A-Level Physics: Applications of Common Unit Conversion Factors | A-Level 物理：常见单位转换因子的应用

📚 A-Level Physics: Applications of Common Unit Conversion Factors | A-Level 物理：常见单位转换因子的应用

In A-Level Physics, you will encounter a wide range of quantities measured in different units. Equations such as F = ma, p = ρgh and others require consistent use of SI units. Incorrect conversion is one of the most common sources of lost marks. This article reviews the conversion factors you should memorise and applies them to typical exam contexts.

在 A-Level 物理中，你会遇到用不同单位计量的各种物理量。公式如 F = ma、p = ρgh 等要求统一使用 SI 单位。换算错误是常见失分原因之一。本文回顾你需要记住的常用换算因子，并应用到典型考试情境中。

1. SI Prefixes and Unit Transformations | 1. SI 词头与单位换算

The SI system uses prefixes to express very large or very small quantities. You must be able to convert between a prefix and the base unit instantly.

SI 单位制使用词头表示极大或极小的量。你必须能立即在词头与基本单位之间进行换算。

Prefix (词头)	Symbol (符号)	Factor (因子)
pico	p	10⁻¹²
nano	n	10⁻⁹
micro	μ	10⁻⁶
milli	m	10⁻³
centi	c	10⁻²
kilo	k	10³
mega	M	10⁶
giga	G	10⁹

For example, 1 mm = 10⁻³ m, 1 μm = 10⁻⁶ m, and 1 μs = 10⁻⁶ s. To convert from a prefix to the base unit, multiply by the factor: 5 mA = 5 × 10⁻³ A.

例如，1 mm = 10⁻³ m，1 μm = 10⁻⁶ m，1 μs = 10⁻⁶ s。从词头换算到基本单位时，乘以相应因子：5 mA = 5 × 10⁻³ A。

2. Speed Unit Conversion (km/h ↔ m/s) | 2. 速度单位换算（千米每小时 ↔ 米每秒）

Speed is frequently given in km/h in everyday contexts, but exam calculations require m/s. The conversion factor is derived from the definitions of kilometre and hour.

日常生活中速度常用 km/h 表示，但考试计算要求使用 m/s。换算因子由千米和小时的定义推导而来。

1 km/h = 1000 m / 3600 s = (5/18) m/s ≈ 0.278 m/s

Thus, to convert from km/h to m/s, multiply by 5/18 or divide by 3.6. For example: 90 km/h = 90 ÷ 3.6 = 25 m/s.

因此，从 km/h 换算到 m/s 时，乘以 5/18 或除以 3.6。例如：90 km/h = 90 ÷ 3.6 = 25 m/s。

Conversely, to convert from m/s to km/h, multiply by 3.6. For example: 30 m/s = 30 × 3.6 = 108 km/h.

反之，从 m/s 换算到 km/h 时，乘以 3.6。例如：30 m/s = 30 × 3.6 = 108 km/h。

3. Area Unit Conversion (cm² ↔ m², mm² ↔ m²) | 3. 面积单位换算（平方厘米 ↔ 平方米，平方毫米 ↔ 平方米）

When converting area, the linear conversion factor must be squared. This is a common source of error in pressure, stress and Young modulus problems.

进行面积单位换算时，长度换算因子需要平方。这是压强、应力和杨氏模量题目中常见的错误来源。

1 cm² = (10⁻² m)² = 10⁻⁴ m²

Likewise, 1 mm² = (10⁻³ m)² = 10⁻⁶ m². Therefore, 1 m² = 10⁴ cm² = 10⁶ mm².

同样，1 mm² = (10⁻³ m)² = 10⁻⁶ m²。因此，1 m² = 10⁴ cm² = 10⁶ mm²。

Example: A surface has an area of 250 cm². Express this in m². Since 1 cm² = 10⁻⁴ m², 250 cm² = 250 × 10⁻⁴ m² = 2.5 × 10⁻² m².

例：某表面面积为 250 cm²，用 m² 表示。因 1 cm² = 10⁻⁴ m²，故 250 cm² = 250 × 10⁻⁴ m² = 2.5 × 10⁻² m²。

4. Volume Unit Conversion (cm³ ↔ m³, litre ↔ m³) | 4. 体积单位换算（立方厘米 ↔ 立方米，升 ↔ 立方米）

Volume conversion requires cubing the linear factor. The litre (L) is a common non-SI unit accepted in physics; 1 litre is exactly 1000 cm³.

体积换算需要对长度因子进行立方。升（L）是物理学中接受的常用非 SI 单位；1 升恰好等于 1000 cm³。

1 cm³ = (10⁻² m)³ = 10⁻⁶ m³

Also, 1 L = 1000 cm³ = 1000 × 10⁻⁶ m³ = 10⁻³ m³. Note that 1 mL = 1 cm³.

同时，1 L = 1000 cm³ = 1000 × 10⁻⁶ m³ = 10⁻³ m³。注意 1 mL = 1 cm³。

Example: Convert 500 cm³ to m³. 500 cm³ = 500 × 10⁻⁶ m³ = 5.0 × 10⁻⁴ m³, which is also 0.5 L.

例：将 500 cm³ 换算为 m³。500 cm³ = 500 × 10⁻⁶ m³ = 5.0 × 10⁻⁴ m³，也为 0.5 L。

5. Density Unit Conversion (g/cm³ ↔ kg/m³) | 5. 密度单位换算（克每立方厘米 ↔ 千克每立方米）

Density is mass divided by volume. Because the SI unit of mass is kg and volume is m³, densities in textbooks are often given in kg/m³. The conversion from g/cm³ to kg/m³ gives a factor of 1000.

密度等于质量除以体积。由于质量的 SI 单位是 kg，体积单位是 m³，因此课本中的密度常用 kg/m³。从 g/cm³ 换算到 kg/m³ 的因子为 1000。

1 g/cm³ = (10⁻³ kg) / (10⁻⁶ m³) = 10³ kg/m³ = 1000 kg/m³

Example: The density of water is 1.0 g/cm³. In SI units, this is 1000 kg/m³. A liquid with density 1.2 g/cm³ has density 1200 kg/m³.

例：水的密度为 1.0 g/cm³。用 SI 单位表示为 1000 kg/m³。密度为 1.2 g/cm³ 的液体，其密度为 1200 kg/m³。

6. Pressure Unit Conversion (Pa, kPa, bar, atm) | 6. 压强单位换算（帕、千帕、巴、标准大气压）

Pressure is a key quantity in gas laws, hydrostatics and Young modulus. The SI unit is the pascal (Pa), but other units such as bar, atmosphere (atm) and mmHg appear in practical contexts.

压强在气体定律、流体静力学和杨氏模量中是关键物理量。SI 单位是帕斯卡（Pa），但实际中也使用巴（bar）、标准大气压（atm）和毫米汞柱（mmHg）。

1 atm = 101325 Pa ≈ 101 kPa = 1.01325 × 10⁵ Pa

Also, 1 bar = 1 × 10⁵ Pa = 100 kPa. With mmHg, 1 atm = 760 mmHg, so 1 mmHg ≈ 133.3 Pa.

另有，1 bar = 1 × 10⁵ Pa = 100 kPa。对于 mmHg，1 atm = 760 mmHg，因此 1 mmHg ≈ 133.3 Pa。

In exam calculations, always convert all pressures to Pa before using the ideal gas law (pV = nRT) or the hydrostatic pressure equation (p = ρgh).

在考试计算中，使用理想气体定律（pV = nRT）或流体静压强公式（p = ρgh）前，务必将所有压强换算为 Pa。

7. Energy Unit Conversion (J, kWh, eV) | 7. 能量单位换算（焦耳、千瓦时、电子伏特）

The SI unit of energy is the joule (J). However, electrical energy is often quoted in kilowatt-hours (kWh), and atomic or nuclear energies are quoted in electronvolts (eV). You need to convert these to joules in calculations.

能量的 SI 单位是焦耳（J）。然而，电能常用千瓦时（kWh）表示，原子或核能常用电子伏特（eV）表示。在计算中需要将它们换算为焦耳。

1 kWh = 1 kW × 1 h = 1000 W × 3600 s = 3.6 × 10⁶ J

For electronvolt: 1 eV = 1.60 × 10⁻¹⁹ J. For example, an energy of 2 eV is 2 × 1.60 × 10⁻¹⁹ J = 3.20 × 10⁻¹⁹ J.

对于电子伏特：1 eV = 1.60 × 10⁻¹⁹ J。例如，2 eV 的能量为 2 × 1.60 × 10⁻¹⁹ J = 3.20 × 10⁻¹⁹ J。

Typical exam question: An electric heater uses 2 kWh of energy. How many joules is this? Answer: 7.2 × 10⁶ J.

典型考题：某电加热器消耗 2 kWh 能量，合多少焦耳？答案：7.2 × 10⁶ J。

8. Mass Unit Conversion (g, kg, tonne) | 8. 质量单位换算（克、千克、吨）

Mass is an SI base quantity with the kilogram as its base unit. In many problems, masses are given in grams or tonnes; you must convert them to kilograms before substituting into equations.

质量是 SI 基本量，基本单位为千克。在许多问题中，质量以克或吨给出；代入公式前必须换算为千克。

1 g = 10⁻³ kg, 1 mg = 10⁻⁶ kg, 1 tonne = 1000 kg

Example: A mass of 250 g is 0.25 kg. A vehicle mass of 1.5 tonnes is 1500 kg.

例：250 g 的质量为 0.25 kg。1.5 吨的车辆质量为 1500 kg。

When calculating weight (W = mg), using kilograms yields the weight in newtons because g has units of N kg⁻¹ or m s⁻².

计算重力（W = mg）时，使用千克可以得到以牛顿为单位的重力，因为 g 的单位为 N kg⁻¹ 或 m s⁻²。

9. Exam Strategies for Unit Conversion | 9. 考试中单位换算的实用策略

Unit conversion errors are avoidable with careful habits. The following strategies will help you handle conversion factors in CIE A-Level Physics exams.

单位换算错误可以通过细心的习惯来避免。以下策略将帮助你在 CIE A-Level 物理考试中正确处理换算因子。

Always convert all quantities to SI base units before substituting into equations. This includes kg, m, s, A, K and mol.

在代入公式前，始终将所有物理量换算为 SI 基本单位，包括 kg、m、s、A、K 和 mol。
Remember squared and cubed factors. For area, square the length conversion factor; for volume, cube it.

牢记平方和立方因子。面积换算时对长度因子平方；体积换算时对长度因子立方。
Write down the conversion step explicitly. For example, 5.0 cm² = 5.0 × (10⁻² m)² = 5.0 × 10⁻⁴ m².

明确写出换算步骤。例如，5.0 cm² = 5.0 × (10⁻² m)² = 5.0 × 10⁻⁴ m²。
Check whether your final answer is physically reasonable. A car speed of 90 km/h is about 25 m/s, not 324 m/s.

检查最终答案是否符合物理常理。汽车速度为 90 km/h 时约为 25 m/s，而不是 324 m/s。
Use dimensional analysis to verify equations: ensure the units on both sides of an equation match after conversion.

用量纲分析检验公式：换算后确保等式两边单位一致。

By mastering these conversion factors, you will reduce careless errors and gain confidence in solving multi-step problems.

掌握这些换算因子后，你将减少粗心错误，并在解决多步问题时更有信心。

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A-Level Physics: Applications of Common Unit Conversion Factors | A-Level 物理：常见单位转换因子的应用