📚 Year 12 WJEC Physics: Core Concepts Summary | WJEC 物理核心知识点梳理
This article provides a structured summary of the core topics covered in Year 12 WJEC Physics, designed to help students consolidate their understanding across mechanics, materials, waves, electricity and quantum phenomena. Each section presents key ideas, equations and typical applications, with content presented in both English and Chinese to support bilingual learning.
本文系统梳理了 Year 12 WJEC 物理课程的核心知识点，旨在帮助学生在力学、材料、波动、电学和量子现象等领域巩固理解。每个小节均提炼了关键概念、重要方程和典型应用，并以中英双语对照的形式呈现，助力双语学习。
1. Scalars, Vectors and Motion | 标量、矢量与运动
Physical quantities are classified as scalars, which have magnitude only, or vectors, which have both magnitude and direction. Examples of scalars include mass, speed and energy, while displacement, velocity, acceleration and force are vectors. Vector addition requires consideration of direction, often using tip-to-tail diagrams or resolving into perpendicular components. Resultant vectors can be calculated using Pythagoras’ theorem and trigonometry when components are at right angles.
物理量分为只有大小的标量和既有大小又有方向的矢量。质量、速率和能量属于标量，而位移、速度、加速度和力则是矢量。矢量相加必须考虑方向，常使用“首尾相连”图示或正交分解法。当分量相互垂直时，可用勾股定理和三角函数计算合矢量。
2. Kinematics: Describing Motion | 运动学：描述运动
Kinematics deals with the description of motion. Key quantities include displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). For uniform acceleration, four SUVAT equations are used. These are frequently applied to free fall under gravity, where a = g = 9.81 m s⁻² and the direction of motion determines sign conventions. Motion graphs (displacement–time, velocity–time) provide visual interpretations where gradients represent velocity or acceleration, and areas under graphs correspond to displacement or change in velocity.
运动学描述物体的运动。关键量包括位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t)。对于匀加速运动，有一套运动学方程（SUVAT 方程）可用。这些方程常应用于自由落体，此时 a = g = 9.81 m s⁻²，并需根据运动方向确定正负号。运动图像（位移–时间图、速度–时间图）提供了直观解读：斜率代表速度或加速度，图下面积对应位移或速度变化量。
v = u + at s = ut + ½at² v² = u² + 2as s = ½(u + v)t
3. Dynamics and Newton’s Laws | 动力学与牛顿定律
Newton’s three laws govern the relationship between force and motion. The first law states that an object remains at rest or in uniform motion unless acted upon by a resultant force. The second law, F = ma, links the net force to the acceleration of a mass. The third law highlights that forces occur in interaction pairs that are equal in magnitude and opposite in direction, acting on different bodies. Momentum, defined as p = mv, is conserved in closed systems. The impulse FΔt equals the change in momentum Δp, which is essential in collision and safety applications.
牛顿三定律支配着力与运动的关系。第一定律指出，若无合力作用，物体将保持静止或匀速直线运动。第二定律 F = ma 将合力与物体的加速度联系起来。第三定律强调力成对出现，大小相等、方向相反，且作用在不同物体上。动量 p = mv 在封闭系统中守恒。冲量 FΔt 等于动量的变化量 Δp，这一关系在碰撞和安全应用中至关重要。
4. Work, Energy and Power | 功、能量与功率
Work is done when a force moves an object in the direction of the force: W = F s cosθ. Energy exists in different forms, including kinetic energy (Eₖ = ½mv²) and gravitational potential energy (Eₚ = mgh). The principle of conservation of energy states that energy can be transferred or transformed but not created or destroyed. Power is the rate of doing work, P = W / t, and for constant force and velocity, P = Fv. Efficiency η is the ratio of useful output power to total input power.
力使物体沿力的方向移动时便做了功：W = F s cosθ。能量以不同形式存在，包括动能 (Eₖ = ½mv²) 和重力势能 (Eₚ = mgh)。能量守恒原理指出，能量可以转移或转化，但不会凭空产生或消失。功率是做功的快慢，P = W / t；在恒力和速度下，P = Fv。效率 η 为有用输出功率与总输入功率之比。
5. Materials: Stress, Strain and Young Modulus | 材料：应力、应变与杨氏模量
When a solid material is subjected to forces, it experiences stress (σ = F / A) and strain (ε = ΔL / L). Hooke’s law applies within the elastic limit, where stress is proportional to strain. The constant of proportionality is the Young modulus, E = σ / ε, which measures the stiffness of a material. The elastic potential energy stored in a stretched wire or spring is given by E = ½FΔL or E = ½k(ΔL)². Force–extension graphs show important features including the limit of proportionality, elastic limit, yield point and breaking stress.
固体材料受力时会产生应力 (σ = F / A) 和应变 (ε = ΔL / L)。在弹性限度内遵循胡克定律，应力与应变成正比。比例常数即杨氏模量 E = σ / ε，它衡量材料的刚度。拉伸的金属丝或弹簧中储存的弹性势能为 E = ½FΔL 或 E = ½k(ΔL)²。力–伸长量曲线图显示了比例极限、弹性极限、屈服点和断裂应力等重要特征。
6. Waves: Properties and Behaviour | 波的特性与行为
Waves transfer energy without net movement of matter. Key wave parameters include amplitude (A), wavelength (λ), frequency (f), period (T) and wave speed (v), linked by v = fλ. Transverse waves have oscillations perpendicular to propagation (e.g. electromagnetic waves), while longitudinal waves have oscillations parallel to propagation (e.g. sound waves). Phase difference describes the shift between two points on a wave, measured in degrees or radians. Reflection, refraction, diffraction and superposition (including interference) are fundamental wave behaviours. Standing waves form when two identical progressive waves travel in opposite directions, producing nodes and antinodes.
波传递能量而不发生物质的净移动。波的关键参数包括振幅 (A)、波长 (λ)、频率 (f)、周期 (T) 和波速 (v)，并由 v = fλ 关联。横波的振动方向与传播方向垂直（如电磁波），纵波的振动方向与传播方向平行（如声波）。相位差描述波上两点之间的偏移，以度或弧度度量。反射、折射、衍射以及叠加（包括干涉）是波的基本行为。当两列完全相同的行波相向传播时会形成驻波，产生波节和波腹。
7. Refraction and Total Internal Reflection | 折射与全内反射
When light passes from one transparent medium to another, its speed changes, causing refraction. Snell’s law relates the angles of incidence and refraction to the refractive indices: n₁ sinθ₁ = n₂ sinθ₂. The refractive index n of a medium is the ratio of the speed of light in vacuum to its speed in the medium. When light travels from a higher to a lower refractive index at an angle greater than the critical angle θc, total internal reflection occurs, where sinθc = n₂ / n₁ (with n₁ > n₂). This principle underpins optical fibres and prisms.
光从一种透明介质进入另一种时速度发生改变，从而产生折射。斯涅尔定律将入射角和折射角与折射率联系起来：n₁ sinθ₁ = n₂ sinθ₂。介质的折射率 n 等于真空光速与介质中光速之比。当光从较高折射率的介质射向较低折射率的介质，且入射角大于临界角 θc 时，发生全内反射，满足 sinθc = n₂ / n₁ (n₁ > n₂)。这一原理是光纤和棱镜工作的基础。
8. DC Electricity: Current, Voltage and Resistance | 直流电：电流、电压与电阻
Electric current I is the rate of flow of charge, I = ΔQ / Δt. Potential difference (p.d.) V is the energy transferred per unit charge. Ohm’s law states that for an ohmic conductor at constant temperature, V ∝ I, giving resistance R = V / I. Components can be combined in series and parallel: in series, Rₜₒₜ = R₁ + R₂ + … and the current is the same; in parallel, 1/Rₜₒₜ = 1/R₁ + 1/R₂ + … and the p.d. is the same across each branch. Power in circuits is given by P = I V = I²R = V² / R.
电流 I 是电荷流动的速率，I = ΔQ / Δt。电势差 V 是每单位电荷转移的能量。欧姆定律指出，对于恒定温度下的欧姆导体，V ∝ I，于是电阻 R = V / I。元件可以串联或并联：串联时 Rₜₒₜ = R₁ + R₂ + … 且电流相同；并联时 1/Rₜₒₜ = 1/R₁ + 1/R₂ + … 且各支路两端电势差相等。电路中的功率为 P = I V = I²R = V² / R。
9. Resistivity and Superconductivity | 电阻率与超导性
The resistance of a wire depends on its length L, cross-sectional area A and the material’s resistivity ρ: R = ρL / A. Resistivity is a temperature-dependent material property. Metals have low resistivity, whereas insulators have very high resistivity. Superconductivity occurs in certain materials when cooled below a critical temperature Tc, where their resistivity drops to exactly zero. This allows lossless current flow and produces strong magnetic effects, such as levitation above magnets.
导线的电阻取决于其长度 L、横截面积 A 以及材料的电阻率 ρ：R = ρL / A。电阻率是与温度相关的材料属性。金属的电阻率很低，而绝缘体的电阻率非常高。某些材料在冷却到临界温度 Tc 以下时出现超导现象，电阻率降为零。这使得电流无损耗流动，并产生强磁效应，如在磁体上方的磁悬浮。
10. Internal Resistance and Potential Dividers | 内阻与分压器
Every real source of e.m.f. has internal resistance r, causing the terminal p.d. to be less than the e.m.f. ε when current flows: V = ε − Ir. The lost volts are Ir. A potential divider circuit uses two or more resistors in series to produce a specific fraction of the input p.d.: Vₒᵤₜ = (R₂ / (R₁ + R₂)) × ε. This arrangement is widely used with sensors such as thermistors and light-dependent resistors (LDRs) to convert changes in resistance into a varying voltage.
每个真实电源都有内阻 r，导致有电流时端电压小于电动势 ε：V = ε − Ir。损失的电压为 Ir。分压电路使用两个或多个串联电阻，从输入电压中获得特定的比例输出：Vₒᵤₜ = (R₂ / (R₁ + R₂)) × ε。这种电路广泛用于与热敏电阻和光敏电阻 (LDR) 等传感器配合，将电阻变化转化为变化的电压。
11. Quantum Phenomena: Photons and Energy Levels | 量子现象：光子与能级
Light exhibits particle-like behaviour through photons, each carrying energy E = h f, where h is the Planck constant. The photoelectric effect demonstrates that electrons are emitted from a metal surface only when the incident photon frequency exceeds the threshold frequency f₀. The photoelectric equation is h f = Φ + Kₘₐₓ, where Φ is the work function and Kₘₐₓ is the maximum kinetic energy of the emitted electrons. Atomic energy levels are discrete, and electrons can move between them by absorbing or emitting photons with energy equal to the energy difference: ΔE = E₂ − E₁ = h f. This explains atomic line spectra and underpins technologies such as lasers.
光通过光子表现出粒子性，每个光子携带能量 E = h f，其中 h 为普朗克常数。光电效应表明，只有当入射光子的频率超过阈频率 f₀ 时，电子才会从金属表面逸出。光电方程为 h f = Φ + Kₘₐₓ，其中 Φ 是逸出功，Kₘₐₓ 是出射电子的最大动能。原子的能级是分立的，电子可通过吸收或发射能量等于能级差的光子进行跃迁：ΔE = E₂ − E₁ = h f。这解释了原子线状光谱，也是激光等技术的基础。
Published by TutorHao | Physics Revision Series | aleveler.com
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