📚 Quick Reference Handbook of Formulas and Theorems for SQA Physics (Year 11) | SQA物理（11年级）公式定理速查手册
Welcome to your essential quick reference guide for SQA National 5 Physics. This handbook collects all the key formulas and theorems you need to master, from kinematics to nuclear radiation. Each section presents a summary of relationships in tabular form, followed by clear explanations to reinforce your understanding. Use it to revise efficiently and boost your confidence for exams.
欢迎使用这本 SQA National 5 物理必备速查手册。本手册汇总了你需要掌握的所有关键公式和定理，涵盖从运动学到核辐射的各个主题。每个部分都以表格形式呈现核心关系，并附有清晰的解释来加深你的理解。用它高效复习，提升应考信心。
1. Kinematics | 运动学
Kinematics describes the motion of objects without considering the forces that cause it. The three fundamental quantities are displacement, velocity and acceleration. Average speed and velocity can be calculated from distance and displacement over time. Graphs of motion provide a powerful tool for analysing movement.
运动学描述物体的运动而不考虑引起运动的力。三个基本量是位移、速度和加速度。平均速率和速度可根据距离和位移随时间的变化计算。运动图像是分析运动的强大工具。
| Formula / Concept (English) | 公式 / 概念 (中文) |
|---|---|
| v = Δs / Δt (average velocity = displacement ÷ time) | v = Δs / Δt（平均速度 = 位移 ÷ 时间） |
| a = Δv / Δt (acceleration = change in velocity ÷ time) | a = Δv / Δt（加速度 = 速度变化量 ÷ 时间） |
| Instantaneous speed = gradient of distance-time graph | 瞬时速率 = 距离-时间图像的斜率 |
| Acceleration = gradient of velocity-time graph; displacement = area under v-t graph | 加速度 = 速度-时间图像的斜率；位移 = v-t 图像下的面积 |
Remember that displacement is a vector quantity having both magnitude and direction, while distance is a scalar. In SQA exams, you are expected to carry out calculations involving these relationships and to interpret motion graphs confidently.
请记住，位移是既有大小又有方向的矢量，而距离是标量。在 SQA 考试中，要求能够熟练运用这些关系进行计算，并能自信地解读运动图像。
2. Dynamics & Newton's Laws | 动力学与牛顿定律
Dynamics connects forces with motion. Newton’s three laws of motion govern how objects behave when forces act on them. The most quantitative of these is the second law, which allows you to calculate the force needed to produce a given acceleration.
动力学将力与运动联系起来。牛顿三大运动定律决定了物体在受力时的行为。其中最具定量意义的是第二定律，它使你能计算产生某一加速度所需的力。
| Formula / Law (English) | 公式 / 定律 (中文) |
|---|---|
| F = m × a (resultant force = mass × acceleration) | F = m × a（合力 = 质量 × 加速度） |
| W = m × g (weight = mass × gravitational field strength, g = 9.8 N/kg on Earth) | W = m × g（重量 = 质量 × 引力场强度，地球上 g = 9.8 N/kg） |
| Newton's First Law: An object remains at rest or moves with constant velocity unless acted on by an unbalanced force. | 牛顿第一定律：物体将保持静止或匀速直线运动状态，除非受到不平衡力的作用。 |
| Newton's Third Law: For every action force there is an equal and opposite reaction force. | 牛顿第三定律：每一个作用力都有一个大小相等、方向相反的反作用力。 |
istance must be subtracted from applied forces to find the net force before using F = m a.
解题时，务必考虑作用在单个物体上的合力。在应用 F = m a 之前，须从施加的力中减去摩擦力或空气阻力，以求得净力。
3. Work, Energy and Power | 功、能与功率
Energy can be stored or transferred. Work done is a measure of energy transfer when a force moves an object. Kinetic and potential energy are the two primary mechanical energy stores. Power tells you how quickly energy is transferred.
能量可以被储存或传递。功是力使物体移动时能量传递的量度。动能和势能是两种主要的机械能储存形式。功率表示能量传递的快慢。
| Formula (English) | 公式 (中文) |
|---|---|
| W = F × d (work done = force × distance moved in direction of force) | W = F × d（功 = 力 × 沿力方向移动的距离） |
| Eₚ = m × g × h (gravitational potential energy = mass × g × height) | Eₚ = m × g × h（重力势能 = 质量 × g × 高度） |
| Eₖ = ½ m v² (kinetic energy = half × mass × speed squared) | Eₖ = ½ m v²（动能 = ½ × 质量 × 速度的平方） |
| P = E / t (power = energy transferred ÷ time) | P = E / t（功率 = 传递的能量 ÷ 时间） |
The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In many exam questions, you are asked to equate initial energy stores to final stores, ignoring air resistance unless stated.
能量守恒定律指出，能量既不能被创造也不能被消灭，只能从一种形式转化为另一种形式。在许多考题中，需要将初始能量储存与最终储存相等处理，除非另有说明，否则忽略空气阻力。
4. Thermal Physics | 热物理
Heating a substance raises its temperature or changes its state. Specific heat capacity tells you how much energy is needed to change the temperature of 1 kg by 1 °C. Specific latent heat applies to phase changes without a temperature change.
加热物质会使其温度升高或改变其状态。比热容表示使1千克物质温度变化1摄氏度所需的能量。比潜热则适用于不发生温度变化的相变过程。
| Formula (English) | 公式 (中文) |
|---|---|
| Q = c × m × ΔT (heat energy = specific heat capacity × mass × temperature change) | Q = c × m × ΔT（热量 = 比热容 × 质量 × 温度变化） |
| Q = m × L (heat energy for change of state = mass × specific latent heat) | Q = m × L（状态变化所需热量 = 质量 × 比潜热） |
melting or boiling, use Q = m L. Ensure you use the correct value of specific latent heat — fusion for melting/freezing, vaporisation for boiling/condensing.
当材料在相同状态下升温或冷却时使用 Q = c m ΔT。熔解或沸腾时使用 Q = m L。务必选用正确的比潜热数值——熔解/凝固用熔解潜热，汽化/凝结用汽化潜热。
5. Gas Laws | 气体定律
The behaviour of a fixed mass of gas can be predicted using the relationships between pressure, volume and temperature (in kelvin). These laws assume that no gas escapes and that the mass remains constant.
固定质量气体的行为可以通过压强、体积和温度（开尔文）之间的关系来预测。这些定律假设气体没有逸出且质量保持不变。
| Law (English) | 定律 (中文) |
|---|---|
| p₁/T₁ = p₂/T₂ (pressure law: for fixed mass and volume, pressure ∝ absolute temperature) | p₁/T₁ = p₂/T₂（压强定律：质量体积一定时，压强与绝对温度成正比） |
| V₁/T₁ = V₂/T₂ (Charles' law: for fixed mass and pressure, volume ∝ absolute temperature) | V₁/T₁ = V₂/T₂（查理定律：质量压强一定时，体积与绝对温度成正比） |
| p₁V₁ = p₂V₂ (Boyle's law: for fixed mass and temperature, pressure × volume = constant) | p₁V₁ = p₂V₂（玻意耳定律：质量温度一定时，压强与体积的乘积为常数） |
Always convert Celsius temperatures to kelvin by adding 273 before applying any gas law. The kelvin scale is essential because it begins at absolute zero, ensuring the proportional relationships hold.
在应用任何气体定律之前，务必通过加上 273 将摄氏温度转换为开尔文。开尔文温标必不可少，因为它始于绝对零度，确保了比例关系成立。
6. Electrical Quantities & Circuits | 电量与电路
Charge, current, voltage and resistance are the building blocks of circuit analysis. Current is the rate of flow of charge, and voltage (potential difference) drives the current through components.
电荷、电流、电压和电阻是电路分析的基本要素。电流是电荷流动的速率，而电压（电势差）驱动电流通过各元件。
| Formula (English) | 公式 (中文) |
|---|---|
| Q = I × t (charge = current × time) | Q = I × t（电荷 = 电流 × 时间） |
| In a series circuit, current is the same at all points; voltage splits across components. | 串联电路中，各处电流相等；电压在各元件上分配。 |
| In a parallel circuit, voltage across each branch is the same; current splits at junctions. | 并联电路中，各支路两端电压相等；电流在节点处分流。 |
You must be able to draw and interpret circuit diagrams using standard symbols. Remember that an ammeter is connected in series and a voltmeter in parallel with the component being tested.
必须能够使用标准符号绘制和解读电路图。请记住，电流表串联在电路中，电压表并联在被测元件两端。
7. Ohm's Law and Resistance | 欧姆定律与电阻
Ohm's law states that the current through a conductor is directly proportional to the potential difference across it, provided temperature remains constant. Resistance is a measure of how much a component opposes the flow of charge.
欧姆定律指出，在温度保持不变的条件下，通过导体的电流与导体两端的电势差成正比。电阻是衡量元件对电荷流动阻碍作用的物理量。
| Formula (English) | 公式 (中文) |
|---|---|
| V = I × R (voltage = current × resistance) | V = I × R（电压 = 电流 × 电阻） |
| Rₜ = R₁ + R₂ + ... (total resistance in series) | Rₜ = R₁ + R₂ + ...（串联总电阻） |
| 1/Rₜ = 1/R₁ + 1/R₂ + ... (total resistance in parallel) | 1/Rₜ = 1/R₁ + 1/R₂ + ...（并联总电阻） |
For resistors in parallel, the total resistance is always less than the smallest individual resistance. Ohm's law applies to ohmic conductors at constant temperature; diodes and filament lamps do not obey it under all conditions.
并联电阻的总电阻总是小于其中最小的单个电阻。欧姆定律适用于恒温下的欧姆导体；二极管和白炽灯并非在所有条件下都遵守该定律。
8. Electrical Power and Energy | 电功率与电能
When charge flows through a component, electrical energy is converted into other forms. Power is the rate at which this energy conversion happens. Different combinations of V, I and R give useful alternative power formulas.
当电荷流过元件时，电能转化为其他形式的能。功率是这种能量转化的速率。组合 V、I 和 R 可以得出有用的替代功率公式。
| Formula (English) | 公式 (中文) |
|---|---|
| P = I × V (power = current × voltage) | P = I × V（功率 = 电流 × 电压） |
| P = I² × R (power = current squared × resistance) | P = I² × R（功率 = 电流的平方 × 电阻） |
| P = V² / R (power = voltage squared ÷ resistance) | P = V² / R（功率 = 电压的平方 ÷ 电阻） |
| E = P × t (electrical energy = power × time) | E = P × t（电能 = 功率 × 时间） |
Energy can be expressed in joules (J) when power is in watts and time in seconds, or in kilowatt-hours (kW h) for domestic usage. Choose the most convenient formula based on the quantities given in the problem.
当功率用瓦特、时间用秒时，能量以焦耳 (J) 表示；家庭用电常用千瓦时 (kW h)。根据题目给出的已知量，选择最方便的公式。
9. Waves | 波
Waves transfer energy without transferring matter. The key wave parameters are frequency, wavelength, speed and amplitude. The wave equation connects these together for all types of wave.
波传递能量而不传递物质。波的关键参数有频率、波长、速度和振幅。波动方程将所有这些量联系在一起，适用于所有类型的波。
| Formula / Concept (English) | 公式 / 概念 (中文) |
|---|---|
| v = f × λ (wave speed = frequency × wavelength) | v = f × λ（波速 = 频率 × 波长） |
| T = 1 / f (period = 1 ÷ frequency) | T = 1 / f（周期 = 1 ÷ 频率） |
| Transverse waves: oscillations perpendicular to direction of energy travel (e.g., light, water waves). | 横波：振动方向与能量传播方向垂直（例如光、水波）。 |
| Longitudinal waves: oscillations parallel to direction of energy travel (e.g., sound). | 纵波：振动方向与能量传播方向平行（例如声波）。 |
Diffraction is the bending of waves around obstacles or through gaps. The amount of diffraction increases when the gap width is similar to the wavelength. This concept is frequently tested with water waves in a ripple tank.
绕射是波遇到障碍物或穿过狭缝时发生弯曲的现象。当缝宽与波长相近时，绕射现象更显著。水波槽实验常用来考查这一概念。
10. Refraction of Light & Total Internal Reflection | 光的折射与全内反射
When light travels from one medium to another, its speed changes, causing it to bend—this is refraction. A critical angle exists when light attempts to pass from a denser to a less dense medium; beyond this angle, total internal reflection occurs.
当光从一种介质进入另一种介质时，其速度改变，导致光线弯曲——这就是折射。当光试图从光密介质射向光疏介质时，存在一个临界角；超过此角则发生全内反射。
| Formula (English) | 公式 (中文) |
|---|---|
| n = sin i / sin r (refractive index = sin of angle of incidence ÷ sin of angle of refraction) | n = sin i / sin r（折射率 = 入射角的正弦 ÷ 折射角的正弦
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