📚 Year 12 SQA Physics: Core Concepts Review | SQA物理：核心知识点梳理
This article provides a structured overview of the essential topics in Year 12 SQA Higher Physics. By reviewing kinematics, dynamics, waves, quantum phenomena and electricity, you will consolidate the key principles and equations needed for exam success and deeper understanding.
本文系统梳理了苏格兰SQA高等物理（Year 12）的核心知识点。通过回顾运动学、动力学、波、量子现象和电学等主题，你将巩固考试所需的关键原理与方程，并加深对物理世界的理解。
1. Motion in a Straight Line | 直线运动
Physical quantities are classified as scalars (magnitude only) or vectors (magnitude and direction). Displacement, velocity and acceleration are vector quantities that describe motion along a straight line.
物理量分为标量（只有大小）和矢量（既有大小又有方向）。位移、速度和加速度都是描述直线运动的矢量。
The mean velocity is v = Δs/Δt. Acceleration is the rate of change of velocity: a = Δv/Δt. For constant acceleration, four equations of motion relate u, v, a, s and t.
平均速度 v = Δs/Δt。加速度是速度的变化率：a = Δv/Δt。当加速度恒定时，四个运动学方程将初速度 u、末速度 v、加速度 a、位移 s 和时间 t 联系起来。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
These equations are derived from the definitions of velocity and acceleration. They are valid only when acceleration remains constant. Free-fall under gravity is a common example, where a = g ≈ 9.8 m s⁻².
这些方程由速度和加速度的定义推导而来，仅在加速度恒定时成立。物体在重力下的自由落体就是一个常见例子，其中 a = g ≈ 9.8 m s⁻²。
2. Forces and Newton’s Laws | 力与牛顿定律
A force causes an object to accelerate, change direction or deform. Newton’s first law states that an object remains at rest or moves with constant velocity unless acted on by an unbalanced force.
力能使物体加速、改变方向或发生形变。牛顿第一定律指出，除非受到非平衡力作用，物体将保持静止或匀速直线运动。
Newton’s second law: net force F = ma, where m is mass and a is acceleration. Weight is the gravitational force: W = mg. Newton’s third law states that forces occur in equal and opposite pairs.
牛顿第二定律：合外力 F = ma，其中 m 为质量，a 为加速度。重力即重量：W = mg。牛顿第三定律指出，力总是成对出现，大小相等、方向相反。
Free-body diagrams help resolve forces into components. Tension, friction, normal reaction and applied forces are balanced or unbalanced according to the situation.
受力图有助于分解力的分量。根据具体情况，拉力、摩擦力、支持力和推力可相互平衡或不平衡。
3. Momentum and Impulse | 动量与冲量
Momentum p is defined as p = mv. It is a vector quantity with direction matching velocity. The principle of conservation of momentum states that in the absence of external forces, total momentum before a collision equals total momentum after.
动量 p 定义为 p = mv，是矢量，方向与速度一致。动量守恒定律指出，在没有外力作用时，碰撞前的总动量等于碰撞后的总动量。
Impulse equals the change in momentum: F Δt = Δp = mv – mu. This relationship is especially useful for analysing collisions and safety features like airbags that increase the impact time, reducing the average force.
冲量等于动量的变化：F Δt = Δp = mv – mu。这一关系特别适用于分析碰撞和安全装置（如气囊），增加碰撞时间可以减小平均冲击力。
In elastic collisions, kinetic energy is conserved; in inelastic collisions, some kinetic energy is converted into other forms. Momentum is conserved in both cases.
弹性碰撞中动能守恒；非弹性碰撞中部分动能转化为其他形式。两种情况下动量都守恒。
4. Circular Motion | 圆周运动
An object moving in a circle at constant speed undergoes centripetal acceleration directed towards the centre. Angular velocity ω = θ/t (rad s⁻¹), and is related to linear speed by v = r ω.
物体以恒定速率做圆周运动时，具有指向圆心的向心加速度。角速度 ω = θ/t（rad s⁻¹），与线速度的关系为 v = r ω。
The centripetal acceleration is a = v²/r = r ω², and the centripetal force required is F = m v²/r = m r ω². This force is provided by tension, friction, gravity or a normal reaction depending on the context.
向心加速度 a = v²/r = r ω²，所需的向心力 F = m v²/r = m r ω²。这个力可以根据情境由拉力、摩擦力、引力或支持力提供。
The period T of circular motion is the time for one complete revolution: T = 2π/ω. Frequency f = 1/T.
圆周运动的周期 T 是转动一周所需的时间：T = 2π/ω，频率 f = 1/T。
5. Gravitation and Cosmology | 万有引力与宇宙学
Newton’s law of universal gravitation: F = G m₁ m₂ / r², where G = 6.67 × 10⁻¹¹ N m² kg⁻². Gravitational field strength g = F/m gives the force per unit mass at a point.
牛顿万有引力定律：F = G m₁ m₂ / r²，其中 G = 6.67 × 10⁻¹¹ N m² kg⁻²。引力场强 g = F/m 表示单位质量所受的力。
Satellites orbit Earth when gravitational force provides the necessary centripetal force. By equating G Mₑ m / r² = m v²/r, orbital speed v = √(G Mₑ / r) can be derived.
当引力提供所需向心力时，卫星绕地球运行。令 G Mₑ m / r² = m v²/r，可推导出轨道速度 v = √(G Mₑ / r)。
Cosmological redshift occurs when light from distant galaxies is stretched to longer wavelengths. Redshift z = Δλ/λ₀. Hubble’s law v = H₀ d shows that recessional velocity is proportional to distance, supporting the expanding universe model.
宇宙学红移是指遥远星系发出的光被拉伸到更长的波长。红移 z = Δλ/λ₀。哈勃定律 v = H₀ d 表明退行速度与距离成正比，支持了宇宙膨胀模型。
Evidence for the Big Bang includes cosmic microwave background radiation (CMBR) and the observed abundance of light elements. Hubble’s constant H₀ is approximately 70 km s⁻¹ Mpc⁻¹.
大爆炸的证据包括宇宙微波背景辐射（CMBR）和轻元素的丰度。哈勃常数 H₀ 大约为 70 km s⁻¹ Mpc⁻¹。
6. Special Relativity | 狭义相对论
When an object moves at speeds close to the speed of light c, time dilation occurs. The time interval measured by a stationary observer Δt is longer than the proper time Δt₀: Δt = Δt₀ / √(1 − v²/c²).
当物体以接近光速 c 运动时，会发生时间膨胀。静止观测者测得的时间间隔 Δt 长于固有时间 Δt₀：Δt = Δt₀ / √(1 − v²/c²)。
Length contraction: the length L measured by an observer moving parallel to the object is shorter than the proper length L₀: L = L₀ √(1 − v²/c²).
长度收缩：与物体平行运动的观测者测得的长度 L 短于固有长度 L₀：L = L₀ √(1 − v²/c²)。
These effects are negligible at everyday speeds but become significant as v approaches c. The constancy of the speed of light in all inertial frames is a fundamental postulate.
这些效应在日常速度下微不足道，但当 v 接近 c 时会变得显著。光速在所有惯性系中不变的假设是相对论的基本出发点。
7. Waves and Interference | 波与干涉
Transverse waves have oscillations perpendicular to the direction of energy transfer; longitudinal waves oscillate parallel. Wave speed v = f λ, period T = 1/f.
横波的振动方向垂直于能量传播方向；纵波的振动方向平行于传播方向。波速 v = f λ，周期 T = 1/f。
Coherent sources have the same frequency and constant phase difference. When coherent waves meet, constructive interference occurs for path difference = nλ, and destructive interference occurs for path difference = (n + ½)λ.
相干波源具有相同的频率和恒定的相位差。相干波相遇时，当波程差 = nλ 时产生相长干涉，波程差 = (n + ½)λ 时产生相消干涉。
Stationary (standing) waves form when two identical waves travel in opposite directions. Nodes are points of zero displacement; antinodes are points of maximum displacement. Distance between adjacent nodes is λ/2.
驻波由两列相同但方向相反的波叠加而成。节点是位移为零的点，腹点是位移最大的点。相邻节点之间的距离为 λ/2。
8. Refraction and Spectra | 折射与光谱
When light passes from one medium to another, its speed changes, causing refraction. Snell’s law: n₁ sin θ₁ = n₂ sin θ₂, or for light entering from air, n = sin i / sin r.
当光从一种介质进入另一种介质时，速度改变，发生折射。斯涅尔定律：n₁ sin θ₁ = n₂ sin θ₂，当光从空气进入时可简化为 n = sin i / sin r。
The critical angle θc occurs when the angle of refraction is 90°, giving sin θc = 1/n. Total internal reflection is used in optical fibres for communications.
当折射角为 90° 时对应的入射角称为临界角 θc，满足 sin θc = 1/n。全内反射现象被用于光纤通信。
Spectra arise from energy level transitions. Continuous spectra are produced by hot solids, line emission spectra by excited gases, and absorption spectra when light passes through a cool gas, creating dark lines at specific wavelengths.
光谱源于能级跃迁。炽热固体产生连续光谱，受激气体产生线状发射光谱，而当白光穿过冷气体时会产生吸收光谱，在特定波长出现暗线。
9. Quantum Phenomena: Photoelectric Effect and Wave-Particle Duality | 量子现象：光电效应与波粒二象性
The photoelectric effect is explained by photon theory: light consists of photons, each with energy E = hf, where h is Planck’s constant (6.63 × 10⁻³⁴ J s).
光电效应可用光子理论解释：光由光子组成，每个光子的能量为 E = hf，其中 h 为普朗克常数（6.63 × 10⁻³⁴ J s）。
A photon can eject an electron if its energy exceeds the work function φ of the metal. The maximum kinetic energy of the ejected electron is Eₖ max = hf − φ. The threshold frequency f₀ is given by h f₀ = φ.
如果光子能量大于金属的功函数 φ，就能击出电子。出射电子的最大动能 Eₖ max = hf − φ。截止频率 f₀ 由 h f₀ = φ 确定。
Wave-particle duality is demonstrated by the de Broglie wavelength: λ = h/p = h/mv. Electron diffraction provides evidence that particles behave like waves.
波粒二象性由德布罗意波长 λ = h/p = h/mv 描述。电子衍射实验证明了粒子具有波动性。
10. Electric Circuits: EMF, Internal Resistance and AC | 电路：电动势、内阻与交流电
Ohm’s law states V = IR for an ohmic conductor at constant temperature. Resistances in series: R_total = R₁ + R₂ + …; in parallel: 1/R_total = 1/R₁ + 1/R₂ + …
欧姆定律指出，对于恒温下的欧姆导体，V = IR。串联电阻 R_total = R₁ + R₂ + …；并联电阻 1/R_total = 1/R₁ + 1/R₂ + …
Electrical power: P = IV = I²R = V²/R. A cell has electromotive force (EMF) E and internal resistance r. The terminal voltage is V = E − Ir.
电功率：P = IV = I²R = V²/R。电源具有电动势 E 和内阻 r，端电压 V = E − Ir。
A potential divider produces a fraction of the input voltage: V_out = (R₂/(R₁ + R₂)) × V_in. A Wheatstone bridge is balanced when R₁/R₂ = R₃/R₄, giving zero current in the galvanometer.
分压器输出一部分输入电压：V_out = (R₂/(R₁ + R₂)) × V_in。当 R₁/R₂ = R₃/R₄ 时惠斯通电桥达到平衡，检流计中电流为零。
In alternating current (AC), voltage and current vary sinusoidally. The root-mean-square (rms) values relate to peak values: V_rms = V_peak/√2, I_rms = I_peak/√2. AC mains in the UK is 230 V rms at 50 Hz.
交流电的电压和电流按正弦规律变化。有效值与峰值的关系为 V_rms = V_peak/√2，I_rms = I_peak/√2。英国市电为 230 V 有效值，频率 50 Hz。
11. Capacitors | 电容器
A capacitor stores charge and energy. Capacitance C = Q/V, measured in farads (F). For a parallel-plate capacitor, C = ε A/d, though this formula is given in the SQA data booklet.
电容器可储存电荷和能量。电容 C = Q/V，单位是法拉（F）。平行板电容器的电容 C = ε A/d，该公式在 SQA 数据手册中提供。
In a CR charging circuit, the voltage across the capacitor rises as V = V₀ (1 − e^(−t/RC)). During discharge, V = V₀ e^(−t/RC). The time constant τ = RC is the time for the voltage to fall to 37% of its initial value.
在 RC 充电电路中，电容两端电压按 V = V₀ (1 − e^(−t/RC)) 上升。放电时 V = V₀ e^(−t/RC)。时间常数 τ = RC 是电压下降到初始值 37% 所需的时间。
Energy stored in a capacitor: E = ½ Q V = ½ C V² = ½ Q²/C. Capacitors are used in smoothing circuits, timing applications and flash photography.
电容器储存的能量：E = ½ Q V = ½ C V² = ½ Q²/C。电容器常用于滤波、定时电路和闪光灯等场合。
12. Semiconductors and p-n Junctions | 半导体与p-n结
Doping pure silicon with group 5 elements creates an n-type semiconductor with extra free electrons; doping with group 3 elements creates a p-type semiconductor with holes as the majority carriers.
向纯硅中掺入第五族元素可形成多出自由电子的 n 型半导体；掺入第三族元素则可形成以空穴为主要载流子的 p 型半导体。
At a p-n junction, electrons and holes diffuse, forming a depletion layer that creates a potential barrier. In forward bias, the depletion layer narrows, allowing a current to flow. In reverse bias, the layer widens and very little current passes.
在 P-N 结处，电子和空穴扩散，形成耗尽层并产生势垒。正向偏置时耗尽层变窄，电流得以导通；反向偏置时耗尽层变宽，几乎没有电流通过。
A light-emitting diode (LED) emits light when forward biased as electrons recombine with holes. A photodiode can generate a current when light creates electron-hole pairs, even with no external bias, demonstrating the photovoltaic effect.
发光二极管（LED）在正向偏置时，电子与空穴复合而发光。光电二极管在光照下产生电子-空穴对，即使没有外加偏置也能产生电流，展示了光生伏特效应。
Published by TutorHao | Physics Revision Series | aleveler.com
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