意味着，在以基本单位进行计算时，绝不能把 kg 中的“k”去掉再当基本单位——kg 本身就是基本单位。

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3. The 2019 Redefinition | 2019 年的重新定义

In May 2019, the SI system underwent a landmark change. All seven base units are now defined in terms of fundamental constants of nature, rather than physical artefacts. This makes the system universally reproducible and immune to damage or drift.

2019 年 5 月，SI 单位制经历了一次里程碑式的变革。所有七个基本单位如今均以自然基本常数来定义，而非实物基准。这使得整个体系可以在任何地方复现，并且不受损坏或漂移影响。

Three definitions appear regularly in CIE questions, so they are worth memorising in precision:

在 CIE 考题中，以下三个定义出现频率较高，值得精确记忆：

• The second is defined by the caesium-133 hyperfine transition frequency: Δν₍Cs₎ = 9 192 631 770 Hz.

  秒的定义基于铯-133 原子超精细跃迁频率：Δν₍Cs₎ = 9 192 631 770 Hz。

• The metre is defined by fixing the speed of light: c = 299 792 458 m s⁻¹.

  米（米制）的定义通过固定光速实现：c = 299 792 458 m s⁻¹。

• The kilogram is defined by fixing the Planck constant: h = 6.626 070 15 × 10⁻³⁴ J s.

  千克的定义通过固定普朗克常数实现：h = 6.626 070 15 × 10⁻³⁴ J s。

For the exam, you do not need to recall numerical values, but you should be able to state that each base unit is defined by a fixed numerical value of a fundamental constant.

对于考试，你不需要回忆这些数值，但应当能够说明每个基本单位都是通过某个基本常数的固定数值来定义的。

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4. Derived Units and Special Names | 导出单位与专用名称

Derived units are formed by combining base units according to the defining equations of physics. Many derived units have special names and symbols that are more convenient in daily use.

导出单位由基本单位按照物理定义方程组合而成。许多导出单位拥有专用名称和符号，在日常使用中更加便捷。

Derived Quantity 导出量	Special Name 专用名称	Symbol 符号	In Base Units 用基本单位表示
Force 力	newton 牛顿	N	kg m s⁻²
Energy 能量	joule 焦耳	J	kg m² s⁻²
Power 功率	watt 瓦特	W	kg m² s⁻³
Pressure 压强	pascal 帕斯卡	Pa	kg m⁻¹ s⁻²
Frequency 频率	hertz 赫兹	Hz	s⁻¹
Electric charge 电荷量	coulomb 库仑	C	A s
Potential difference 电势差	volt 伏特	V	kg m² s⁻³ A⁻¹
Electrical resistance 电阻	ohm 欧姆	Ω	kg m² s⁻³ A⁻²

You should be fluent in converting between the special name and the base-unit expression. For example, a question that asks you to derive the SI unit of the gravitational constant G should lead you through N m² kg⁻² to m³ kg⁻¹ s⁻².

你应当能够熟练地在专用名称与基本单位表达式之间相互转换。例如，要求推导万有引力常量 G 的 SI 单位时，应从 N m² kg⁻² 逐步导出为 m³ kg⁻¹ s⁻²。

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5. Expressing Derived Quantities in Base Units | 用基本单位表达导出量

The ability to express a derived quantity in base units is a core CIE skill. The method is always the same: start from the defining equation of the quantity, substitute the known unit expressions, and simplify.

用基本单位表示导出量是 CIE 的核心技能。方法始终一致：从该量的定义方程出发，代入已知的单位表达式，然后化简。

Example — the base units of the gravitational constant G. From Newton’s law of gravitation:

示例——导出万有引力常量 G 的基本单位。由牛顿万有引力定律：

F = G m₁m₂ / r²

Rearranging, G = F r² / (m₁m₂). Since [F] = kg m s⁻² and [r²] = m², we obtain:

整理得 G = F r² / (m₁m₂)。由于 [F] = kg m s⁻²，[r²] = m²，可得：

[G] = (kg m s⁻²)(m²) / kg² = m³ kg⁻¹ s⁻²

This technique — start from the defining equation, substitute, simplify — applies to every derived unit you will meet, including the tesla (magnetic flux density) and the weber (magnetic flux).

这种技巧——从定义方程出发，代入，化简——适用于你遇到的一切导出单位，包括特斯拉（磁通密度）和韦伯（磁通量）。

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6. SI Prefixes | SI 词头

SI prefixes allow us to express very large or very small quantities conveniently. A prefix multiplies the base unit by a power of ten.

SI 词头让我们可以方便地表示极大或极小的量。词头将基本单位乘以十的幂次。

Prefix 词头	Symbol 符号	Factor 倍率
pico 皮	p	10⁻¹²
nano 纳	n	10⁻⁹
micro 微	μ	10⁻⁶
milli 毫	m	10⁻³
centi 厘	c	10⁻²
kilo 千	k	10³
mega 兆	M	10⁶
giga 吉	G	10⁹
tera 太	T	10¹²

Two lower-case traps appear often: “m” (milli) versus “M” (mega) — they differ by a factor of 10⁹. Similarly, “n” (nano) and “p” (pico) are easy to confuse in handwritten work. Write the symbol clearly and always check whether your final answer has a physically reasonable magnitude.

两个小写陷阱经常出现：“m”（毫）与“M”（兆）相差 10⁹ 倍。同样地，“n”（纳）与“p”（皮）在手写时容易混淆。请清晰书写符号，并始终检查最终答案的数量级是否在物理上合理。

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7. Dimensional Analysis | 量纲分析

Dimensional analysis is a powerful tool that checks whether a derived equation is physically consistent. The principle is simple: every term in a valid physical equation must have the same dimensions.

量纲分析是检验导出方程是否物理自洽的有力工具。原理很简单：任何成立的物理方程中，每一项都必须具有相同的量纲。

In A-Level work, you can use base units directly as a proxy for dimensions. For example, consider the kinetic energy equation Eₖ = ½mv². The left-hand side has units kg m² s⁻² (joule). The right-hand side gives kg × (m s⁻¹)² = kg m² s⁻². Both sides agree.

在 A-Level 学习中，可以直接用基本单位作为量纲的代理。例如动能方程 Eₖ = ½mv²。左侧单位为 kg m² s⁻²（焦耳）。右侧得 kg × (m s⁻¹)² = kg m² s⁻²。两边一致。

Dimensional analysis is frequently used in CIE structured questions where you are asked to determine whether a proposed equation could be correct, or to find unknown exponents. Always work symbolically and do not drop the numerical constants such as ½ or π during the check — they are dimensionless but their presence does not affect unit consistency.

量纲分析在 CIE 结构题中经常使用，例如判断一个假定的方程是否可能正确，或确定未知指数。进行检验时务必全程使用符号运算，不要随意丢弃 ½ 或 π 这类数值常数——它们是无量纲的，但存在与否不影响单位的一致性。

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8. Unit Conversion | 单位换算

You should be able to perform conversions both between SI prefixes and between related non-SI units that appear in the syllabus, such as the electronvolt (eV).

你应当能够进行 SI 词头之间的换算，也能进行课程大纲中出现的相关非 SI 单位之间的换算，例如电子伏特（eV）。

The electronvolt is defined as the energy transferred when an electron moves through a potential difference of one volt:

电子伏特定义为电子通过一伏特电势差时所获得的能量：

1 eV = 1.6 × 10⁻¹⁹ J

This conversion factor appears throughout particle physics and atomic physics questions, and you will often need to combine it with E = hf or E = mc². It is not an SI unit, but the SI unit for energy — the joule — is always used in final calculated answers unless otherwise stated.

这个换算系数在粒子物理和原子物理题目中反复出现，你常需要将它和 E = hf 或 E = mc² 结合使用。eV 不是 SI 单位，但除非题目另有说明，最终计算答案中能量的 SI 单位始终是焦耳。

When converting squared or cubed units, remember that the factor applies to the power as well. For example, 1 cm² = 10⁻⁴ m², not 10⁻² m². A square of side 1 cm has area 0.0001 m².

当换算平方或立方单位时，请记住倍率的幂次也要变化。例如 1 cm² = 10⁻⁴ m²，而不是 10⁻² m²。边长为 1 cm 的正方形面积为 0.0001 m²。

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9. Exam Pitfalls and Common Errors | 考试陷阱与常见错误

CIE examiners report the same unit-related errors year after year. Knowing these traps in advance is a direct route to higher marks.

CIE 考官每年都会报告同样的单位相关错误。提前了解这些陷阱是提高分数的直接途径。

• Writing “sec” instead of “s” — only the symbol “s” is accepted for second in CIE physics.

  将秒写成“sec”而非“s”——在 CIE 物理中，只有符号“s”被接受为秒的单位。

• Confusing weight (a force, unit N) with mass (unit kg). Weight = mass × g.

  混淆重量（力，单位 N）与质量（单位 kg）。重量 = 质量 × g。

• Leaving square brackets inconsistently: [F] = kg m s⁻² is correct, but writing F = kg m s⁻² is acceptable shorthand in many exam answers — the key is to stay consistent throughout a calculation.

  方括号使用不一致：[F] = kg m s⁻² 是严谨写法，而 F = kg m s⁻² 在很多考试答案中也是可以接受的简写——关键是整个计算过程保持一致。

• Forgetting that the kelvin is a base unit, not an SI prefix. The degree Celsius is not an SI base unit.

  忘记开尔文是基本单位而不是 SI 词头。摄氏温度并非 SI 基本单位。

• Writing the ampere as a derived unit — it is one of the seven base units.

  将安培当作导出单位——它是七个基本单位之一。

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10. Revision Priorities and Exam Strategy | 复习重点与应试策略

For CIE A-Level physics, unit-based questions typically take one of three forms. Prepare for each deliberately.

在 CIE A-Level 物理中，单位类题目通常有三种形式。请有针对性地进行准备。

First, direct questions: “State the SI base units of X.” These are memory questions — use a mnemonic or write flash cards for force, energy, pressure, power, charge, potential difference, resistance, and frequency.

第一，直接提问：“写出 X 的 SI 基本单位。”这类是记忆题——使用口诀或闪卡记忆力、能量、压强、功率、电荷量、电势差、电阻和频率的基本单位表达。

Second, derivation questions: “Show that the unit of Y is equivalent to …” These test your ability to start from the defining equation and manipulate units algebraically. Practise with pressure P = F/A, density ρ = m/V, the ideal gas equation pV = nRT, and the period of a pendulum T = 2π√(l/g).

第二，推导题：“证明 Y 的单位等价于……”这类题考查你从定义方程出发并代数化处理单位的能力。请练习 P = F/A（压强），ρ = m/V（密度），理想气体方程 pV = nRT，以及单摆周期 T = 2π√(l/g)。

Third, equation-consistency questions: you are given a possibly incorrect equation and asked to use units to justify whether it is homogeneous. Solve by checking that both sides reduce to the same base-unit combination.

第三，方程一致性题：给出一个可能错误的方程，要求你用单位判断其是否齐次。解法是检查等号两边是否约化为相同的基本单位组合。

Finally, always state your units in final numerical answers — an answer without a unit is often awarded zero marks at CIE, regardless of the value.

最后，在最终的数值答案中务必写出单位——在 CIE 评分中，没有单位的答案即使数值正确也经常得零分。

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