📚 Year 12 OCR Physics: Core Knowledge Summary | Year 12 OCR 物理：核心知识点梳理
Year 12 OCR Physics provides the essential foundation for the full A Level, covering classical mechanics, electricity, waves and quantum phenomena. This summary organises the key ideas from Modules 2, 3 and 4 of the OCR specification into twelve manageable sections, pairing each concept with its Chinese explanation so that bilingual learners can master the syllabus with confidence.
Year 12 OCR 物理为完整 A Level 课程奠定核心基础，涵盖经典力学、电学、波动和量子现象。本篇梳理将 OCR 考纲中模块二、三、四的核心知识归纳为十二个模块，每项概念都配有中文解释，帮助双语学习者扎实掌握考纲。
1. Physical Quantities and Units | 物理量与单位
All physical quantities are expressed in SI units. There are seven base quantities: length (metre, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), temperature (kelvin, K), amount of substance (mole, mol) and luminous intensity (candela, cd). Derived units, such as the newton (kg m s⁻²) or the joule (kg m² s⁻²), are formed by combining base units. Checking the homogeneity of an equation using base units is a powerful way to catch errors. Prefixes like kilo (10³), milli (10⁻³) and micro (10⁻⁶) are used to express very large or very small numbers concisely.
所有物理量均使用国际单位制（SI）。七个基本量分别是：长度（米，m）、质量（千克，kg）、时间（秒，s）、电流（安培，A）、温度（开尔文，K）、物质的量（摩尔，mol）和发光强度（坎德拉，cd）。导出单位如牛顿（kg m s⁻²）或焦耳（kg m² s⁻²）由基本单位组合而成。利用基本单位检验方程量纲一致性是发现错误的利器。常用词头例如千（10³）、毫（10⁻³）和微（10⁻⁶）可简洁地表示极大或极小的数值。
2. Kinematics: Motion in a Straight Line | 运动学：直线运动
Kinematics describes motion in terms of displacement, velocity and acceleration without considering the forces causing it. Displacement is a vector quantity measuring the shortest distance from the starting point; distance is a scalar representing the total path length. The five SUVAT equations link initial velocity u, final velocity v, acceleration a, displacement s and time t when acceleration is constant. For example:
运动学用位移、速度和加速度描述运动，但不涉及产生运动的力。位移是矢量，表示起点到终点的最短距离；路程是标量，表示运动路径的总长度。五个 SUVAT 方程在加速度恒定时将初速度 u、末速度 v、加速度 a、位移 s 和时间 t 联系起来。例如：
v = u + at s = ut + ½ at² v² = u² + 2as
These equations are essential for analysing free fall under gravity (where a = g = 9.81 m s⁻²) and motion from rest (u = 0). Interpreting graphs of displacement–time, velocity–time and acceleration–time is equally important for extracting gradients, areas and intercepts.
这些方程对分析自由落体（取 a = g = 9.81 m s⁻²）和从静止开始的运动（u = 0）至关重要。解释位移–时间图、速度–时间图和加速度–时间图，提取斜率、面积和截距，同样是一项核心技能。
3. Forces and Newton’s Laws of Motion | 力与牛顿运动定律
Newton’s three laws form the backbone of classical mechanics. The first law states that an object remains at rest or in uniform motion unless acted upon by a resultant force. The second law quantifies this: resultant force equals rate of change of momentum, which for constant mass simplifies to F = ma. The third law reminds us that if body A exerts a force on body B, body B exerts an equal and opposite force on body A. Free-body diagrams help visualise all forces acting on an object, including weight, normal reaction, tension, friction and drag.
牛顿三定律构成经典力学的支柱。第一定律说明，若无合力作用，物体保持静止或匀速直线运动状态。第二定律给出定量关系：合力等于动量的变化率；在质量不变时简化为 F = ma。第三定律指出，若物体 A 对物体 B 施力，则物体 B 必定对物体 A 施加大小相等、方向相反的力。受力示意图可清晰地呈现作用在物体上的所有力，如重力、支持力、张力、摩擦力和阻力。
4. Momentum and Impulse | 动量与冲量
Linear momentum p is defined as the product of mass and velocity: p = mv. It is a vector quantity. Impulse is the change in momentum produced by a force acting over a time interval: impulse = F Δt = Δp. In a closed system, the total momentum before a collision equals the total momentum after – the principle of conservation of momentum. Collisions can be perfectly elastic (kinetic energy conserved) or inelastic (kinetic energy not conserved). Calculations often involve equating total momentum before and after events, paying careful attention to sign conventions for direction.
线动量 p 定义为质量与速度的乘积：p = mv，是矢量。冲量是力在一段时间内造成的动量变化：冲量 = F Δt = Δp。在封闭系统中，碰撞前的总动量等于碰撞后的总动量——这就是动量守恒原理。碰撞可以是完全弹性的（动能守恒）或非弹性的（动能不守恒）。相关计算常需令事件前后总动量相等，并特别注意方向的符号规定。
5. Equilibrium, Moments and Centre of Mass | 平衡、力矩与质心
A body is in equilibrium when the resultant force and the resultant moment about any point are both zero. The moment of a force about a pivot is given by moment = F × d, where d is the perpendicular distance from the pivot to the line of action of the force. This principle explains how levers, seesaws and bridges balance. The centre of mass of a regular object lies at its geometric centre; for irregular objects it can be found experimentally by suspension. For a body to be stable, its centre of mass must lie within the base of support.
当合力为零且对任意点的合力矩也为零时，物体处于平衡状态。力对支点的力矩定义为 力矩 = F × d，其中 d 是支点到力作用线的垂直距离。该原理解释了杠杆、跷跷板和桥梁如何保持平衡。规则物体的质心位于几何中心；不规则物体的质心可通过悬挂实验测定。物体要想稳定，其质心必须落在支撑面以内。
6. Work, Energy and Power | 功、能和功率
Work is done when a force moves its point of application in the direction of the force: W = F s cosθ. Energy is the capacity to do work and exists in many forms – kinetic, gravitational potential, elastic potential, thermal and chemical. The principle of conservation of energy states that energy can neither be created nor destroyed, only transferred or transformed. Power is the rate of doing work: P = W/t or P = Fv for constant velocity. Efficiency is calculated as useful output power divided by input power.
力使其作用点沿力的方向移动时便做功：W = F s cosθ。能量是做功的本领，有多种形式——动能、重力势能、弹性势能、热能和化学能。能量守恒原理表明，能量既不能被创造也不能被消灭，只能转移或转化。功率是做功的速率：P = W/t，在匀速运动时也可表示为 P = Fv。效率等于有用输出功率与输入功率之比。
7. Materials: Stress, Strain and Young Modulus | 材料：应力、应变和杨氏模量
When a material is stretched, it experiences tensile stress and tensile strain. Stress is defined as force per unit cross-sectional area: σ = F/A. Strain is the extension per unit original length: ε = ΔL/L (a dimensionless ratio). The Young modulus E is a measure of stiffness: E = stress/strain, valid up to the limit of proportionality. A stress–strain graph reveals important features such as the elastic limit, yield point and ultimate tensile strength. Brittle materials break without noticeable plastic deformation, while ductile materials undergo significant plastic flow before fracture.
材料拉伸时承受拉应力和拉应变。应力定义为单位截面积上的力：σ = F/A。应变是单位原长上的伸长量：ε = ΔL/L（无量纲的比值）。杨氏模量 E 衡量材料刚度：E = 应力/应变，在比例极限以内成立。应力–应变图能够显示弹性极限、屈服点和抗拉强度等重要特征。脆性材料断裂前几乎没有可察觉的塑性变形，而延性材料在断裂前会经历明显的塑性流动。
8. Electric Current, Charge and Potential Difference | 电流、电荷与电势差
Electric current I is the rate of flow of charge: I = Q/t. In metals, current is carried by delocalised electrons, whereas in electrolytes it is carried by ions. The conventional direction of current is the direction positive charges would move. Potential difference (p.d.) between two points is the energy transferred per unit charge: V = W/Q. A voltmeter measures p.d. in volts, and an ammeter measures current in amperes. For any component, the resistance R is defined by the ratio V/I.
电流 I 是电荷流动的速率：I = Q/t。在金属中，电流由离域电子携带；在电解液中则由离子携带。电流的参考方向是正电荷移动的方向。两点之间的电势差（p.d.）是单位电荷转移的能量：V = W/Q。电压表测量电势差，单位为伏特；电流表测量电流，单位为安培。任何元件的电阻 R 定义为比值 V/I。
9. Resistance and Resistivity | 电阻与电阻率
The resistance of a wire depends on its length L, cross-sectional area A and the resistivity ρ of the material: R = ρL/A. Resistivity is an intrinsic property of the material and is temperature dependent. For a metallic conductor, resistance increases with temperature due to increased lattice vibrations. Ohmic conductors obey Ohm’s law (V ∝ I) at constant temperature, giving a straight-line I–V graph through the origin. Many components, such as filament lamps and diodes, deviate from Ohm’s law; their I–V characteristics must be learnt.
导线的电阻取决于其长度 L、截面积 A 和材料的电阻率 ρ：R = ρL/A。电阻率是材料的固有属性，随温度变化。对金属导体而言，温度升高时晶格振动加剧，电阻随之增大。欧姆导体在恒温下遵循欧姆定律（V ∝ I），其 I–V 图为一条过原点的直线。许多元件——如灯丝和二极管——不遵循欧姆定律，必须掌握它们的 I–V 特性曲线。
10. DC Circuits and Internal Resistance | 直流电路与内阻
A real power source, such as a cell, has an internal resistance r. The terminal p.d. is given by V = ε – Ir, where ε is the electromotive force (e.m.f.) – the energy transferred per unit charge when no current flows. When a load resistance R is connected, the current is I = ε/(R + r). Internal resistance can be found from the gradient of a V–I graph. Kirchhoff’s laws govern complex circuits: the first law deals with conservation of charge at a junction, and the second law states that the sum of e.m.f.s equals the sum of p.d.s around any closed loop. Potential dividers using two resistors (or one variable resistor) are widely used to supply a fraction of a voltage.
真实电源（例如电池）具有内阻 r。端电压由 V = ε – Ir 给出，其中 ε 为电动势（e.m.f.），即无电流时单位电荷转移的能量。接入负载电阻 R 后，电流为 I = ε/(R + r)。通过 V–I 图像的斜率可求出内阻。基尔霍夫定律支配复杂电路：第一定律处理节点的电荷守恒，第二定律指出环绕任何闭合回路，电动势之和等于电势差之和。由两个电阻（或一个可变电阻）组成的分压电路被广泛用于提供部分电压。
11. Waves: Properties, Superposition and Interference | 波：性质、叠加与干涉
Waves transfer energy without net transfer of matter. In transverse waves (e.g. light, water waves) the oscillation is perpendicular to the direction of energy travel; in longitudinal waves (e.g. sound) it is parallel. The wave equation links speed, frequency and wavelength: v = f λ. Reflection, refraction and diffraction are characteristic behaviours. Refraction obeys Snell’s law: n₁ sinθ₁ = n₂ sinθ₂, where n = c/v. When two or more waves meet, the principle of superposition applies: displacements add algebraically. This leads to stationary (standing) waves on strings and in pipes, formed when two identical progressive waves travel in opposite directions. Nodes and antinodes appear at fixed positions, and the fundamental frequency depends on length and wave speed.
波传递能量而不发生物质的净转移。横波（如光波、水波）的振动方向与能量传播方向垂直；纵波（如声波）的振动方向则与之平行。波动方程将波速、频率和波长联系起来：v = f λ。反射、折射和衍射是波的特征行为。折射遵循斯涅尔定律：n₁ sinθ₁ = n₂ sinθ₂，其中 n = c/v。两列或多列波相遇时适用叠加原理：位移进行代数相加。由此在弦和管内形成驻波，它由两列沿相反方向传播的相同行波叠加而成。波节和波腹固定在特定位置，基频取决于长度和波速。
12. Quantum Physics: Photons, Energy Levels and Photoelectric Effect | 量子物理：光子、能级与光电效应
Light behaves as discrete packets of energy called photons. The energy of a photon is E = hf, where h is Planck’s constant. Electrons in atoms occupy discrete energy levels. When an electron falls from a higher to a lower level, it emits a photon of energy equal to the difference: ΔE = hf. Absorption spectra are formed when electrons absorb photons and move to higher levels. The photoelectric effect provides evidence for the particle nature of light: electrons are emitted from a metal surface only if the incident photon has a frequency above the threshold frequency f₀. The maximum kinetic energy of emitted electrons is given by Einstein’s equation: hf = Φ + ½ m v²_max, where Φ is the work function. The wave–particle duality of light and electrons lies at the heart of quantum physics.
光的行为如同不连续的能量包，称为光子。光子的能量为 E = hf，其中 h 为普朗克常数。原子中的电子处于分立的能级。当电子从高能级向低能级跃迁时，会发射能量等于能级差的光子：ΔE = hf。吸收光谱则是电子吸收光子跃迁到高能级时产生。光电效应为光的粒子性提供了证据：只有当入射光子的频率高于金属的截止频率 f₀ 时，电子才会从金属表面逸出。逸出电子的最大动能由爱因斯坦方程给出：hf = Φ + ½ m v²_max，其中 Φ 为功函数。光与电子的波粒二象性正是量子物理的核心所在。
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