📚 Core Knowledge Summary for WJEC Physics (Pre-U) | WJEC 物理核心知识点梳理
This revision guide distils the essential topics of the WJEC A-level Physics syllabus (Pre-U), providing a structured overview of the key principles, definitions and equations you need to master. Whether you are preparing for AS Unit 1 & 2 or the full A2, this summary covers mechanics, waves, electricity, thermal physics, fields, nuclear physics and practical skills.
本复习指南提炼了 WJEC A-level 物理（大学预科）课程的核心主题，为你搭建关键原理、定义与公式的知识框架。无论你在准备 AS 第一、二单元还是完整的 A2 考试，这份梳理都涵盖力学、波、电学、热物理、场、核物理及实验技能。
1. Scalars, Vectors and Measurements | 标量、矢量和测量
All physical quantities are classified as scalars or vectors. Scalars have magnitude only (e.g. distance, speed, mass, energy). Vectors have both magnitude and direction (e.g. displacement, velocity, force, acceleration). Vector addition can be performed graphically using tip-to-tail method or by resolving into perpendicular components.
所有物理量分为标量和矢量。标量仅有大小（如距离、速率、质量、能量）。矢量同时具有大小和方向（如位移、速度、力、加速度）。矢量相加可通过作图法（首尾相接）或将矢量分解为互相垂直的分量来求解。
SI base units (metre, kilogram, second, ampere, kelvin, mole, candela) form the foundation of all measurements. Prefixes such as kilo (10³), mega (10⁶), milli (10⁻³) and micro (10⁻⁶) enable efficient expression of very large or very small quantities. Homogeneity of equations can be checked using base units.
国际单位制基本单位（米、千克、秒、安培、开尔文、摩尔、坎德拉）构成所有测量的基础。诸如千 (10³)、兆 (10⁶)、毫 (10⁻³) 和微 (10⁻⁶) 等词头方便地表达极大或极小的量。通过基本单位可以检验物理方程的齐次性。
2. Kinematics and Motion Graphs | 运动学与运动图像
Kinematics describes motion without reference to its causes. Displacement, velocity and acceleration are central concepts. For uniform acceleration, three ‘suvat’ equations link these variables:
运动学描述物体的运动而不涉及引起运动的原因。位移、速度和加速度是核心概念。对于匀加速运动，三个运动学方程将这些变量联系在一起：
v = u + at s = ut + ½at² v² = u² + 2as
Velocity–time graphs give displacement as the area under the line, and acceleration as the gradient. A curved graph indicates changing acceleration. Free-fall under gravity ignores air resistance, where a = g = 9.81 m s⁻².
速度–时间图像中，线下面积表示位移，斜率表示加速度。若图线弯曲则加速度在变化。忽略空气阻力的自由落体运动中 a = g = 9.81 m s⁻²。
3. Newton’s Laws and Momentum | 牛顿定律与动量
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 F = ma (resultant force = mass × acceleration). The Third Law states that forces between two objects are equal in magnitude and opposite in direction.
牛顿第一定律：物体在不受合外力作用时总保持静止或匀速直线运动。第二定律给出 F = ma（合外力 = 质量 × 加速度）。第三定律：两物体间的作用力与反作用力大小相等、方向相反。
Linear momentum p = mv is conserved in any interaction provided no external resultant force acts. Impulse = F Δt = Δp, linking force and momentum change. Elastic collisions conserve both momentum and kinetic energy; inelastic collisions conserve momentum only.
线动量 p = mv 在没有合外力的相互作用中守恒。冲量 = F Δt = Δp，把力与动量变化联系起来。弹性碰撞同时守恒动量和动能；非弹性碰撞仅守恒动量。
4. Work, Energy and Power | 功、能量与功率
Work done by a force is W = F s cosθ, where θ is the angle between force and displacement. Energy is the capacity to do work. Kinetic energy Eₖ = ½mv², gravitational potential energy Eₚ = mgΔh. The principle of conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another.
力所做的功 W = F s cosθ，其中 θ 是力与位移间的夹角。能量是做功的本领。动能 Eₖ = ½mv²，重力势能 Eₚ = mgΔh。能量守恒原理指出能量不能凭空产生或消灭，只能从一种形式转化为另一种形式。
Power P = W / t, the rate of doing work, with the unit watt (W). Efficiency = (useful output energy / total input energy) × 100%.
功率 P = W / t，表示做功的速率，单位为瓦特 (W)。效率 = (有用的输出能量 / 总输入能量) × 100%。
5. Materials and Hooke’s Law | 材料与胡克定律
Hooke’s law states that, for an elastic material, extension is proportional to applied force up to the limit of proportionality: F = kx, where k is the spring constant. Elastic limit is the point beyond which the material becomes permanently deformed. Stress (σ = F/A) and strain (ε = ΔL/L) define Young modulus E = σ / ε.
胡克定律：弹性材料在比例限度内，伸长量与所施加的力成正比：F = kx，k 为劲度系数。弹性限度是材料发生永久变形的临界点。应力 (σ = F/A) 和应变 (ε = ΔL/L) 定义杨氏模量 E = σ / ε。
Force–extension graphs yield the work done as the area under the curve – equal to elastic potential energy for a spring. Plastic deformation is permanent and cannot be recovered.
力–伸长量图像中，曲线下方面积表示做功——对弹簧而言等于弹性势能。塑性形变是永久的、不可恢复的形变。
6. Waves and Optics | 波动与光学
Progressive waves transfer energy without net movement of matter. Key parameters: amplitude, wavelength λ, frequency f, period T and wave speed v = fλ. Transverse waves (oscillation perpendicular to propagation, e.g. light, water waves) and longitudinal waves (oscillation parallel to propagation, e.g. sound) are distinguished.
行波传递能量而没有物质的净移动。关键参数：振幅、波长 λ、频率 f、周期 T 和波速 v = fλ。横波（振动方向垂直于传播方向，如光波、水波）与纵波（振动方向平行于传播方向，如声波）有明显区别。
Superposition leads to interference and standing waves. Young’s double-slit experiment demonstrates interference and allows measurement of wavelength: Δx = λD / a, where Δx is fringe spacing, D is slit-to-screen distance, a is slit separation. Diffraction gratings produce sharp maxima described by nλ = d sinθ.
波的叠加产生干涉和驻波。杨氏双缝实验演示干涉并可用于测量波长：Δx = λD / a，其中 Δx 为条纹间距，D 为缝屏距，a 为双缝间距。衍射光栅产生锐利的极大值，满足 nλ = d sinθ。
7. Electricity and Circuits | 电学与电路
Current I = ΔQ / Δt, potential difference V = W / Q, and resistance R = V / I provide the basic electrical definitions. Ohm’s law states that, at constant temperature, current through a metallic conductor is proportional to the p.d. across it. Resistivity ρ links resistance to geometry: R = ρL / A.
电流 I = ΔQ / Δt，电压 V = W / Q，电阻 R = V / I 为基本电学定义。欧姆定律指出在恒温条件下，流过金属导体的电流与其两端电压成正比。电阻率 ρ 将电阻与导体几何尺寸联系起来：R = ρL / A。
Kirchhoff’s laws are essential for circuit analysis. The junction rule: ΣIᵢₙ = ΣIₒᵤₜ. The loop rule: Σε = ΣIR around any closed loop. In series, Rₜₒₜₐₗ = R₁ + R₂ + … ; in parallel, 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + … . Internal resistance r of a cell reduces terminal p.d.: V = ε – Ir.
基尔霍夫定律是电路分析的基础。节点电流定律：ΣIᵢₙ = ΣIₒᵤₜ。回路电压定律：Σε = ΣIR。串联电阻 Rₜₒₜₐₗ = R₁ + R₂ + …；并联电阻 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + …。电池内阻 r 使端电压降低：V = ε – Ir。
8. Quantum Physics and Particles | 量子物理与粒子
Photoelectric effect provides evidence for the particle nature of light. Einstein’s photoelectric equation: hf = φ + ½mv²ₘₐₓ, where φ is the work function. The threshold frequency f₀ = φ / h. Stopping potential Vₛ relates to maximum kinetic energy: eVₛ = ½mv²ₘₐₓ.
光电效应为光的粒子性提供了证据。爱因斯坦光电效应方程：hf = φ + ½mv²ₘₐₓ，其中 φ 为逸出功。截止频率 f₀ = φ / h。遏止电压 Vₛ 与最大动能的关系为 eVₛ = ½mv²ₘₐₓ。
Energy levels in atoms are quantised. Electron transitions between levels produce photons of energy ΔE = hf. Line spectra (emission and absorption) are unique to each element. De Broglie wavelength λ = h/p demonstrates wave–particle duality for matter.
原子能级是量子化的。电子在能级间跃迁发射或吸收能量为 ΔE = hf 的光子。线状光谱（发射谱和吸收谱）是每种元素独有的特征。德布罗意波长 λ = h/p 证明了物质的波粒二象性。
9. Thermal Physics and Gases | 热物理与气体
Temperature is related to the average kinetic energy of particles. Absolute zero (0 K = –273.15 °C) is the lowest possible temperature. The ideal gas law is pV = nRT where n is the number of moles and R = 8.31 J mol⁻¹ K⁻¹. Also pV = NkT, where N is molecule number and k is Boltzmann’s constant.
温度与粒子的平均动能相关。绝对零度 (0 K = –273.15 °C) 是最低可能温度。理想气体状态方程为 pV = nRT，n 为摩尔数，R = 8.31 J mol⁻¹ K⁻¹。也可表示为 pV = NkT，N 为分子数，k 为玻尔兹曼常数。
Kinetic theory links macroscopic quantities to microscopic behaviour. Mean kinetic energy of a molecule = (3/2)kT. Internal energy of an ideal gas depends only on temperature. The first law of thermodynamics: ΔU = Q + W, with sign convention for work done on system.
分子动理论将宏观量与微观行为联系起来。分子平均动能 = (3/2)kT。理想气体的内能仅取决于温度。热力学第一定律：ΔU = Q + W，做功正负号约定为外界对系统做功。
10. Gravitational and Electric Fields | 引力场与电场
A gravitational field g is a region where a mass experiences a force. g = F/m. For a point mass, g = GM/r². Gravitational potential Vᵧ = –GM/r. Escape velocity from a planet is vₑₛ = √(2GM/R). Satellites in circular orbit satisfy v² = GM/r and T² ∝ r³.
引力场 g 是质量受到力作用的区域。g = F/m。对于点质量，g = GM/r²。引力势 Vᵧ = –GM/r。行星的逃逸速度 vₑₛ = √(2GM/R)。在圆形轨道上的卫星满足 v² = GM/r 且 T² ∝ r³。
An electric field E exerts a force on a charge: F = qE. For a point charge, E = kQ/r² (or Q/(4πε₀r²)). Electric potential V = kQ/r. Uniform fields between parallel plates give E = V/d. Capacitance C = Q/V; energy stored U = ½QV = ½CV². Charging and discharging of capacitors follow exponential forms.
电场 E 对电荷施加力：F = qE。对于点电荷，E = kQ/r²（或 Q/(4πε₀r²)）。电势 V = kQ/r。平行板间的匀强电场 E = V/d。电容 C = Q/V；储存的能量 U = ½QV = ½CV²。电容器的充放电过程遵循指数规律。
11. Nuclear Physics and Radioactivity | 核物理与放射性
The nucleus is characterised by proton number Z and nucleon number A. The strong nuclear force holds the nucleus together, overcoming electrostatic repulsion. Radioactive decay is spontaneous and random: alpha decay (reduces Z by 2, A by 4), beta-minus decay (n → p + e⁻ + ν̄ₑ), beta-plus decay (p → n + e⁺ + νₑ). Gamma radiation is a high-energy photon.
原子核由质子数 Z 和核子数 A 描述。强核力将核子束缚在一起，克服静电斥力。放射性衰变是自发且随机的：α 衰变（Z 减 2，A 减 4），β⁻ 衰变（n → p + e⁻ + ν̄ₑ），β⁺ 衰变（p → n + e⁺ + νₑ）。γ 射线是高能光子。
Activity A = λN decays exponentially: N = N₀ e⁻λᵗ and A = A₀ e⁻λᵗ. Half-life t½ = ln2 / λ. Nuclear fission (splitting of heavy nuclei) and fusion (joining of light nuclei) release energy due to a mass defect, calculated from E = mc².
活度 A = λN 按指数衰减：N = N₀ e⁻λᵗ，A = A₀ e⁻λᵗ。半衰期 t½ = ln2 / λ。核裂变（重核分裂）和核聚变（轻核结合）因质量亏损而释放能量，用 E = mc² 计算。
12. Practical Skills and Data Analysis | 实验技能与数据分析
WJEC places strong emphasis on practical competencies. You must be able to identify independent, dependent and control variables; select appropriate instruments to minimise uncertainty; and record data with suitable significant figures. Repeated readings improve reliability, and anomalies should be evaluated.
WJEC 物理强调实验能力。你必须能识别独立、因变及控制变量；选用合适的仪器以减小不确定度；并以适当的有效数字记录数据。重复测量提高可靠性，异常数据应加以评判。
Uncertainty can be absolute (±Δx) or percentage (Δx/x × 100%). Combining uncertainties: for addition/subtraction add absolute uncertainties; for multiplication/division add percentage uncertainties. Graphs should render error bars, and lines of best fit allow gradient and intercept determination.
不确定度可分为绝对不确定度（±Δx）和百分比不确定度（Δx/x × 100%）。不确定度的合成：加减运算时绝对不确定度相加；乘除运算时百分比不确定度相加。作图需画出误差棒，最佳拟合线用于确定斜率和截距。
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