📚 IB Physics: Measurement Methods and Unit Conversion | IB 物理：物理量测量方法与单位换算
Measurement is the foundation of physics. Every physical quantity must be expressed with a number and a unit, and accurate measurement methods allow us to compare observations and test theories. Unit conversion, meanwhile, is an essential skill for solving problems and communicating results across different systems.
测量是物理学的基础。每一个物理量都必须用数值和单位来表达，而准确的测量方法使我们能够比较观察结果并检验理论。同时，单位换算也是解决问题和在不同体系之间交流结果的基本技能。
1. SI Base Units | SI 基本单位
The International System of Units (SI) defines seven base units. All other physical quantities are derived from these base units. In IB Physics, you must know their names, symbols and the quantities they measure.
国际单位制（SI）定义了七个基本单位。所有其他物理量都是由这些基本单位导出的。在IB物理中，你必须记住它们的名称、符号以及所测量的物理量。
| Quantity (物理量) | Unit (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 (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 with a prefix (kilo). Also remember that the kelvin is not written with a degree symbol in SI.
注意，千克是唯一带有前缀（千）的基本单位。另外，开尔文在SI中不使用度符号。
2. Derived Units | 导出单位
Derived units are combinations of base units. Many have special names, such as the newton (N) for force, the joule (J) for energy, the pascal (Pa) for pressure, and the watt (W) for power.
导出单位是基本单位的组合。许多有特殊名称，例如力的单位牛顿（N）、能量的单位焦耳（J）、压强的单位帕斯卡（Pa）和功率的单位瓦特（W）。
| Derived Quantity (导出量) | Special Unit (特殊单位) | In Base Units (用基本单位表示) |
|---|---|---|
| Force (力) | newton, N | kg·m·s⁻² |
| Energy (能量) | joule, J | kg·m²·s⁻² |
| Pressure (压强) | pascal, Pa | kg·m⁻¹·s⁻² |
| Power (功率) | watt, W | kg·m²·s⁻³ |
| Charge (电荷) | coulomb, C | A·s |
| Voltage (电压) | volt, V | kg·m²·s⁻³·A⁻¹ |
| Resistance (电阻) | ohm, Ω | kg·m²·s⁻³·A⁻² |
To derive these expressions, substitute the base units of each quantity according to its defining equation. For example, pressure = force / area, so 1 Pa = 1 N / 1 m² = 1 (kg·m·s⁻²) / m² = 1 kg·m⁻¹·s⁻².
要推导这些表达式，需要根据定义方程代入每个量的基本单位。例如，压强 = 力 / 面积，所以 1 Pa = 1 N / 1 m² = 1 (kg·m·s⁻²) / m² = 1 kg·m⁻¹·s⁻²。
3. Metric Prefixes and Decimal Conversion | 十进制前缀与换算
SI uses prefixes to denote powers of ten. The most common in IB physics are 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) and tera (T, 10¹²).
SI使用前缀表示十的幂。IB物理中最常见的是皮（p，10⁻¹²）、纳（n，10⁻⁹）、微（μ，10⁻⁶）、毫（m，10⁻³）、厘（c，10⁻²）、千（k，10³）、兆（M，10⁶）、吉（G，10⁹）和太（T，10¹²）。
| Prefix (前缀) | Symbol (符号) | Factor (因子) | Example (示例) |
|---|---|---|---|
| pico | p | 10⁻¹² | 1 pm = 10⁻¹² m |
| nano | n | 10⁻⁹ | 1 nm = 10⁻⁹ m |
| micro | μ | 10⁻⁶ | 1 μs = 10⁻⁶ s |
| milli | m | 10⁻³ | 1 mA = 10⁻³ A |
| centi | c | 10⁻² | 1 cm = 10⁻² m |
| kilo | k | 10³ | 1 km = 10³ m |
| mega | M | 10⁶ | 1 MW = 10⁶ W |
| giga | G | 10⁹ | 1 GHz = 10⁹ Hz |
| tera | T | 10¹² | 1 TBq = 10¹² Bq |
When converting, write the prefix as its power of ten and multiply. For squared or cubed units, apply the factor to the whole power. For example, 1 cm² = (10⁻² m)² = 10⁻⁴ m², not 10⁻² m².
换算时，将前缀写成相应的十的幂并相乘。对于平方或立方单位，因子要应用于整个幂。例如，1 cm² = (10⁻² m)² = 10⁻⁴ m²，而不是 10⁻² m²。
4. Measuring Length, Mass and Time | 长度、质量与时间的测量
Length can be measured using a metre ruler (precision ±0.1 cm), a vernier calliper (precision ±0.01 cm) or a micrometer screw gauge (precision ±0.001 cm). Choose the instrument according to the required significant figures.
长度可以用米尺（精度±0.1厘米）、游标卡尺（精度±0.01厘米）或千分尺（精度±0.001厘米）测量。根据所需的有效数字选择合适的仪器。
Mass is usually measured with a digital balance or an analytical balance. For very small masses, such as individual atoms, other techniques are needed, but in the laboratory a balance is sufficient.
质量通常用数字天平或分析天平测量。对于非常小的质量，例如单个原子，需要其他技术，但在实验室中天平就足够了。
Time is measured with a stopwatch, a light gate or a data logger. Modern atomic clocks define the second using caesium-133 vibrations, reaching precision better than 10⁻⁹ s.
时间用秒表、光电门或数据记录器测量。现代原子钟利用铯-133的振动定义秒，精度可达10⁻⁹秒以上。
Every measurement has uncertainty. The uncertainty of an analogue instrument is usually half the smallest scale division; for digital instruments it is often the smallest displayed digit.
每一次测量都有不确定度。模拟仪器的不确定度通常是最小分度的一半；数字仪器的不确定度通常是最小显示位数。
5. Measuring Area, Volume and Density | 面积、体积与密度的测量
Area is derived from length squared and has the unit m². Volume is length cubed with unit m³. In practical work, area can be found from dimensions for regular shapes, or by counting squares on graph paper for irregular shapes.
面积由长度的平方导出，单位是m²。体积是长度的三次方，单位是m³。在实验中，规则图形的面积可以通过尺寸计算，不规则图形可以用方格纸数格法。
For liquids, a measuring cylinder measures volume directly in cm³ or mL. Note that 1 cm³ = 1 mL. For irregular solids, the displacement method is used: record the volume of liquid before and after completely submerging the object.
对于液体，量筒直接以cm³或mL给出体积。注意1 cm³ = 1 mL。对于不规则固体，使用排水法：记录物体完全浸入前后液体的体积差。
Density is defined as mass per unit volume:
ρ = m / V
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