📚 Year 12 AQA Physics: Core Concept Review | 核心知识点梳理
Year 12 AQA Physics lays the groundwork for the full A-level by building conceptual understanding and mathematical fluency across five core areas: measurements and their errors, particles and radiation, waves, mechanics and materials, and electricity. Each topic is interwoven with practical skills and an appreciation of how physicists test and refine models. This article distills the essential ideas, definitions, equations, and common pitfalls you need to master for success on the AS and Year 12 assessments.
AQA 物理 Year 12 课程为整个 A-level 打下坚实基础，围绕五大核心模块构建概念理解和数学运用能力：测量及其误差、粒子与辐射、波、力学与材料、以及电学。每个主题都与实验技能以及对物理学家如何检验和完善模型的理解交织在一起。本文提炼了你必须掌握的基本概念、定义、公式和常见易错点，助你在 AS 与 Year 12 考试中取得成功。
1. Measurements and Errors | 测量与误差
Every physical measurement has an associated uncertainty. Systematic errors cause readings to be consistently too high or too low, usually due to poorly calibrated instruments or experimental design, while random errors lead to scatter around the true value, which can be reduced by taking repeat readings and calculating a mean.
每一个物理测量都伴随着不确定度。系统误差导致读数持续偏高或偏低，通常源于仪器校准不良或实验设计缺陷；随机误差则使数据围绕真值波动，可以通过重复读数并计算平均值来减小。
You must learn to estimate absolute uncertainties from the smallest scale division or from the range of repeats, and to combine them when data are added, subtracted, multiplied, or divided. For independent uncertainties in a quantity calculated as y = ab/c, the percentage uncertainty in y is the sum of the percentage uncertainties in a, b, and c.
精密度反映重复读数之间的一致程度，而准确度描述测量值与真值的接近程度。你需要学会根据最小刻度或重复读数的范围估算绝对不确定度，并能在数据加减乘除时合成不确定度。对于独立不确定度，若计算式为 y = ab/c，则 y 的百分不确定度等于 a、b、c 百分不确定度之和。
Absolute uncertainty = ± smallest division OR ± ½ range (repeats)
绝对不确定度 = ±最小刻度 或 ±½ 范围（重复测量）
Always quote the uncertainty to 1 significant figure and round the measurement to the same number of decimal places. The gradient and intercept of a graph carry uncertainties; lines of worst fit drawn by eye provide an estimate of the maximum and minimum plausible slopes.
务必以一位有效数字给出不确定度，并将测量值修约至相同的小数位数。图线的斜率和截距也带有不确定度；通过目视绘制的最大、最小可接受直线可以估算出斜率的可能范围。
2. Particles and Antiparticles | 粒子与反粒子
and lepton number. When a particle and its antiparticle meet, annihilation occurs, converting all their rest mass into two photons of total energy E = 2 m c².
物质由基本粒子构成：夸克和轻子。反物质伙伴拥有相同的质量，但电荷、重子数和轻子数符号相反。当粒子与反粒子相遇时发生湮灭，其全部静质量转化为两个光子，总能量 E = 2 m c²。
ction is the reverse of annihilation: a photon of sufficient energy (≥ 1.022 MeV) can transform into an electron–positron pair near a nucleus to conserve momentum.
光子是电磁相互作用的规范玻色子。它的能量与频率关系为 E = h f，与波长关系为 E = h c / λ。电子对产生是湮灭的逆过程：能量足够高（≥ 1.022 MeV）的光子在原子核附近可转化为电子–正电子对以保持动量守恒。
E = h f = h c / λ
E = h f = h c / λ
- Hadrons (baryons and mesons) feel the strong nuclear force; leptons do not.
- 强子（重子和介子）感受强核力；轻子不感受。
- Baryon number is conserved in all interactions; proton is the only stable baryon.
- 所有相互作用中重子数守恒；质子是唯一稳定的重子。
3. Quarks, Leptons, and Conservation Laws | 夸克、轻子与守恒律
There are six quark flavours (up, down, charm, strange, top, bottom) and six leptons (electron, muon, tau, and their neutrinos). At AQA Year 12, you focus on up, down, and strange quarks, and on electron and electron neutrino. The up quark carries charge +⅔ e, down and strange quarks carry –⅓ e. Baryons are qqq combinations; mesons are q anti-q.
夸克有六种味（上、下、粲、奇、顶、底），轻子有六种（电子、μ子、τ子及其中微子）。AQA Year 12 阶段集中学习上、下、奇异夸克，以及电子和电子中微子。上夸克带 +⅔ e 电荷，下夸克和奇异夸克带 –⅓ e 电荷。重子是三个夸克的组合，介子是夸克–反夸克对。
hanges into an up quark, emitting an electron and an electron antineutrino: d → u + e⁻ + ν̅ rk flavour change. Always check conservation of charge, baryon number, and lepton number when analysing particle reactions.
在 β⁻ 衰变中，下夸克变为上夸克，放出电子和反电子中微子：d → u + e⁻ + ν̅ₑ。在 β⁺ 衰变中，上夸克变为下夸克，放出正电子和电子中微子。弱相互作用负责夸克味的改变。分析粒子反应时，务必检查电荷、重子数和轻子数守恒。
Proton: uud ; Neutron: udd ; Charged pion: ud̅ or du̅
质子：uud ；中子：udd ；带电 π 介子：ud̅ 或 du̅
4. Quantum Phenomena – Photoelectric Effect | 量子现象——光电效应
The photoelectric effect provides evidence for the particle nature of light. When electromagnetic radiation above the threshold frequency f₀ strikes a metal surface, electrons are emitted instantaneously. The maximum kinetic energy of the emitted electrons depends only on the frequency of the light, not on its intensity, which is inexplicable in the classical wave model.
光电效应为光的粒子性提供了证据。当频率高于截止频率 f₀ 的电磁辐射照射金属表面时，电子立即逸出。逸出电子的最大动能只与光的频率有关，与光强无关，这是经典波动模型无法解释的。
Einstein’s photoelectric equation states: Eₖ(max) = h f – tial energy: e Vₛ = Eₖ(max). A graph of Eₖ(max) against f yields a straight line with gradient h and intercept –φ on the kinetic energy axis.
爱因斯坦光电效应方程为：Eₖ(max) = h f – φ，其中 φ 为功函数（使电子逸出的最小能量）。遏止电压 Vₛ 将动能转回电势能：e Vₛ = Eₖ(max)。以 Eₖ(max) 对 f 作图得到一条直线，斜率为 h，在动能轴上的截距为 –φ。
Eₖ(max) = h f – φ
Eₖ(max) = h f – φ
Intensity controls the rate of photons arriving, hence the photocurrent, but cannot change the maximum kinetic energy if f > f₀.
光强控制光子到达的速率，从而控制光电流大小，但只要 f > f₀，光强就无法改变最大动能。
5. Energy Levels and Spectra | 能级与光谱
tron drops from a higher level E₂ to a lower level E₁, it emits a photon of energy ΔE = E₂ – energy and jump to a higher level. These line spectra are unique fingerprints of elements.
原子中的电子存在分立的能级。当电子从高能级 E₂ 跃迁到低能级 E₁ 时，会发出能量为 ΔE = E₂ – E₁ = h f 的光子。当电子恰好吸收适当能量的光子并跃迁到高能级时，就形成吸收光谱。这些线状谱是元素的独特指纹。
Excitation requires a specific photon energy, whereas ionisation removes the electron completely. The ionisation energy of hydrogen from the ground state is 13.6 eV. Fluorescent lamps use electron collisions to excite mercury atoms; the emitted UV photons then strike a phosphor coating, producing visible light.
激发需要特定的光子能量，电离则是将电子完全移除。氢原子基态的电离能为 13.6 eV。荧光灯利用电子碰撞激发汞原子，发出的紫外线光子再撞击荧光涂层，产生可见光。
ΔE = h f = h c / λ
ΔE = h f = h c / λ
6. Progressive and Stationary Waves | 行进波与驻波
speed v = f λ. The phase difference between two points on a wave is measured in radians; points separated by a whole number of wavelengths are in phase (Δφ = 0, 2π, 4π …).
行进波传播能量而不传递物质。关键参数：振幅 A、波长 λ、频率 f、周期 T = 1/f 以及波速 v = f λ。波上两点之间的相位差以弧度度量；相距整数倍波长的点同相（Δφ = 0, 2π, 4π …）。
Two types of wave: transverse (oscillations perpendicular to energy transfer, e.g. EM waves) and longitudinal (oscillations parallel to energy transfer, e.g. sound). Polarisation provides conclusive evidence that a wave is transverse; only transverse waves can be polarised.
波有两种类型：横波（振动垂直于能量传递方向，如电磁波）和纵波（振动平行于能量传递方向，如声波）。偏振是横波的决定性证据；只有横波可以偏振。
tinodes (maximum amplitude) are fixed in space. On a string fixed at both ends, the fundamental frequency f₁ = v/(2L); harmonics are integer multiples of the fundamental.
驻波由两列相同且相向传播的行进波干涉形成。波节（位移为零）和波腹（振幅最大）在空间中固定。在两端固定的弦上，基频 f₁ = v/(2L)；谐频是基频的整数倍。
v = f λ ; f₁ = v / (2L)
v = f λ ; f₁ = v / (2L)
7. Refraction, Diffraction, and Interference | 折射、衍射与干涉
n two media, causing a change in direction unless the wave arrives along the normal. Snell' entering a more optically dense medium, it bends towards the normal and slows down; frequency remains constant, so wavelength decreases.
折射发生在波穿过两种介质界面速度改变时，除非波沿法线入射，否则方向会改变。斯涅尔定律：n₁ sin θ₁ = n₂ sin θ₂，其中 n 为折射率，n = c / v。光进入光密介质时向法线弯折且速度减小；频率不变，因此波长减小。
ngle C, where sin C = n₂ / n₁ (n₁ > n₂). Optical fibres exploit TIR for data transmission.
当入射角大于临界角 C 时发生全内反射，临界角满足 sin C = n₂ / n₁ (n₁ > n₂)。光纤利用全内反射传输数据。
the effect is most significant when the slit width is comparable to the wavelength. Young' ng w = λ D / s, where D is the distance from slits to screen and s is the slit separation.
衍射是波遇到障碍物或穿过狭缝时扩展的现象；当缝宽与波长可比拟时衍射最显著。杨氏双缝实验展示了干涉：相干光产生等间距的条纹。条纹间距 w = λ D / s，其中 D 为双缝到屏幕的距离，s 为双缝间距。
n₁ sin θ₁ = n₂ sin θ₂ ; w = λ D / s ; sin C = 1 / n (for air)
n₁ sin θ₁ = n₂ sin θ₂ ; w = λ D / s ; sin C = 1/n（相对空气）
8. Motion and Forces | 运动与力
Kinematics describes motion in terms of displacement s, initial velocity u, final velocity v, acceleration a, and time t. The SUVAT equations are valid only for constant acceleration in a straight line.
运动学用位移 s、初速度 u、末速度 v、加速度 a 和时间 t 描述运动。SUVAT 方程仅适用于匀加速直线运动。
v = u + at ; s = ut + ½ a t² ; v² = u² + 2 a s ; s = ½ (u + v) t
v = u + at ; s = ut + ½ a t² ; v² = u² + 2 a s ; s = ½ (u + v) t
Acceleration–time and velocity–time graphs: area under a v–t graph gives displacement; gradient of a v– ts; horizontal velocity is constant (ignore air resistance), and vertical motion obeys a = –g.
加速度–时间和速度–时间图像：v–t 图下的面积代表位移；v–t 图的斜率代表加速度。处理抛体运动时，将初速度分解为水平和竖直分量；水平速度恒定（忽略空气阻力），竖直方向遵循 a = –g。
Newton' nt force equals rate of change of momentum. (3) Every action has an equal and opposite reaction.
牛顿定律：（1）物体保持静止或匀速直线运动状态，除非受到合力作用。（2）F = m a，合力等于动量的变化率。（3）作用力与反作用力大小相等、方向相反、作用在不同物体上。
g acts from the centre of mass; normal contact force is perpendicular to the surface; tension acts along a string; friction opposes relative motion.
隔离体受力图：画出作用在单个物体上的所有力。重力 W = m g 作用于质心；法向接触力垂直于表面；拉力沿绳子方向；摩擦力阻碍相对运动。
9. Energy, Power, and Momentum | 能量、功率与动量
y cannot be created or destroyed, only transferred into different forms. Efficiency = (useful output energy / total input energy) × 100%.
做功 W = F s cos θ。动能 Eₖ = ½ m v²；重力势能 ΔEₚ = m g Δh。能量守恒定律指出能量不能被创生或消灭，只能在不同形式之间转化。效率 = （有用输出能量 / 总输入能量）× 100%。
e moving at constant speed on level ground, the driving force equals the resistive forces.
功率 P = W / t = F v。车辆水平匀速行驶时，驱动力大小等于阻力。
of conservation of momentum: in a closed system, total momentum before a collision equals total momentum afterwards, provided no external resultant force acts. Collisions are either elastic (kinetic energy conserved) or inelastic (kinetic energy not conserved, but momentum is always conserved).
线动量 p = m v。动量守恒定律：在无外力合作用的封闭系统中，碰撞前的总动量等于碰撞后的总动量。碰撞分为弹性碰撞（动能守恒）和非弹性碰撞（动能不守恒，但动量总是守恒的）。
Impulse = F Δt = Δp. The area under a force– and airbags increase collision time, reducing the average force experienced by occupants.
冲量 = F Δt = Δp。力–时间图下的面积代表冲量。溃缩区和安全气囊延长了碰撞时间，从而减小乘员承受的平均力。
Eₖ = ½ m v² ; p = m v ; impulse = Δp = m v – m u
Eₖ = ½ m v² ; p = m v ; 冲量 = Δp = m v – m u
10. Materials – Hooke's Law and Stress–Strain | 材料——胡克定律与应力应变
Hooke' y. The spring constant for springs in series: 1/k = 1/k₁ + 1/k₂; in parallel: k = k₁ + k₂.
胡克定律：F = k ΔL，k 为劲度系数（N m⁻¹），ΔL 为伸长量。该定律仅在比例限度内成立。弹簧串联：1/k = 1/k₁ + 1/k₂；并联：k = k₁ + k₂。
y deformed. Elastic strain energy stored in a stretched spring is the area under the force–extension graph: E = ½ F ΔL = ½ k ΔL².
弹性极限：超过此点材料发生永久变形。拉伸弹簧储存的弹性势能为力–伸长图下的面积：E = ½ F ΔL = ½ k ΔL²。
asure of stiffness. A material with a larger Young modulus is harder to stretch. For a ductile material, the stress– necking, and fracture. Brittle materials fracture without significant plastic deformation.
应力 σ = F / A（单位 Pa），应变 ε = ΔL / L（无量纲）。杨氏模量 E = σ / ε，用于衡量刚度。杨氏模量越大，材料越难拉伸。延性材料的应力–应变曲线呈现线性区、屈服点、塑性流动、颈缩和断裂。脆性材料在断裂前没有明显塑性形变。
σ = F / A ; ε = ΔL / L ; E = σ / ε
σ = F / A ; ε = ΔL / L ; E = σ / ε
11. DC Circuits and Potential Dividers | 直流电路与分压器
Electric current I = ΔQ / Δt. One ampere is one coulomb per second. Ohm' here ρ is resistivity. Superconductors have zero resistivity below a critical temperature.
电流 I = ΔQ / Δt。1 安培 = 1 库仑每秒。欧姆定律：V = I R，对恒定温度下的欧姆导体成立。电阻 R = ρ L / A，ρ 为电阻率。超导体在临界温度以下电阻率为零。
= I V t. The emf ε of a source is the energy per unit charge supplied; terminal p.d. V = ε – I r, where r is internal resistance.
电路功率：P = I V = I² R = V² / R。传递的能量 W = I V t。电源电动势 ε 是每单位电荷提供的能量；端电压 V = ε – I r，r 为内阻。
h as LDRs and thermistors placed in potential divider circuits convert changes in light or temperature into a variable voltage, which can be used in sensing and control.
分压器由两个串联电阻构成。输出电压 Vₒᵤₜ = Vₛ × R₂ / (R₁ + R₂)。将光敏电阻或热敏电阻接入分压电路，可以把光强或温度的变化转化为变化的电压，用于传感和控制。
Vₒᵤₜ = Vₛ × R₂ / (R₁ + R₂) ; ε = I (R + r) ; P = I V
Vₒᵤₜ = Vₛ × R₂ / (R₁ + R₂) ; ε = I (R + r) ; P = I V
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