📚 Year 12 CAIE Physics: Core Knowledge Compilation | Year 12 CAIE 物理：核心知识点梳理
Year 12 CAIE Physics builds the essential framework for understanding the physical world, covering mechanics, waves, electricity, and modern physics. This article distills the key concepts, definitions, and equations you must master for the AS Level examination. Use this as a revision roadmap to solidify your foundations.
Year 12 CAIE 物理为理解物理世界搭建了核心框架，涵盖力学、波、电学以及近代物理。本文提炼了 AS 阶段必须掌握的关键概念、定义和方程。请把这份梳理当作复习路线图，来夯实你的基础。
1. Physical Quantities and Units | 物理量与单位
All physical quantities can be expressed in terms of base quantities. The SI system defines seven base quantities: mass (kg), length (m), time (s), electric current (A), temperature (K), amount of substance (mol), and luminous intensity (cd). Every other quantity is a derived quantity, expressed as a product of these base units.
所有物理量都可以用基本量来表示。国际单位制定义了七个基本量：质量（kg）、长度（m）、时间（s）、电流（A）、温度（K）、物质的量（mol）和发光强度（cd）。其他所有量都是导出量，可用这些基本单位的乘积来表示。
Homogeneity of physical equations means each term must have the same base units. Checking dimensions is a powerful way to catch errors. For example, the kinetic energy formula Ek = ½mv² gives units kg·m²·s⁻², which match the joule (J).
物理方程的量纲一致性意味着每一项必须具有相同的基本单位。检查量纲是发现错误的有力方法。例如，动能公式 Ek = ½mv² 得出的单位是 kg·m²·s⁻²，与焦耳一致。
Measurement uncertainty arises from systematic and random errors. Precision is the range of values of repeated measurements, while accuracy describes how close a measurement is to the true value. Expressing uncertainty as an absolute or percentage value is essential.
测量误差来自系统误差和随机误差。精密度指重复测量值的分散范围，而准确度描述测量值接近真值的程度。以绝对或百分比形式表达不确定度至关重要。
2. Kinematics | 运动学
Kinematics describes motion without considering its causes. Displacement, velocity, and acceleration are vector quantities, while distance and speed are scalars. The gradient of a displacement–time graph gives velocity, and the area under a velocity–time graph gives change in displacement.
运动学描述运动而不考虑其原因。位移、速度和加速度是矢量，而路程和速率是标量。位移–时间图的斜率给出速度，速度–时间图下的面积给出位移的变化。
The four equations of uniformly accelerated motion are central tools. For motion with constant acceleration a, initial velocity u, and final velocity v after time t:
匀加速运动的四个方程是核心工具。对于加速度恒为 a，初速度 u，经过时间 t 后末速度为 v 的运动：
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
All four equations apply only when acceleration is constant. In free fall under gravity, a = g ≈ 9.81 m s⁻², acting downward.
这四个方程都只适用于加速度恒定的情况。在重力作用下的自由落体中，a = g ≈ 9.81 m s⁻²，方向竖直向下。
3. Dynamics | 动力学
Newton's laws govern the link between force and motion. Newton's first law states that a body remains at rest or in uniform motion unless a resultant force acts on it. Newton's second law is expressed as F = ma, where resultant force equals mass times acceleration. Newton's third law highlights action–reaction pairs: forces always occur in equal and opposite pairs on different bodies.
牛顿定律支配着力与运动的关系。牛顿第一定律指出，除非有合力作用，否则物体将保持静止或匀速直线运动。牛顿第二定律表示为 F = ma，合力等于质量乘以加速度。牛顿第三定律强调了作用力与反作用力对：力总是成对出现，大小相等、方向相反，作用在不同物体上。
Linear momentum is a vector p = mv. The principle of conservation of momentum states that total momentum in an isolated system remains constant, provided no external forces act. Impulse is the change in momentum, Δp = FΔt, linking force to momentum change.
动量是矢量 p = mv。动量守恒定律指出，如果没有外力作用，孤立系统的总动量保持不变。冲量是动量的变化量，Δp = FΔt，将力与动量变化联系起来。
In collisions, when two bodies stick together, it is a perfectly inelastic collision; kinetic energy is not conserved but momentum is conserved.
在碰撞中，当两个物体粘在一起时，是完全非弹性碰撞；动能不守恒，但动量守恒。
4. Forces, Density and Pressure | 力、密度与压强
Density is mass per unit volume, ρ = m / V. Pressure is force per unit area, p = F / A. In a fluid, pressure increases with depth: Δp = ρgΔh, where g is gravitational field strength.
密度是单位体积的质量，ρ = m / V。压强是单位面积上的力，p = F / A。在流体中，压强随深度增加：Δp = ρgΔh，其中 g 是重力场强度。
Upthrust (buoyancy) is the resultant upward force experienced by an object in a fluid. Archimedes' principle states that the upthrust equals the weight of the fluid displaced. This explains why objects float or sink.
浮力（上推力）是物体在流体中受到的向上的合力。阿基米德原理指出，浮力等于排开流体的重量。这解释了物体为何漂浮或下沉。
Turning effect of a force is called moment. The principle of moments for equilibrium: sum of clockwise moments about any pivot equals sum of anticlockwise moments. A couple is a pair of equal and opposite forces producing rotation without translation.
力的转动效应称为力矩。力矩的平衡原理：对于任意支点，顺时针力矩之和等于逆时针力矩之和。力偶是一对大小相等、方向相反的力，产生转动而不产生平动。
5. Work, Energy and Power | 功、能量与功率
Work is done when a force moves its point of application in the direction of the force: W = Fs cos θ. The work–energy theorem states that the net work done on an object equals its change in kinetic energy.
当力沿着力的方向移动其作用点时，就做了功：W = Fs cos θ。功能定理指出，对物体做的净功等于其动能的变化。
Kinetic energy Ek = ½mv² and gravitational potential energy Ep = mgΔh. In a conservative system, total mechanical energy remains constant if only gravity does work.
动能 Ek = ½mv²，重力势能 Ep = mgΔh。在保守系统中，如果只有重力做功，总机械能保持不变。
Power is the rate of doing work, P = W/t = Fv (for constant force and velocity). Efficiency is the ratio of useful output power to input power, always less than 1.
功率是做功的速率，P = W/t = Fv（对于恒力和恒速度）。效率是有用输出功率与输入功率之比，总小于 1。
6. Deformation of Solids | 固体变形
Hooke’s law states that extension is directly proportional to applied force, provided the elastic limit is not exceeded: F = kx, where k is the spring constant. The elastic limit is the maximum stress for which the material returns to its original shape when the load is removed.
胡克定律指出，只要不超过弹性限度，伸长量与施加的力成正比：F = kx，其中 k 是劲度系数。弹性限度是材料在卸除负载后能恢复原状的最大应力。
Stress σ = F/A and strain ε = ΔL/L describe internal resistance to deformation. The Young modulus E = σ/ε measures stiffness of a material; it is a constant for a given material within the limit of proportionality.
应力 σ = F/A 和应变 ε = ΔL/L 描述对变形的内部抵抗。杨氏模量 E = σ/ε 衡量材料的刚度；在比例限度内，它是特定材料的常数。
Elastic potential energy stored in a stretched spring or wire is given by the area under the force–extension graph: E = ½Fx = ½kx² for Hookean materials.
拉伸的弹簧或金属丝中储存的弹性势能由力–伸长图下的面积给出：对于胡克材料为 E = ½Fx = ½kx²。
7. Waves | 波
Progressive waves transfer energy without transferring matter. Transverse waves have oscillations perpendicular to direction of energy transfer; longitudinal waves have oscillations parallel to it. Key quantities: frequency f, wavelength λ, amplitude A, and wave speed v = fλ.
行波传递能量而不传递物质。横波的振动垂直于能量传递方向；纵波的振动平行于该方向。关键量：频率 f、波长 λ、振幅 A 和波速 v = fλ。
The Doppler effect is the change in observed frequency when a source of waves moves relative to an observer: f' = f v/(v ± vs), where v is wave speed and vs is speed of source. Use the minus sign when the source approaches, plus when receding.
多普勒效应是波源相对于观测者运动时观测频率发生的变化：f' = f v/(v ± vs)，其中 v 为波速，vs 为波源速度。波源接近时用减号，远离时用加号。
Electromagnetic waves travel at speed c = 3.00×10⁸ m s⁻¹ in vacuum and can be ordered by wavelength into the spectrum from radio waves to gamma rays.
电磁波在真空中以速度 c = 3.00×10⁸ m s⁻¹ 传播，可按波长从无线电波到伽马射线排列成谱。
8. Superposition | 叠加
When two or more waves meet, the resultant displacement is the vector sum of individual displacements. This principle explains interference and stationary waves.
当两个或更多波相遇时，合位移是各分位移的矢量和。这个原理解释了干涉和驻波。
Two-source interference of coherent waves yields alternating maxima and minima. For double slits, bright fringes occur at d sin θ = nλ, where d is slit spacing and n is an integer (0,1,2...).
相干波的双源干涉产生明暗交替的条纹。对于双缝，亮条纹出现在 d sin θ = nλ 处，其中 d 为缝间距，n 为整数。
Stationary waves form when two identical progressive waves travel in opposite directions. Nodes have zero displacement; antinodes have maximum displacement. In a pipe or string, harmonics obey specific boundary conditions: for a string fixed at both ends, L = nλ/2.
驻波由两列相同行波沿相反方向传播形成。波节处位移为零；波腹处位移最大。在管或弦中，谐波遵循特定的边界条件：对于两端固定的弦，L = nλ/2。
9. Electric Fields | 电场
An electric field is a region where a charged particle experiences a force. Electric field strength is defined as force per unit positive charge: E = F/q. For a uniform field between parallel plates, E = V/d, where V is potential difference and d the separation.
电场是带电粒子受力的区域。电场强度定义为每单位正电荷所受的力：E = F/q。对于平行板间的匀强电场，E = V/d，其中 V 为电势差，d 为间距。
Coulomb's law gives the force between two point charges: F = kQ₁Q₂/r², where k = 1/(4πε₀). The force is attractive for unlike charges and repulsive for like charges.
库仑定律给出两点电荷间的力：F = kQ₁Q₂/r²，其中 k = 1/(4πε₀)。异种电荷相吸，同种电荷相斥。
Work done in moving a charge in an electric field relates to potential difference W = QV. The electronvolt (eV) is the energy gained by an electron moved through 1V: 1 eV = 1.6×10⁻¹⁹ J.
在电场中移动电荷所做的功与电势差相关：W = QV。电子伏特（eV）是一个电子经过 1V 电势差获得的能量：1 eV = 1.6×10⁻¹⁹ J。
10. Current of Electricity | 电流
Electric current is the rate of flow of charge: I = ΔQ/Δt. Conventional current direction is that of positive charge flow. The elementary charge e = 1.60×10⁻¹⁹ C.
电流是电荷流动的速率：I = ΔQ/Δt。常规电流方向为正电荷流动的方向。元电荷 e = 1.60×10⁻¹⁹ C。
Ohm's law states that for a metallic conductor at constant temperature, the current is proportional to potential difference: V = IR. Resistance depends on resistivity ρ, length L and cross-sectional area A: R = ρL/A.
欧姆定律指出，对于恒温下的金属导体，电流与电势差成正比：V = IR。电阻取决于电阻率 ρ、长度 L 和横截面积 A：R = ρL/A。
The I–V characteristics of a filament lamp, diode, and thermistor reveal non-ohmic behaviour since resistance changes with temperature or applied voltage.
白炽灯、二极管和热敏电阻的 I–V 特性曲线显示了非欧姆行为，因为电阻随温度或外加电压而变。
11. D.C. Circuits | 直流电路
Kirchhoff's first law (junction rule): total current entering a junction equals total current leaving it. Kirchhoff's second law (loop rule): the sum of e.m.f.s around any closed loop equals the sum of p.d.s.
基尔霍夫第一定律（节点法则）：流入节点的总电流等于流出节点的总电流。基尔霍夫第二定律（回路法则）：任一闭合回路中电动势之和等于电势差之和。
Resistors in series: Rtotal = R₁ + R₂ + .... In parallel: 1/Rtotal = 1/R₁ + 1/R₂ + .... These rules allow simplification of complex networks.
串联电阻：R总 = R₁ + R₂ + ...。并联电阻：1/R总 = 1/R₁ + 1/R₂ + ...。这些法则可简化复杂网络。
A potential divider produces a fraction of the input voltage: Vout = Vin × R₂/(R₁ + R₂). It is widely used in sensor circuits with thermistors or LDRs.
电位分压器可产生输入电压的一部分：V出 = V入 × R₂/(R₁ + R₂)。它广泛用于带有热敏电阻或光敏电阻的传感器电路中。
12. Particle and Nuclear Physics | 粒子与核物理
The atom consists of a nucleus containing protons and neutrons, surrounded by electrons. The proton number Z defines the element; the nucleon number A is the total number of protons and neutrons.
原子由包含质子和中子的原子核以及绕核的电子组成。质子数 Z 定义了元素；核子数 A 是质子与中子总数。
Radioactive decay causes unstable nuclei to emit alpha (⁴₂He nuclei), beta (fast electrons or positrons), and gamma (electromagnetic) radiation. Activity is measured in becquerels, and the decay law is exponential: A = A₀ e⁻ᵏᵗ, with half-life t½ = ln 2 / λ.
放射性衰变使不稳定核发射 α 粒子（⁴₂He 核）、β 粒子（快电子或正电子）和 γ 射线（电磁）。活度以贝克勒尔计量，衰变规律为指数形式：A = A₀ e⁻ᵏᵗ，半衰期 t½ = ln 2 / λ。
The unified atomic mass unit u relates to the mass–energy equivalence E = mc²: 1 u = 1.66×10⁻²⁷ kg = 931.5 MeV. Nuclear reactions conserve mass–energy, charge, and nucleon number.
统一原子质量单位 u 与质能等价 E = mc² 相关：1 u = 1.66×10⁻²⁷ kg = 931.5 MeV。核反应遵守质能、电荷和核子数守恒。
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