📚 Year 12 WJEC Physics: Core Knowledge Review | 核心知识点梳理
This article provides a structured overview of all essential topics in the Year 12 WJEC Physics specification. It covers the foundational principles of mechanics, electricity, materials, waves and quantum phenomena, giving you a reliable revision map for the AS exams.
本文系统梳理了 Year 12 WJEC 物理课程的所有核心知识点，涵盖力学、电学、材料、波动和量子现象的基本原理，为 AS 阶段的复习提供清晰的知识脉络。
1. Scalars and Vectors | 标量与向量
A scalar quantity has magnitude only, such as speed, energy and mass. A vector quantity has both magnitude and direction, for example displacement, velocity and force. Vector addition can be performed using a tip-to-tail diagram or by resolving vectors into perpendicular components.
标量只有大小没有方向，如速率、能量和质量。向量既有大小又有方向，如位移、速度和力。向量可以通过三角形法则相加，或分解为互相垂直的分量进行计算。
Fₓ = F cosθ , F_y = F sinθ
The component of a force along a chosen axis is found by multiplying the magnitude by the cosine of the angle between the force and that axis. The perpendicular component is found using the sine. This technique is vital for solving inclined plane and equilibrium problems.
力在选定轴上的分量等于力的大小乘以力与该轴夹角的余弦，垂直分力则用正弦求得。这种技巧对于解决斜面平衡问题至关重要。
2. Kinematics | 运动学
Kinematics describes motion without considering its causes. The key quantities are displacement (s), velocity (v) and acceleration (a). For uniform acceleration in a straight line, the equations of motion are used.
运动学描述物体的运动而不考虑引起运动的原因。核心物理量包括位移 s、速度 v 和加速度 a。对于匀变速直线运动，可以运用运动学公式。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u+v)t
Here u is the initial velocity and t is time. Remember to assign a positive direction and treat all vectors consistently. The acceleration due to gravity, g = 9.81 m s⁻², points downward.
公式中 u 为初速度，t 为时间。解题时需规定正方向并一致处理所有向量。重力加速度 g = 9.81 m s⁻²，方向竖直向下。
Motion graphs also give insights: a displacement–time graph’s gradient gives velocity; a velocity–time graph’s gradient gives acceleration and its area gives displacement.
运动图像也能提供信息：位移-时间图的斜率表示速度；速度-时间图的斜率表示加速度，图线与时间轴围成的面积表示位移。
3. Dynamics and Momentum | 动力学与动量
Newton’s First Law states that an object remains at rest or in uniform motion unless acted upon by a resultant force. The Second Law gives the relationship F = m a, where F is the resultant force. The Third Law states that action and reaction forces are equal in magnitude and opposite in direction, but act on different bodies.
牛顿第一定律指出，物体在不受合力作用时保持静止或匀速直线运动。第二定律给出 F = m a 的关系。第三定律说明作用力与反作用力大小相等、方向相反，但作用在不同物体上。
Linear momentum is defined as p = m v. The impulse of a force equals the change in momentum: F Δt = Δp. In a closed system, total momentum is conserved. Collisions are classified as elastic (kinetic energy conserved) or inelastic.
线动量定义为 p = m v。冲量等于动量的变化量 F Δt = Δp。在封闭系统中总动量守恒。碰撞可分为弹性碰撞（动能守恒）和非弹性碰撞。
4. Work, Energy and Power | 功、能与功率
Work is done when a force moves its point of application. W = F s cosθ, where θ is the angle between force and displacement. Energy is transferred when work is done. Kinetic energy is Eₖ = ½mv²; gravitational potential energy change is ΔEₚ = mgΔh.
力作用在物体上并使其在力的方向上有位移时，力做了功 W = F s cosθ。做功的过程伴随着能量的转移。动能为 Eₖ = ½mv²，重力势能的变化为 ΔEₚ = mgΔh。
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred between different stores. Efficiency = (useful output energy / total input energy) × 100%. Power, measured in watts, is the rate of doing work: P = W/t = F v.
能量守恒定律指出，能量既不能创生也不能消灭，只能在不同的能量形式之间转移。效率 =（有用输出能量 / 总输入能量）× 100%。功率的单位是瓦特，表示做功的快慢：P = W/t = F v。
5. Solids and Materials | 固体与材料
Hooke’s Law states that the extension ΔL of a spring or wire is directly proportional to the applied force F, provided the elastic limit is not exceeded: F = k ΔL. Stress σ is defined as force per unit cross‑sectional area, σ = F/A. Strain ε is the extension per unit original length, ε = ΔL/L.
胡克定律指出，在弹性限度内，弹簧或金属丝的伸长量 ΔL 与外力 F 成正比：F = k ΔL。应力 σ 定义为单位横截面积上的力，σ = F/A。应变 ε 为单位原长的伸长量，ε = ΔL/L。
Young modulus E = σ/ε = (F L)/(A ΔL)
The Young modulus is a measure of the stiffness of a material. A stress–strain graph reveals the proportional limit, elastic limit, yield point and ultimate tensile strength. Elastic strain energy stored in a stretched spring is U = ½FΔL = ½k(ΔL)².
杨氏模量是材料刚度的量度。应力-应变曲线可以显示比例极限、弹性极限、屈服点和抗拉强度。弹簧中储存的弹性势能为 U = ½FΔL = ½k(ΔL)²。
6. Stars and Electromagnetic Radiation | 恒星与电磁辐射
All objects above absolute zero emit electromagnetic radiation. A black body is a perfect absorber and emitter. Wien’s displacement law relates the peak wavelength λₘₐₓ to the temperature: λₘₐₓ T = 2.9×10⁻³ m K. The Stefan–Boltzmann law gives the luminosity L = 4πR² σ T⁴, where σ = 5.67×10⁻⁸ W m⁻² K⁻⁴.
所有高于绝对零度的物体都会向外发出电磁辐射。黑体是理想的吸收体和辐射体。维恩位移定律给出峰值波长 λₘₐₓ 与温度的关系：λₘₐₓ T = 2.9×10⁻³ m K。斯特藩-玻尔兹曼定律给出光度 L = 4πR² σ T⁴。
| Colour | Approximate Temperature (K) | Example Star |
| Blue | >25 000 | Rigel |
| White | 7 500 – 10 000 | Sirius |
| Yellow | 5 000 – 6 000 | Sun |
| Red | <3 500 | Betelgeuse |
Stellar spectra show absorption lines that indicate the chemical composition and surface temperature. The Hertzsprung–Russell (H–R) diagram plots luminosity against temperature and reveals groups such as the main sequence, giants and white dwarfs.
恒星光谱中的吸收线可以揭示恒星的化学组成和表面温度。赫罗图以光度对温度为坐标，显示出主序星、巨星和白矮星等恒星的分布。
7. Electric Current and Circuits | 电流与电路
Electric current is the rate of flow of charge: I = ΔQ/Δt. Charge is measured in coulombs, and one coulomb per second equals one ampere. Potential difference V between two points is the energy transferred per unit charge: V = W/Q.
电流是电荷流动的速率 I = ΔQ/Δt。电荷的单位是库仑，每秒流过 1 库仑的电流为 1 安培。两点间的电势差 V 是单位电荷转移的能量 V = W/Q。
Ohm’s law states that the current through a conductor is directly proportional to the potential difference across it, provided temperature remains constant: V = IR. Resistance arises due to collisions between conduction electrons and the lattice.
欧姆定律指出，在温度不变的条件下，通过导体的电流与导体两端的电势差成正比：V = IR。电阻产生的原因是自由电子与晶格发生碰撞。
Resistance of a wire: R = ρL/A
The resistivity ρ is a material property. For series circuits: Rₜₒₜₐₗ = R₁ + R₂ + … . For parallel circuits: 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + … .
电阻率 ρ 是材料的属性。串联电路总电阻 Rₜₒₜₐₗ = R₁ + R₂ + …；并联电路总电阻 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + …。
8. EMF and Internal Resistance | 电动势与内阻
Electromotive force (emf) ε is the energy supplied per unit charge by a source. Due to internal resistance r, the terminal potential difference V is less than the emf when current flows: V = ε − Ir.
电动势 ε 是电源内部对单位电荷所做的功。由于电源内阻 r 的存在，当有电流流过时，路端电压 V 小于电动势：V = ε − Ir。
Plotting terminal V against current I gives a straight‑line graph with intercept ε and gradient −r. Resistance of metallic conductors increases with temperature; superconductors have zero resistivity below a critical temperature.
作出路端电压 V 随电流 I 的变化图线，可得到截距为 ε、斜率为 −r 的直线。金属导体的电阻随温度升高而增大；超导体在低于临界温度时电阻率降为零。
9. Capacitors | 电容器
Capacitance C is the charge stored per unit potential difference: C = Q/V, measured in farads (F). For a parallel‑plate capacitor, C = ε₀ A/d, where ε₀ is the permittivity of free space (8.85×10⁻¹² F m⁻¹).
电容 C 是单位电势差下电容器储存的电荷量：C = Q/V，单位是法。平行板电容器的电容为 C = ε₀ A/d，其中 ε₀ 为真空介电常数。
Energy stored in a capacitor: E = ½ Q V = ½ C V² = ½ Q²/C
During charging or discharging, the time constant τ = RC describes how quickly the process occurs. After a time of about 5 τ, charging or discharging is considered complete.
充放电过程中，时间常数 τ = RC 描述过程进行的快慢。经过大约 5 τ 的时间后，充放电基本完成。
10. Waves and Light | 波与光
A wave transfers energy without transferring matter. Transverse waves (e.g. light, water ripples) have oscillations perpendicular to the direction of energy transfer. Longitudinal waves (e.g. sound) have oscillations parallel to the direction of energy transfer. Key quantities: frequency f = 1/T, wave speed v = f λ.
波传递能量而不传递物质。横波（如光、水波）的振动方向与能量传递方向垂直。纵波（如声波）的振动方向与能量传递方向平行。关键关系：频率 f = 1/T，波速 v = f λ。
Diffraction occurs when waves spread out after passing through a gap or around an obstacle. Superposition leads to interference: constructive when path difference = nλ, destructive when path difference = (n+½)λ. In Young’s double‑slit experiment, fringe spacing Δy = λD/s.
衍射是指波经过小孔或绕过障碍物后扩展的现象。叠加导致干涉：当波程差为 nλ 时出现相长干涉，为 (n+½)λ 时出现相消干涉。杨氏双缝实验中，条纹间距 Δy = λD/s。
Refraction is described by Snell’s law: n₁ sin θ₁ = n₂ sin θ₂. The refractive index n = sin i / sin r. Total internal reflection occurs when light travels from a denser to a less dense medium at an angle greater than the critical angle: sin C = 1/n.
折射遵循斯涅耳定律 n₁ sin θ₁ = n₂ sin θ₂。折射率 n = sin i / sin r。当光从光密介质射入光疏介质且入射角大于临界角时发生全内反射：sin C = 1/n。
11. Photons and Lasers | 光子与激光
The energy of a photon is directly proportional to its frequency: E = h f = hc/λ, where h is Planck’s constant (6.63×10⁻³⁴ J s). The photoelectric effect provides evidence for the particle nature of light. The energy of the incident photon must overcome the work function Φ for an electron to be emitted: h f = Φ + Eₖ(max).
光子的能量与其频率成正比：E = h f = hc/λ，其中 h 为普朗克常数。光电效应证明了光的粒子性。入射光子能量必须克服金属的逸出功 Φ 才能使电子逸出：h f = Φ + Eₖ(max)。
Threshold frequency f₀ is the minimum frequency required to emit photoelectrons, given by Φ = h f₀. Electrons in atoms exist in discrete energy levels; emission spectra arise when electrons drop to lower levels and emit photons of specific wavelengths.
截止频率 f₀ 是发生光电效应的最低频率，满足 Φ = h f₀。原子中的电子处于分立的能级；当电子跃迁回低能级时会发射特定波长的光子，形成发射光谱。
A laser produces light by stimulated emission. Its output is monochromatic, coherent and highly directional. In a simplified laser, population inversion is needed so that stimulated emission dominates over absorption.
激光通过受激辐射产生光。激光具有单色性好、相干性强和方向性高的特点。简单激光器需要实现粒子数反转，使受激辐射超过受激吸收。
Published by TutorHao | Physics Revision Series | aleveler.com
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