📚 Year 12 SQA Physics: Core Knowledge Review | SQA 物理（12年级）核心知识点梳理
This article provides a structured summary of the key concepts in the SQA Higher Physics course, often taken in Year 12 (S5) in Scotland. It covers the three main units: Our Dynamic Universe, Particles and Waves, and Electricity. Each section is designed to reinforce understanding for exam revision.
本文系统梳理了苏格兰 SQA 高阶物理（Higher Physics）的核心知识点，通常对应 12 年级（S5）课程。内容涵盖三大模块：动态宇宙、粒子与波、电学，旨在帮助同学们构建清晰的知识框架，高效备考。
1. Equations of Motion and Graphs | 运动方程与图像分析
Kinematics describes motion using displacement, velocity and acceleration. The three key equations for uniform acceleration are:
运动学用位移、速度和加速度描述运动。匀加速运动的三个基本方程为：
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
Velocity–time graphs give displacement as the area under the line, and acceleration as the gradient. A horizontal line indicates constant velocity, while a sloping line shows uniform acceleration.
速度–时间图像中，图线下方面积表示位移，斜率表示加速度。水平线代表匀速，倾斜直线代表匀加速。
Motion can also be analysed for projectiles, where horizontal and vertical components are independent. The horizontal velocity remains constant, while vertically the object accelerates at 9.8 m s⁻² downwards.
抛体运动需分解为水平和竖直两个独立分量。水平速度保持不变，竖直方向受重力加速度 9.8 m s⁻² 作用。
2. Newton’s Laws, Momentum and Impulse | 牛顿定律、动量与冲量
Newton’s First Law states that an object remains at rest or in uniform motion unless acted on by an unbalanced force. The Second Law gives F = m a, and the Third Law states that forces occur in equal and opposite pairs.
牛顿第一定律指出，物体在不受外力或合外力为零时保持静止或匀速直线运动。第二定律 F = m a 将力与加速度联系起来；第三定律强调作用力与反作用力等大反向。
Momentum is defined as p = m v. Impulse equals the change in momentum, expressed as F Δt = m v − m u. The law of conservation of momentum applies to collisions and explosions in a closed system.
动量定义为 p = m v。冲量等于动量的变化量，即 F Δt = m v − m u。在封闭系统中，碰撞与爆炸过程遵循动量守恒定律。
Elastic collisions conserve both momentum and kinetic energy. In inelastic collisions, momentum is conserved but kinetic energy is not – some is converted to heat, sound or deformation.
弹性碰撞同时守恒动量和动能；非弹性碰撞中动量守恒但动能不守恒，部分动能转化为热、声或形变能。
3. Work, Energy and Power | 功、能量与功率
Work done is defined as the component of force in the direction of displacement multiplied by displacement: W = F d cos θ. Energy is the capacity to do work, measured in joules (J).
功等于力在位移方向上的分量与位移的乘积：W = F d cos θ。能量是做功的本领，单位为焦耳 (J)。
Kinetic energy is Eₖ = ½ m v² and gravitational potential energy is Eₚ = m g h. In a conservative system, total mechanical energy is conserved if no external work is done.
动能为 Eₖ = ½ m v²，重力势能为 Eₚ = m g h。在保守力系统中，若无外力做功，总机械能守恒。
Power is the rate of doing work: P = W / t. It can also be expressed as P = F v for an object moving at constant velocity against a force.
功率是做功的快慢：P = W / t。对于克服恒力匀速运动的物体，功率也可表示为 P = F v。
4. Circular Motion and Gravitation | 圆周运动与万有引力
For an object moving in a circle of radius r at constant speed, the velocity is tangential and the acceleration is directed towards the centre. Centripetal acceleration is given by a = v² / r = r ω².
物体做匀速圆周运动时，速度沿切线方向，加速度指向圆心。向心加速度为 a = v² / r = r ω²，其中 ω 为角速度。
Centripetal force is F = m v² / r = m r ω². This is not a separate type of force but the resultant force directed to the centre, such as tension, gravity or friction.
向心力为 F = m v² / r = m r ω²。这不是一种新的力，而是指向圆心的合力，可由拉力、引力或摩擦力等提供。
Newton’s Law of Universal Gravitation states F = G M m / r², where G = 6.67 × 10⁻¹¹ N m² kg⁻². This force provides the centripetal force for satellites and planets.
万有引力定律 F = G M m / r² 描述两质点间的吸引力，G = 6.67 × 10⁻¹¹ N m² kg⁻²。该引力为卫星和行星提供向心力。
5. Special Relativity: Time Dilation and Length Contraction | 狭义相对论：时间膨胀与长度收缩
Einstein’s theory of special relativity shows that measurements of time and length depend on the relative motion of the observer. The Lorentz factor is γ = 1 / √(1 − v² / c²).
爱因斯坦狭义相对论指出，时间和空间的测量与观察者的相对运动有关。洛伦兹因子为 γ = 1 / √(1 − v² / c²)，其中 c 为光速。
Time dilation means that a moving clock runs slower: Δt = γ Δt₀, where Δt₀ is the proper time interval measured in the rest frame of the event.
时间膨胀效应表明运动时钟变慢：Δt = γ Δt₀，Δt₀ 为在事件静止参考系中测得的固有时间。
Length contraction occurs along the direction of motion: L = L₀ / γ, where L₀ is the proper length. Both effects become significant only at speeds close to c.
沿运动方向的长度收缩：L = L₀ / γ，L₀ 为固有长度。这两种效应仅在接近光速时才显著。
6. The Expanding Universe and Big Bang | 膨胀的宇宙与大爆炸理论
The redshift of light from distant galaxies shows that they are moving away from us. The recessional velocity is given by Hubble’s Law: v = H₀ d, where H₀ is the Hubble constant.
遥远星系的光谱红移表明它们正在远离我们。哈勃定律 v = H₀ d 给出退行速度与距离的关系，H₀ 为哈勃常数。
The cosmic microwave background (CMB) radiation is strong evidence for the Big Bang theory. It is almost uniform at a temperature of about 2.7 K and corresponds to radiation left over from the early hot universe.
宇宙微波背景辐射（CMB）是大爆炸理论的重要证据。它近乎各向同性，温度约 2.7 K，是早期高温宇宙遗留的辐射。
The Big Bang theory states that the universe began from a singularity around 13.8 billion years ago and has been expanding ever since. The abundance of light elements (hydrogen and helium) also supports this model.
大爆炸理论认为宇宙约 138 亿年前起源于一个奇点，之后不断膨胀。宇宙中轻元素（氢和氦）的丰度也支持这一模型。
7. The Standard Model and Fundamental Particles | 标准模型与基本粒子
The Standard Model classifies all known elementary particles. Quarks and leptons are fermions, which make up matter. Hadrons, such as protons and neutrons, are composed of quarks.
标准模型将已知基本粒子分类。夸克和轻子属于费米子，是组成物质的粒子。强子（如质子和中子）由夸克构成。
Protons consist of two up quarks and one down quark (uud), while neutrons are udd. The up quark charge is +⅔ e and the down quark charge is −⅓ e.
质子由两个上夸克和一个下夸克 (uud) 组成，中子为 udd。上夸克电荷 +⅔ e，下夸克 −⅓ e。
Leptons include the electron, muon, tau and their associated neutrinos. Each particle has a corresponding antiparticle with opposite charge and same mass.
轻子包括电子、μ子、τ子及相应的中微子。每种粒子都有对应的反粒子，带相反电荷而质量相同。
Gauge bosons mediate the fundamental forces: photon (electromagnetic), W and Z bosons (weak), gluons (strong). Gravity is not yet included in the Standard Model.
规范玻色子传递基本相互作用：光子（电磁力）、W 和 Z 玻色子（弱力）、胶子（强力）。引力尚未纳入标准模型。
8. Wave-Particle Duality and Photoelectric Effect | 波粒二象性与光电效应
The photoelectric effect demonstrates that light behaves as a stream of photons. A photon has energy E = h f, where h is Planck’s constant.
光电效应表明光表现为粒子流。光子能量为 E = h f，h 为普朗克常数。
The equation for the photoelectric effect is Eₖₘₐₓ = h f − φ, where Eₖₘₐₓ is the maximum kinetic energy of emitted electrons and φ is the work function of the metal.
光电效应方程为 Eₖₘₐₓ = h f − φ，其中 Eₖₘₐₓ 是放出电子的最大动能，φ 为金属的逸出功。
The threshold frequency f₀ is the minimum frequency to eject an electron, given by f₀ = φ / h. Below f₀, no electrons are emitted regardless of intensity.
截止频率 f₀ 是能打出电子的最低频率：f₀ = φ / h。低于 f₀ 时无论光强多大都不会有电子逸出。
De Broglie proposed that particles have an associated wavelength: λ = h / p = h / (m v). Electron diffraction confirms wave nature of matter.
德布罗意提出粒子具有波动性，波长为 λ = h / p = h / (m v)。电子衍射实验证实了物质波。
9. Interference, Diffraction and Spectra | 干涉、衍射与光谱
Waves undergo constructive interference when the path difference is a whole number of wavelengths: d sin θ = m λ, for m = 0, ±1, ±2…
当波程差为波长的整数倍时发生相长干涉：d sin θ = m λ，其中 m 为整数。
Young’s double-slit experiment produces a pattern of bright and dark fringes, demonstrating the wave nature of light. The fringe separation Δx is given by Δx = λ D / d, where D is the slit–screen distance and d is slit spacing.
杨氏双缝实验产生明暗相间的条纹，证实光的波动性。条纹间距 Δx = λ D / d，D 为缝与屏距离，d 为双缝间距。
A diffraction grating, with many slits, produces sharper maxima. The same grating equation d sin θ = m λ applies, where d = 1 / N (N is lines per metre).
衍射光栅具有大量等间距狭缝，产生更锐亮的主极大。依然满足光栅方程 d sin θ = m λ，d = 1/N，N 为每米刻线数。
Spectra produced by prisms or gratings reveal the composition of light sources. Continuous spectra come from hot solids or liquids, while line emission/absorption spectra are unique to each element.
棱镜或光栅产生的光谱可揭示光源组成。连续谱来自炽热的固体或液体，而线状发射/吸收光谱则对应每种元素的特征谱线。
10. Electricity, Semiconductors and p-n Junctions | 电路、半导体与 p-n 结
Ohmic conductors obey V = I R at constant temperature. In series circuits, current is the same and voltage divides; in parallel, voltage is the same and current divides.
欧姆导体在恒温下满足 V = I R。串联电路中电流相等、电压分配；并联电路中电压相等、电流分配。
Resistance combinations: Rₛ = R₁ + R₂ + … (series); 1/Rₚ = 1/R₁ + 1/R₂ + … (parallel). Internal resistance r of a source reduces terminal p.d. as V = E − I r.
电阻组合：串联 Rₛ = R₁ + R₂ + …；并联 1/Rₚ = 1/R₁ + 1/R₂ + …。电源内阻 r 使路端电压降低：V = E − I r。
Capacitors store charge Q = C V. The time constant for an RC circuit is τ = R C. During charging, voltage rises exponentially; during discharging, it falls exponentially.
电容器储存电荷 Q = C V。RC 电路的时间常数 τ = R C。充电时电压按指数增长，放电时按指数衰减。
Semiconductors can be doped to form n-type (extra electrons) or p-type (holes). A p-n junction diode allows current in forward bias and blocks it in reverse bias due to the depletion layer.
半导体可掺杂为 n 型（多余电子）或 p 型（空穴）。p-n 结二极管在正向偏压下导通，反向偏压下由于耗尽层而截止。
LEDs emit light when forward biased, and the photon energy corresponds to E = h f = h c / λ. Photodiodes generate a current when light creates electron-hole pairs in the depletion region.
发光二极管 (LED) 在正向偏压时发光，光子能量 E = h f = h c / λ。光电二极管在光照下于耗尽区产生电子–空穴对，形成光电流。
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