📚 SI Base Units and Derived Units in IB Physics | IB物理：SI基本单位与导出单位
One of the first and most fundamental topics in any IB Physics course is the International System of Units (SI). Understanding the distinction between base units and derived units is not just a matter of memorisation—it underpins every formula, calculation and data analysis you will ever perform in the course. This article gives you a complete, exam-ready guide to SI base units and derived units, including worked examples and common traps to avoid.
任何IB物理课程中最基础、最早涉及的主题之一就是国际单位制（SI）。理解基本单位与导出单位之间的区别，不仅仅是为了记忆，它支撑着你将在课程中进行的每一个公式、计算和数据分析。这篇文章将为你提供一份完整、紧扣考点的SI基本单位与导出单位指南，包括计算示例和常见陷阱提醒。
1. Why SI Units Matter | 为什么SI单位如此重要
Physics is a quantitative science. Every measurement we make—length, time, mass, current, temperature—requires a standardised system of units so that results can be compared and reproduced worldwide. The SI (Système International) is that system. Since the 2019 redefinition, all seven SI base units are defined in terms of fundamental physical constants, making the system stable and independent of any physical artefact.
物理是一门定量科学。我们进行的每一次测量——长度、时间、质量、电流、温度——都需要一套标准化的单位体系，以便结果能在全球范围内进行比较和复现。SI（国际单位制）就是这样的体系。自2019年重新定义以来，所有七个SI基本单位都依据基本物理常数来定义，使该体系稳定且不依赖于任何实物原器。
In IB Physics, you are expected to know the seven base units, recognise derived units, and be able to express derived units in terms of base units. This skill is frequently tested in Paper 1 and Paper 2, often in the context of definitions or unit-conversion questions.
在IB物理中，你应当熟记七个基本单位、识别导出单位，并能用基本单位来表示导出单位。这一技能在Paper 1和Paper 2中经常被考查，通常以定义题或单位换算题的形式出现。
2. The Seven SI Base Units | 七个SI基本单位
The seven base units are the building blocks of the SI system. Each corresponds to a fundamental physical quantity. The table below shows each base unit, its symbol, and the quantity it measures.
七个基本单位是SI体系的基石。每个基本单位对应一个基本物理量。下表显示了每个基本单位、其符号以及它测量的物理量。
| Quantity 物理量 | Base Unit 基本单位 | Symbol 符号 |
|---|---|---|
| Length 长度 | metre 米 | m |
| Mass 质量 | kilogram 千克 | kg |
| 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 |
For IB Physics, the most commonly used base units in calculations are m, kg, s, A, K and mol. The candela (cd) is less relevant to the core syllabus but is still a required base unit. Notice that the kilogram is the only base unit with a prefix (kilo-) built into its name. This has an important consequence: when you use prefixes with the kilogram, the prefix applies to the gram, not to the kilogram.
在IB物理中，计算中最常用的基本单位是m、kg、s、A、K和mol。坎德拉（cd）与核心大纲相关性较低，但仍是一个要求掌握的基本单位。请注意，千克（kilogram）是唯一一个在名称中自带词头（千，kilo-）的基本单位。这有一个重要后果：当你给质量加上词头时，词头是加在“克（gram）”上的，而不是加在“千克”上。
Example: 1 milligram (mg) = 1 × 10⁻³ g = 1 × 10⁻⁶ kg. Many students incorrectly write 1 mg = 10⁻³ kg. Be careful!
示例：1毫克（mg）= 1 × 10⁻³ 克 = 1 × 10⁻⁶ 千克。许多学生错误地写成1 mg = 10⁻³ kg。请务必小心！
3. Derived Units: How They Are Formed | 导出单位：如何形成
A derived unit is any unit obtained by combining base units through multiplication, division, or both. Some derived units have special names (e.g. newton, joule, watt), while others are simply written as combinations of base units (e.g. m·s⁻¹ for speed).
导出单位是任何通过乘、除或两者结合基本单位而得到的单位。有些导出单位有专用名称（如牛顿、焦耳、瓦特），而其他导出单位则直接写成基本单位的组合（如速度的单位m·s⁻¹）。
The general approach to forming a derived unit is simple: start from the defining equation, substitute the units of each quantity, and simplify.
形成导出单位的一般方法很简单：从定义方程出发，代入每个量的单位，然后化简。
Speed (速度): v = d/t → unit = m/s = m·s⁻¹
Acceleration (加速度): a = Δv/t → unit = (m·s⁻¹)/s = m·s⁻²
Note that the SI convention writes compound units with a centred dot (·) for multiplication and negative powers for division, e.g. m·s⁻² rather than m/s². IB exam papers generally use the negative-power notation, so you should be comfortable with both.
请注意，SI规定复合单位用居中圆点（·）表示乘法，用负指数表示除法，例如应写m·s⁻²而不是m/s²。IB试卷通常使用负指数记法，但你也应熟悉两种写法。
4. Named Derived Units You Must Know | 必须掌握的专用名称导出单位
The following named derived units appear frequently in the IB Physics syllabus. You should be able to recall each one’s special name, symbol, and its expression in base units.
以下带专用名称的导出单位在IB物理大纲中频繁出现。你应当能够回忆出每个单位的专用名称、符号以及用基本单位表示的表达式。
| Quantity 物理量 | Name 名称 | Symbol 符号 | In base units 基本单位表示 |
|---|---|---|---|
| Force 力 | newton 牛顿 | N | kg·m·s⁻² |
| Pressure 压强 | pascal 帕斯卡 | Pa | kg·m⁻¹·s⁻² |
| Energy, work 能量、功 | joule 焦耳 | J | kg·m²·s⁻² |
| Power 功率 | watt 瓦特 | W | kg·m²·s⁻³ |
| Electric charge 电荷量 | coulomb 库仑 | C | A·s |
| Electric 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 |
| Frequency 频率 | hertz 赫兹 | Hz | s⁻¹ |
The hertz (Hz) deserves special attention: although it represents cycles per second, in most IB contexts 1 Hz = 1 s⁻¹. One subtle point is that for angular frequency ω, the unit rad·s⁻¹ is used; the radian is a dimensionless derived unit, so rad·s⁻¹ is equivalent to s⁻¹.
赫兹（Hz）需要特别关注：尽管它表示每秒的周期数，但在大多数IB情境中1 Hz = 1 s⁻¹。一个细微之处是，对于角频率ω，使用单位rad·s⁻¹；弧度是一个无量纲的导出单位，因此rad·s⁻¹等同于s⁻¹。
5. Expressing Derived Units in Base Units: Worked Examples | 用基本单位表示导出单位：计算示例
In IB exams, you may be asked to express a given unit in base units. The key is to always start with the relevant formula. Let us go through three common examples step by step.
在IB考试中，你可能会被要求用基本单位表示给定的单位。关键在于始终从相关公式出发。让我们逐步讲解三个常见示例。
Example 1: Express the volt (V) in base units.
示例1：用基本单位表示伏特（V）。
The volt is defined from the relationship between electric potential difference and energy: V = W/q, where W is energy and q is charge. The base unit of energy (joule) is kg·m²·s⁻², and the base unit of charge (coulomb) is A·s. Therefore:
伏特由电势差与能量之间的关系定义：V = W/q，其中W是能量，q是电荷。能量（焦耳）的基本单位是kg·m²·s⁻²，电荷（库仑）的基本单位是A·s。因此：
V = (kg·m²·s⁻²) / (A·s) = kg·m²·s⁻³·A⁻¹
Example 2: Express the ohm (Ω) in base units.
示例2：用基本单位表示欧姆（Ω）。
Using Ohm’s law, R = V/I. Since V = kg·m²·s⁻³·A⁻¹ and I has base unit A, we get:
根据欧姆定律，R = V/I。已知V = kg·m²·s⁻³·A⁻¹，而I的基本单位是A，因此：
Ω = (kg·m²·s⁻³·A⁻¹) / A = kg·m²·s⁻³·A⁻²
Example 3: Express the pascal (Pa) in base units.
示例3：用基本单位表示帕斯卡（Pa）。
Pressure is defined as force per unit area, P = F/A. Force F = ma, so the newton is kg·m·s⁻². Area has unit m². Therefore:
压强定义为力除以面积，P = F/A。力F = ma，所以牛顿为kg·m·s⁻²。面积的单位是m²。因此：
Pa = (kg·m·s⁻²) / m² = kg·m⁻¹·s⁻²
Notice how the negative exponent appears when we move the metre to the numerator. Always check that you have simplified the expression fully.
注意当米被移到分子时如何出现负指数。务必检查你是否已完整化简表达式。
6. Dimensional Analysis and Homogeneity | 量纲分析与齐次性
One of the most powerful skills in IB Physics is checking whether an equation is dimensionally consistent, also called homogeneous. This means that both sides of an equation must have the same SI base units. If they do not, the equation cannot be physically correct.
IB物理中最强大的技能之一是检查方程是否量纲一致，也称为齐次性。这意味着方程两边必须具有相同的SI基本单位。如果不一致，方程在物理上就不可能正确。
Consider the equation of motion: v² = u² + 2as. Let us check units. The left side v² has units (m·s⁻¹)² = m²·s⁻². On the right side, u² clearly has the same units as v². The term 2as has units (m·s⁻²)(m) = m²·s⁻². Both sides match, so the equation is homogeneous.
考虑运动学方程：v² = u² + 2as。让我们检查单位。左边v²的单位是(m·s⁻¹)² = m²·s⁻²。在右边，u²显然与v²单位相同。项2as的单位是(m·s⁻²)(m) = m²·s⁻²。两边匹配，因此该方程是齐次的。
Dimensional analysis can also help you determine unknown exponents in physical relationships. For example, if a period T of a pendulum depends on length L and gravitational acceleration g, you can deduce that T ∝ √(L/g), because the only way to obtain seconds from L and g is:
量纲分析还可以帮助你确定物理关系中未知的指数。例如，如果摆的周期T取决于摆长L和重力加速度g，你可以推导出T ∝ √(L/g)，因为从L和g得到秒的唯一方式是：
√(L/g) has units √(m / (m·s⁻²)) = √(s²) = s
In an exam, if you ever suspect an error in a formula, always perform a quick unit check. This can catch algebra mistakes before you commit to an answer.
在考试中，如果你怀疑公式有误，请始终快速进行单位检查。这可以在你确定答案之前发现代数错误。
7. SI Prefixes and Scientific Notation | SI词头与科学记数法
Quantities in physics span an enormous range—from the size of an atomic nucleus (10⁻¹⁵ m) to the distance to distant galaxies (10²⁶ m). SI prefixes allow us to express such extreme magnitudes conveniently. You are expected to know the prefixes shown in the table below.
物理量的数值跨越极其巨大的范围——从原子核的大小（10⁻¹⁵ m）到遥远星系的距离（10²⁶ m）。SI词头使我们能够方便地表达如此极端的量级。你应当掌握下表中列出的词头。
| Prefix 词头 | Symbol 符号 | Factor 倍数 |
|---|---|---|
| tera 太 | T | 10¹² |
| giga 吉 | G | 10⁹ |
| mega 兆 | M | 10⁶ |
| kilo 千 | k | 10³ |
| deci 分 | d | 10⁻¹ |
| centi 厘 | c | 10⁻² |
| milli 毫 | m | 10⁻³ |
| micro 微 | μ | 10⁻⁶ |
| nano 纳 | n | 10⁻⁹ |
| pico 皮 | p | 10⁻¹² |
In IB Physics, you are not required to memorise all prefixes, but you should be comfortable with those from pico (10⁻¹²) to tera (10¹²). When expressing answers, use scientific notation and choose an appropriate prefix so that the numerical value is neither too large nor too small. A common convention is to keep numbers between 1 and 1000 when using prefixes.
在IB物理中，并不要求你记住所有词头，但你应当熟练使用从皮（10⁻¹²）到太（10¹²）的词头。在表达答案时，请使用科学记数法并选择合适的词头，使数值既不太大也不太校一个常见惯例是使用词头时保持数值在1到1000之间。
Example: A capacitor has a value of 4700 μF. Express this in farads (F). Answer: 4700 × 10⁻⁶ F = 4.7 × 10⁻³ F = 4.7 mF.
示例：一个电容器的值为4700 μF。用法拉表示是多少？答案：4700 × 10⁻⁶ F = 4.7 × 10⁻³ F = 4.7 mF。
8. Common Errors in IB Examinations | IB考试中的常见错误
Even strong students lose marks on this topic through avoidable mistakes. The following list covers the most frequent errors seen in IB examinations.
即使是优秀学生也会在这个主题上因可避免的错误而失分。以下列表涵盖了IB考试中最常见的错误。
- Confusing mass and weight: Mass is measured in kilograms (kg), while weight is a force measured in newtons (N). They are different physical quantities.
- 混淆质量与重量：质量以千克（kg）为单位，而重量是一种力，以牛顿（N）为单位。它们是不同的物理量。
- Writing unit prefixes incorrectly with kg: As noted earlier, 1 mg equals 10⁻⁶ kg, not 10⁻³ kg. Watch out for this in conversions.
- 把词头错误地用于千克：如前所述，1 mg = 10⁻⁶ kg，而不是10⁻³ kg。换算时要特别注意这一点。
- Forgetting to square or cube units: When calculating area or volume, the units must also be squared or cubed. For example, a square of side 2 cm has area 4 cm² = 4 × 10⁻⁴ m², not 4 × 10⁻² m².
- 忘记对单位取平方或立方：在计算面积或体积时，单位也必须平方或立方。例如，边长为2 cm的正方形面积为4 cm² = 4 × 10⁻⁴ m²，而不是4 × 10⁻² m²。
- Mixing up base units and derived units: The newton is a derived unit, not a base unit. When a question asks for a quantity in base units, you must express N as kg·m·s⁻², J as kg·m²·s⁻², and so on.
- 混淆基本单位与导出单位：牛顿是导出单位，不是基本单位。当问题要求以基本单位表示一个量时，你必须将N写成kg·m·s⁻²，将J写成kg·m²·s⁻²，依此类推。
- Using °C instead of K in temperature-related equations: In IB Physics, most thermodynamic calculations require temperature in kelvin. Always convert from Celsius to kelvin first.
- 在与温度相关的方程中使用°C而不是K：在IB物理中，大多数热力学计算要求温度以开尔文为单位。务必先将摄氏度转换为开尔文。
Always read the question carefully: if it asks for the answer in SI base units, give the fully expanded form. If it asks for the answer in named derived units, you may use N, J, V, etc.
务必仔细阅读问题：如果要求以SI基本单位作答，请给出完整展开形式。如果要求以专用名称导出单位作答，则可以使用N、J、V等。
9. Quick Check and Exam-Style Practice | 快速自测与考题式练习
Let us test your understanding with a few quick questions. Try to answer them before reading the solutions.
让我们用几个快速问题测试你的理解。请在阅读解答前尝试作答。
Question 1: Express the watt (W) in base units.
问题1：用基本单位表示瓦特（W）。
Solution: W = J/s, where J = kg·m²·s⁻². Therefore W = kg·m²·s⁻³.
解答： W = J/s，其中J = kg·m²·s⁻²。因此W = kg·m²·s⁻³。
Question 2: What is the SI base unit of electric charge?
问题2：电荷的SI基本单位是什么？
Solution: The coulomb (C) is a derived unit. In base units, C = A·s.
解答： 库仑（C）是导出单位。用基本单位表示为C = A·s。
Question 3: A length is measured as 250 nm. Express this in metres and in micrometres.
问题3：某长度测得为250 nm。请用米和微米表示。
Solution: 250 nm = 250 × 10⁻⁹ m = 2.5 × 10⁻⁷ m. Since 1 μm = 10⁻⁶ m, we have 2.5 × 10⁻⁷ m = 0.25 μm.
解答： 250 nm = 250 × 10⁻⁹ m = 2.5 × 10⁻⁷ m。由于1 μm = 10⁻⁶ m，因此2.5 × 10⁻⁷ m = 0.25 μm。
Question 4: The period of a simple pendulum T is given by T = 2π√(L/g). Show that this equation is dimensionally consistent.
问题4：单摆的周期T由T = 2π√(L/g)给出。证明该方程量纲一致。
Solution: The constant 2π is dimensionless. The quantity L/g has units m / (m·s⁻²) = s². Taking the square root gives s. Since the period T is measured in seconds, the equation is dimensionally consistent.
解答：常数2π是无量纲的。量L/g的单位为m / (m·s⁻²) = s²。取平方根得到s。由于周期T以秒为单位测量，该方程量纲一致。
10. Conclusion and Final Tips | 结论与最终建议
Mastering SI base units and derived units is essential for success in IB Physics. This topic appears in many forms across the syllabus: in definitions, in calculations, in data analysis and in practically every equation you will use. The key takeaway is to understand how units are built from definitions, to be able to express any derived unit in terms of base units, and to use dimensional analysis as a check on your work.
掌握SI基本单位和导出单位对于IB物理的成功至关重要。这一主题以多种形式出现在大纲中：定义题、计算题、数据分析，以及你能用到的几乎每一个方程中。关键在于理解单位如何从定义构建，能够用基本单位表示任何导出单位，并用量纲分析检查你的工作。
Here are our final tips for exam revision on this topic:
以下是关于这一主题的最终考试复习建议：
- Make a table of the seven base units and their symbols. Recite them until automatic.
- 制作七个基本单位及其符号的表格。反复背诵直到脱口而出。
- Create flashcards for named derived units, including their base-unit expression.
- 为带专用名称的导出单位制作闪卡，包括其基本单位表达式。
- Practise expressing units in base units using formulas like F = ma, P = F/A, W = qV, E = mc².
- 练习使用F = ma、P = F/A、W = qV、E = mc²等公式将单位表示为基本单位。
- Always check the homogeneity
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