SI Units and Measurements | 国际单位制与测量

📚 SI Units and Measurements | 国际单位制与测量

The International System of Units (SI) provides a universal language for measurement in physics and across all sciences. In AQA A-level Physics, a deep understanding of SI units, their definitions, prefixes, and uncertainties is essential for both written examinations and practical assessments.

国际单位制（SI）为物理学及所有科学领域提供了一种通用的测量语言。在AQA A-level物理中，深入理解SI单位、其定义、词头以及不确定度，是应对笔试和实验考核的基础。

1. The Importance of Standard Units | 标准单位的重要性

Physics is a quantitative science; every measurement must be compared to a fixed, reproducible standard. Without internationally agreed units, scientific communication would be chaotic and measurements from different laboratories could not be compared reliably.

物理学是一门定量科学；每一项测量都必须与一个固定且可复现的标准进行比较。如果没有国际统一的单位，科学交流将陷入混乱，不同实验室的测量结果也无法可靠比较。

SI units are based on fundamental constants of nature, which are invariant and can be replicated anywhere in the universe. This ensures that a metre in London is exactly the same length as a metre in Tokyo or on Mars.

SI单位基于自然界的物理常数，这些常数是不变的，且可在宇宙任意位置复现。这保证了伦敦的1米与东京或火星上的1米严格相等。

2. The Seven Base Quantities and Units | 七个基本量与基本单位

AQA A-level Physics requires you to know the seven base quantities and their corresponding SI units. These are the building blocks from which all other units are derived.

AQA A-level物理要求你掌握七个基本量及其对应的SI单位。这些是从中导出所有其他单位的基础。

Base Quantity	Base Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

3. Modern Definitions of Base Units | 基本单位的现代定义

Since 2019, all SI base units are defined in terms of exact numerical values of fundamental constants. AQA A-level exams may ask you to recall or interpret these definitions.

自2019年起，所有SI基本单位都通过基本常数的精确数值来定义。AQA A-level考试可能要求你回忆或解释这些定义。

Metre: defined by setting the speed of light in vacuum c = 299 792 458 m s⁻¹. The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

米：通过设定真空中光速 c = 299 792 458 m s⁻¹ 来定义。1米是光在真空中于1/299 792 458秒的时间间隔内传播的路径长度。

Kilogram: defined by setting the Planck constant h = 6.626 070 15 × 10⁻³⁴ J s. The kilogram is now realised through the Kibble balance or the X-ray crystal density method.

千克：通过设定普朗克常数 h = 6.626 070 15 × 10⁻³⁴ J s 来定义。现在通过基布尔天平或X射线晶体密度法来复现千克。

Second: defined by the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, Δν(Cs) = 9 192 631 770 Hz. The second is the duration of 9 192 631 770 periods of this radiation.

秒：通过铯-133原子基态超精细能级跃迁频率 Δν(Cs) = 9 192 631 770 Hz 来定义。1秒是该辐射9 192 631 770个周期的持续时间。

Ampere: defined by setting the elementary charge e = 1.602 176 634 × 10⁻¹⁹ A s. The ampere is the electric current corresponding to the flow of 1/1.602 176 634 × 10⁻¹⁹ elementary charges per second.

安培：通过设定基本电荷 e = 1.602 176 634 × 10⁻¹⁹ A s 来定义。1安培是每秒流过1/1.602 176 634 × 10⁻¹⁹个基本电荷所对应的电流。

Kelvin: defined by setting the Boltzmann constant k = 1.380 649 × 10⁻²³ J K⁻¹. The kelvin is equal to the change in thermodynamic temperature that results in a change of thermal energy kT of 1.380 649 × 10⁻²³ J.

开尔文：通过设定玻尔兹曼常数 k = 1.380 649 × 10⁻²³ J K⁻¹ 来定义。1开尔文是使热能量 kT 变化1.380 649 × 10⁻²³ J所对应的热力学温度变化。

Mole: defined by the Avogadro constant Nₐ = 6.022 140 76 × 10²³ mol⁻¹. One mole contains exactly this number of elementary entities.

摩尔：通过阿伏伽德罗常数 Nₐ = 6.022 140 76 × 10²³ mol⁻¹ 来定义。1摩尔恰好包含该数目的基本实体。

Candela: defined by the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² Hz, with a value of 683 lm W⁻¹. This is rarely tested at A-level.

坎德拉：通过频率为540 × 10¹² Hz的单色辐射的光视效能683 lm W⁻¹ 来定义。此定义在A-level中很少考查。

4. Derived Units | 导出单位

Derived units are combinations of base units. You should be able to express any physical quantity in terms of base units. This skill is often tested in exam questions.

导出单位是基本单位的组合。你应该能够用基本单位表示任意物理量。这一技能在考试中经常考查。

Newton (N) = kg m s⁻²
Joule (J) = kg m² s⁻²
Watt (W) = kg m² s⁻³
Pascal (Pa) = kg m⁻¹ s⁻²
Hertz (Hz) = s⁻¹
Coulomb (C) = A s
Volt (V) = kg m² s⁻³ A⁻¹
Ohm (Ω) = kg m² s⁻³ A⁻²
Tesla (T) = kg s⁻² A⁻¹

For example, the volt can be derived from the definition of potential difference: power = V × I, so V = W/A = kg m² s⁻³ A⁻¹.

例如，伏特可从电势差的定义推导：功率 = 电压 × 电流，所以 V = W/A = kg m² s⁻³ A⁻¹。

5. Prefixes and Powers of Ten | 词头与十的幂

SI prefixes allow quantities to be expressed in convenient magnitudes. AQA A-level expects you to know and apply prefixes from 10⁻¹⁵ to 10¹⁵.

SI词头使我们能够以方便的尺度表示物理量。AQA A-level要求你掌握并应用从10⁻¹⁵到10¹⁵的词头。

Prefix	Symbol	Power
peta	P	10¹⁵
tera	T	10¹²
giga	G	10⁹
mega	M	10⁶
kilo	k	10³
centi	c	10⁻²
milli	m	10⁻³
micro	μ	10⁻⁶
nano	n	10⁻⁹
pico	p	10⁻¹²
femto	f	10⁻¹⁵

When converting between units, count the number of powers of ten. For example, a nanometre (nm) is 10⁻⁹ m, so 1 m = 10⁹ nm.

在进行单位换算时，计算十的幂的数目。例如，1纳米(nm) = 10⁻⁹ m，所以1 m = 10⁹ nm。

6. Significant Figures and Scientific Notation | 有效数字与科学记数法

Every measurement in physics has an associated uncertainty, and the way we record results must reflect the precision of the instrument. This is the basis of significant figures.

物理中的每次测量都伴随不确定度，记录结果的方式必须反映仪器的精度。这就是有效数字的基础。

Rules for counting significant figures:

计算有效数字的规则：

All non-zero digits are significant.
Zeros between non-zero digits are significant.
Leading zeros are not significant (e.g. 0.0052 has two significant figures).
Trailing zeros after a decimal point are significant (e.g. 2.50 has three).

所有非零数字均为有效。
非零数字之间的零是有效的。
前导零无效（例如0.0052有两位有效数字）。
小数点后的末尾零有效（例如2.50有三位有效数字）。

In calculations, the final answer should generally be given to the same number of significant figures as the least precise value used. Scientific notation is used for very large or very small quantities: e.g. 6.63 × 10⁻³⁴ J s.

在计算中，最终答案通常应与所用最低精度的值的有效数字位数相同。对于非常大或非常小的量使用科学记数法，例如6.63 × 10⁻³⁴ J s。

7. Uncertainties in Measurements | 测量的不确定度

Uncertainty quantifies the doubt about a measurement. For a digital instrument, the uncertainty is usually ±1 in the last digit. For an analogue scale, it is typically ±half the smallest division.

不确定度量化了测量的可疑程度。对于数字仪器，不确定度通常为末位±1。对于模拟刻度，通常为最小分度的一半。

Types of uncertainty:

不确定度的类型：

Absolute uncertainty – the actual uncertainty in a measured quantity, e.g. length = 5.0 ± 0.1 cm.
Fractional uncertainty = (absolute uncertainty) ÷ (measured value).
Percentage uncertainty = fractional uncertainty × 100%.

绝对不确定度——测量量本身的不确定度，例如长度 = 5.0 ± 0.1 cm。
分数不确定度 =（绝对不确定度）÷（测量值）。
百分比不确定度 = 分数不确定度 × 100%。

Example: A resistor has resistance 220 Ω ± 5%. The fractional uncertainty is 0.05 and the absolute uncertainty is 11 Ω.

例如：一电阻为220 Ω ± 5%。分数不确定度为0.05，绝对不确定度为11 Ω。

8. Combining Uncertainties | 不确定度的合成

You must be able to combine uncertainties when performing arithmetic operations. The rules are:

你必须能够在进行算术运算时合成不确定度。规则如下：

Addition or subtraction: add the absolute uncertainties.

加或减：将绝对不确定度相加。

(a ± Δa) + (b ± Δb) = (a + b) ± (Δa + Δb)

Multiplication or division: add the percentage (or fractional) uncertainties.

乘或除：将百分比（或分数）不确定度相加。

(a × b) has percentage uncertainty = %Δa + %Δb

Powers: multiply the percentage uncertainty by the power.

幂：将百分比不确定度乘以幂指数。

If y = aⁿ, then %Δy = n × %Δa

9. Measurement Instruments and Their Precision | 测量仪器及其精度

AQA practical work requires familiarity with common lab instruments and the precision each offers. You should know the resolution of each device.

AQA实验考核要求熟悉常用实验室仪器及其精度。你应该了解每种设备的分辨率。

Instrument	Typical resolution
Ruler (metre rule)	1 mm
Vernier callipers	0.1 mm
Micrometer screw gauge	0.01 mm
Digital stopwatch	0.01 s (but human reaction time limits accuracy)
Digital balance	0.1 g or 0.01 g
Voltmeter / ammeter	depending on scale, e.g. 0.1 V or 0.01 A

When using a stopwatch, the uncertainty from human reaction time can be around ±0.2 s. Taking repeated measurements and calculating the mean reduces random uncertainty.

使用秒表时，人体反应时间引入的不确定度约为±0.2 s。重复测量并计算平均值可减小随机不确定度。

10. Graphs and Error Bars | 图像与误差棒

Graphs are essential for analysing experimental data. AQA expects you to plot data with appropriate scales, draw error bars, and determine the line of best fit.

图像是分析实验数据的关键。AQA要求你以合适的比例绘图、绘制误差棒并确定最佳拟合线。

Error bars represent the uncertainty of each data point. They are drawn as vertical or horizontal lines centred on the point, with length equal to twice the absolute uncertainty.

误差棒表示每个数据点的不确定度，以点为中心绘制垂直或水平线段，其长度等于两倍绝对不确定度。

The line of best fit should pass as close as possible to all points and error bars, and need not go through every point. The gradient of the line is calculated using two widely separated points on the line.

最佳拟合线应尽可能靠近所有点和误差棒，但不必穿过每个点。直线的斜率通过线上两个相距较远的点计算。

To find the uncertainty in the gradient, draw lines of maximum and minimum slope that still pass through all error bars. The uncertainty is half the difference between their gradients.

为了求斜率的不确定度，画出仍能穿过所有误差棒的最大和最小斜率线。不确定度是它们斜率差的一半。

11. Estimation and Order of Magnitude | 估算与数量级

A-level physics often asks you to estimate quantities to within a factor of ten, known as an order of magnitude. This is a valuable skill for checking the reasonableness of results.

A-level物理经常要求你在十倍以内估算物理量，即数量级。这是检验结果合理性的重要技能。

Examples to memorise:

需要记住的例子：

Mass of a car: ~1000 kg (10³ kg)
Mass of an electron: 9.11 × 10⁻³¹ kg
Speed of sound in air: ~340 m s⁻¹
Wavelength of visible light: ~500 nm (5 × 10⁻⁷ m)
Charge on one electron: 1.6 × 10⁻¹⁹ C

汽车质量：约1000 kg (10³ kg)
电子质量：9.11 × 10⁻³¹ kg
空气中的声速：约340 m s⁻¹
可见光波长：约500 nm (5 × 10⁻⁷ m)
单个电子的电荷：1.6 × 10⁻¹⁹ C

When estimating, choose one or two significant figures and use approximate values of constants. For example, to estimate the number of atoms in a solid, use density, molar mass and Avogadro constant.

估算时选择一两位有效数字并使用常数的近似值。例如，估算固体中的原子数时，使用密度、摩尔质量和阿伏伽德罗常数。

12. Practical Skills and Exam Tips | 实验技能与考试策略

In AQA A-level physics, 15% of the final grade is based on practical competence. You must be able to plan experiments, identify variables, collect data safely, and evaluate methods.

在AQA A-level物理中，15%的最终成绩基于实验能力。你必须能够设计实验、识别变量、安全地收集数据并评估方法。

Key points for written exams:

笔试要点：

Always quote units with every numerical answer, unless the question asks for a ratio.
State uncertainties in the same precision as the measurement (e.g. 2.43 ± 0.01 cm, not 2.43 ± 0.1 cm).
When calculating percentage uncertainty, keep enough significant figures in intermediate steps.
For graph questions, label axes with quantity and unit (e.g. “Force / N”).
Check that your final answer is to a sensible number of significant figures.

除非题目要求比值，否则每个数值答案都必须带单位。
不确定度应与测量值具有相同的小数位（例如2.43 ± 0.01 cm，而不是2.43 ± 0.1 cm）。
在计算百分比不确定度时，中间步骤要保留足够的有效数字。
对于图像题，坐标轴必须标注物理量和单位（例如”力 / N”）。
检查最终答案是否使用了合理的有效数字位数。

Common mistakes include confusing fractional and absolute uncertainty, using an incorrect number of significant figures, and forgetting to convert units before substituting into equations.

常见错误包括混淆分数不确定度和绝对不确定度、有效数字位数错误，以及在代入方程前忘记转换单位。

Mastery of SI units, uncertainties, and practical measurement is not just a topic in itself – it underpins every other area of A-level physics. By understanding these foundations, you will solve numerical problems with greater confidence and accuracy.

掌握SI单位、不确定度和实验测量本身不仅是一个课题——它支撑着A-level物理的所有其他领域。通过理解这些基础，你将更加自信和准确地解决数值问题。

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SI Units and Measurements | 国际单位制与测量