📚 High-Frequency Key Points Summary for IB & CIE Physics | IB 与 CIE 物理高频考点总结
This article consolidates the most frequently examined topics across both IB and CIE A-Level Physics syllabi, providing concise yet comprehensive revision notes. Mastering these key concepts will boost your confidence for the final exams.
本文汇总了IB和CIE A-Level物理课程大纲中最常考的知识点，内容精炼全面。掌握这些核心概念将帮助你在考试中提升信心。
1. Kinematics and Projectile Motion | 运动学与抛体运动
In both IB and CIE Physics, the four kinematic equations for uniformly accelerated motion are fundamental: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u + v)t. They apply ONLY when acceleration is constant.
在IB和CIE物理中，匀速直线运动的四个基本方程为：v = u + at，s = ut + ½at²，v² = u² + 2as，s = ½(u + v)t。它们仅适用于加速度恒定的情况。
For projectile motion, separate horizontal and vertical components. Horizontal velocity remains constant (aₓ = 0), while vertical motion experiences constant downward acceleration due to gravity (g). The time of flight is governed entirely by the vertical component.
在抛体运动中，需将水平和竖直分量分开处理。水平速度恒定(aₓ = 0)，竖直方向则受到重力加速度(g)向下的恒定作用。飞行时间完全由竖直分量决定。
Maximum height H = (u² sin²θ) / (2g)
最大高度 H = (u² sin²θ) / (2g)
The range R of a projectile launched from level ground is given by R = (u² sin 2θ) / g, maximised when θ = 45°.
从水平地面发射的抛体，其射程 R = (u² sin 2θ) / g，当 θ = 45° 时射程最大。
2. Newton’s Laws and Free-Body Diagrams | 牛顿定律与受力分析
Newton’s First Law states that an object remains at rest or in uniform motion unless acted upon by a net external force. The Second Law is expressed as Fₙₑₜ = ma, linking resultant force to acceleration. The Third Law reminds us that forces occur in equal and opposite action–reaction pairs acting on different bodies.
牛顿第一定律指出，除非受到净外力作用，物体将保持静止或匀速直线运动。第二定律 Fₙₑₜ = ma 将合外力与加速度联系起来。第三定律则强调力以大小相等、方向相反的作用力与反作用力成对出现，且作用在不同物体上。
Free-body diagrams (FBDs) are essential for solving connected-body problems. Show all forces as arrows (weight, normal reaction, tension, friction) acting on a single object. In incline plane problems, resolve weight into components parallel and perpendicular to the slope.
受力图(FBD)对于解决连接体问题至关重要。用箭头标出单个物体所受的所有力（重力、法向反力、张力、摩擦力）。在斜面问题中，需将重力分解为平行和垂直斜面的分量。
On a slope: weight component down slope = mg sinθ, normal = mg cosθ
斜面上：重力的分力沿斜面向下 = mg sinθ，法向力 = mg cosθ
3. Work, Energy and Power | 功、能与功率
Work done by a constant force is W = Fs cosθ, where θ is the angle between force and displacement. The area under a force–distance graph represents work done. Kinetic energy (KE = ½mv²) and gravitational potential energy (GPE = mgh) are scalar quantities.
恒力所做的功 W = Fs cosθ，其中 θ 是力与位移之间的夹角。力–距离图下的面积代表做功的大小。动能(KE = ½mv²)和重力势能(GPE = mgh)都是标量。
The work–energy theorem states that the net work done on an object equals its change in kinetic energy. Conservation of mechanical energy (KE + PE = constant) applies only when no external non-conservative forces (like friction) do work.
动能定理指出，合力对物体所做的净功等于物体动能的变化量。机械能守恒（动能 + 势能 = 常量）仅在没有外部非保守力（如摩擦力）做功时适用。
Power is the rate of doing work, P = W/t = Fv for a constant force and velocity in the same direction. Efficiency = (useful power output) / (total power input).
功率是做功的速率，P = W/t，若力与速度同向且恒定，还有 P = Fv。效率 = 有用的输出功率 / 总输入功率。
4. Momentum and Impulse | 动量与冲量
Linear momentum p = mv is a vector. Impulse J = FΔt = Δp, equal to the area under a force–time graph. Momentum is always conserved in collisions and explosions, provided no external resultant force acts on the system.
线动量 p = mv 是矢量。冲量 J = FΔt = Δp，等于力–时间图下的面积。若无外部合外力作用于系统，碰撞与爆炸过程中动量总是守恒的。
For a two-body collision: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
两体碰撞：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Elastic collisions conserve kinetic energy; inelastic collisions do not. In a perfectly inelastic collision, objects stick together and kinetic energy loss is maximum. CIE and IB both require analysis of such collisions.
弹性碰撞中动能守恒，非弹性碰撞则不然。在完全非弹性碰撞中，物体粘合在一起，动能损失最大。CIE和IB都要求对此类碰撞进行分析。
5. Circular Motion and Gravitation | 圆周运动与引力
An object moving in a circle at constant speed experiences centripetal acceleration directed toward the centre: a = v²/r = ω²r. The centripetal force is F = mv²/r = mω²r. It is not a separate force but the resultant of existing forces (tension, gravity, friction).
物体以恒定速率做圆周运动时，会受到指向圆心的向心加速度：a = v²/r = ω²r。向心力 F = mv²/r = mω²r。它不是一种独立的力，而是现有力（张力、重力、摩擦力）的合力。
Newton’s law of universal gravitation: F = Gm₁m₂ / r². Gravitational field strength g = F/m, and near Earth’s surface g = GM / r². For orbits, gravitational force provides centripetal force, enabling derivation of satellite velocity and period.
万有引力定律：F = Gm₁m₂ / r²。重力场强 g = F/m，在地表附近 g = GM / r²。对于环绕轨道，引力提供向心力，由此可推导出卫星速度和周期。
Orbital speed v = √(GM/r); period T² ∝ r³ (Kepler’s Third Law)
轨道速度 v = √(GM/r)；周期 T² ∝ r³（开普勒第三定律）
6. Simple Harmonic Motion (SHM) | 简谐运动
SHM occurs when acceleration is directly proportional to displacement from equilibrium and always directed toward it: a = −ω²x. General solution: x = A cos(ωt + φ) or x = A sin(ωt + φ). Maximum speed vₘₐₓ = ωA, maximum acceleration aₘₐₓ = ω²A.
当加速度与相对平衡位置的位移成正比且始终指向平衡位置时，就发生简谐运动：a = −ω²x。其一般解：x = A cos(ωt + φ) 或 x = A sin(ωt + φ)。最大速度 vₘₐₓ = ωA，最大加速度 aₘₐₓ = ω²A。
For a mass–spring system, T = 2π√(m/k). For a simple pendulum, T = 2π√(L/g). Energy continuously transforms between kinetic and potential, but total mechanical energy remains constant for undamped SHM.
对于质量–弹簧系统，T = 2π√(m/k)。对于单摆，T = 2π√(L/g)。能量在动能和势能之间持续转化，但在无阻尼的简谐运动中总机械能保持不变。
Damping (light, critical, heavy) and resonance are also common exam topics. Resonance occurs when the driving frequency equals the natural frequency, causing maximum amplitude.
阻尼（欠阻尼、临界阻尼、过阻尼）和共振也是常见考点。当驱动频率等于固有频率时发生共振，此时振幅达到最大。
7. Wave Characteristics and Superposition | 波的性质与叠加
Wave speed: v = fλ. Phase difference Δφ (in radians) relates to path difference Δx by Δφ = (2π/λ)Δx. Waves transfer energy without net transfer of matter. Transverse and longitudinal waves feature in both syllabi, with polarisation as a key test for transverse waves.
波速：v = fλ。相位差 Δφ（单位为弧度）与路径差 Δx 的关系为 Δφ = (2π/λ)Δx。波传播能量，而不发生物质的净转移。横波和纵波在两套大纲中均有要求，偏振是检验横波的关键手段。
The principle of superposition states that when two waves meet, the resultant displacement is the vector sum of individual displacements. This leads to constructive interference (path difference = nλ) and destructive interference (path difference = (n + ½)λ).
波的叠加原理指出，两列波相遇时，合位移是各分位移的矢量和。这导致相长干涉（路径差 = nλ）和相消干涉（路径差 = (n + ½)λ）。
8. Interference, Diffraction and Standing Waves | 干涉、衍射与驻波
Young’s double-slit experiment: fringe separation Δx = λD / d, where D is the distance to the screen and d is slit separation. Sharp, well-defined fringes require coherent, monochromatic sources.
杨氏双缝实验：条纹间距 Δx = λD / d，其中 D 为屏幕到双缝的距离，d 为双缝间距。获得清晰条纹需要相干、单色光源。
For a diffraction grating, maxima occur at d sinθ = nλ. Gratings produce sharper, brighter fringes than double slits, enabling precise wavelength measurement. The number of orders visible depends on d and λ.
对于衍射光栅，极大满足 d sinθ = nλ。光栅产生的条纹比双缝更锐利、更明亮，从而能够精确测量波长。可见的级次数量取决于 d 和 λ。
Standing waves form when two identical waves travel in opposite directions. Nodes (zero displacement) and antinodes (maximum displacement) appear at fixed positions. For a string fixed at both ends: λₙ = 2L/n; for a pipe open at both ends: same, but open/closed pipes have quarter-wavelength relationships.
当两个完全相同的波沿相反方向传播时会形成驻波。波节（位移为零）和波腹（位移最大）出现在固定位置。两端固定的弦：λₙ = 2L/n；两端开口的管：和谐波关系相同，而一端封闭的管则满足四分之一波长的关系。
9. Electric Fields, Circuits and Kirchhoff’s Laws | 电场、电路与基尔霍夫定律
Electric field strength E = F/q. For a uniform field between parallel plates, E = V/d. The force on a charge in an electric field is F = qE. Potential difference (p.d.) is work done per unit charge.
电场强度 E = F/q。对于平行板间的匀强电场，E = V/d。电荷在电场中所受的力 F = qE。电势差(p.d.)是单位电荷所做的功。
Ohm’s law: V = IR, valid for ohmic conductors at constant temperature. Resistance R = ρL/A. In series circuits, current is constant and p.d. splits; in parallel, p.d. is constant and current splits.
欧姆定律：V = IR，对恒温下的欧姆导体成立。电阻 R = ρL/A。串联电路中电流处处相等，电压分压；并联电路中各支路电压相等，电流分流。
Kirchhoff’s first law: ΣI into a junction = ΣI out. Second law: Σ emf = Σ p.d. around any closed loop. Internal resistance r of a cell causes terminal p.d. to drop when current flows: V = ε − Ir.
基尔霍夫第一定律：流入节点的电流之和等于流出节点的电流之和。第二定律：沿任一闭合回路，电动势代数和等于电压降代数和。电源内阻 r 导致有电流时路端电压下降：V = ε − Ir。
10. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
A current-carrying conductor in a magnetic field experiences a force: F = BIL sinθ (Fleming’s left-hand rule). A moving charge in a field experiences F = Bqv sinθ, moving in a circular path if perpendicular.
磁场中的载流导体会受到力的作用：F = BIL sinθ（弗莱明左手定则）。运动电荷在磁场中受力 F = Bqv sinθ，若速度与磁场垂直，电荷将做圆周运动。
Magnetic flux Φ = BA cosθ; flux linkage = NΦ. Faraday’s law: induced emf ε = −N ΔΦ/Δt. Lenz’s law states that the direction of induced current opposes the change causing it — incorporated in the minus sign.
磁通量 Φ = BA cosθ；磁链 = NΦ。法拉第定律：感应电动势 ε = −N ΔΦ/Δt。楞次定律指出，感应电流的方向总是阻碍引起感应电流的磁通变化——这就是公式中负号的含义。
For a rod moving perpendicular to field: ε = BLv
导体棒垂直切割磁感线时：ε = BLv
Transformers, generators and AC theory appear in both IB and CIE. An ideal transformer: Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ (100% efficiency).
变压器、发电机和交流电理论在IB和CIE中均有涉及。理想变压器：Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ（效率100%）。
11. Thermal Physics and Ideal Gases | 热物理与理想气体
Temperature is a measure of average kinetic energy of particles. Specific heat capacity c = Q/(mΔT); specific latent heat L = Q/m. Internal energy U is the sum of random kinetic and potential energies of molecules.
温度是粒子平均动能的量度。比热容 c = Q/(mΔT)；比潜热 L = Q/m。内能 U 是分子无规则运动动能与势能的总和。
The ideal gas equation is pV = nRT, or pV = NkT. Boyle’s law (pV = constant at fixed T), Charles’s law (V ∝ T at fixed p) and the pressure law (p ∝ T at fixed V) are special cases. The kinetic theory relates pressure to mean square speed: pV = ⅓ Nm
理想气体状态方程为 pV = nRT，或 pV = NkT。玻意耳定律（恒温下 pV = 常量）、查理定律（恒压下 V ∝ T）和压强定律（恒容下 p ∝ T）是特例。分子动理论将压强与均方速率联系起来：pV = ⅓ Nm
The first law of thermodynamics: ΔU = Q + W, where W is work done ON the gas. Sign conventions vary between syllabi: CIE often writes ΔU = Q − W (work done BY gas). Always check your exam board’s convention.
热力学第一定律：ΔU = Q + W，其中 W 是对气体做的功。不同考试局的符号约定不同：CIE 常写作 ΔU = Q − W（系统对外做功）。务必确认所在考试局的约定。
12. Atomic, Nuclear and Particle Physics | 原子、核与粒子物理
The Bohr model explains line spectra through transitions between discrete energy levels. Photon energy E = hf = hc/λ. In both IB and CIE, students must interpret energy level diagrams and calculate emitted or absorbed photon energies.
玻尔模型通过离散能级之间的跃迁来解释线状光谱。光子能量 E = hf = hc/λ。在IB和CIE中，学生必须能够解读能级图，并计算发射或吸收的光子能量。
Radioactive decay: activity A = −dN/dt = λN. Exponential decay N = N₀ e^{-λt}, with half-life t½ = ln2 / λ. Background radiation corrections are common in practical questions.
放射性衰变：活度 A = −dN/dt = λN。指数衰减 N = N₀ e^{-λt}，半衰期 t½ = ln2 / λ。实验题中常涉及本底辐射的修正。
Mass defect and binding energy: E = Δm c². The binding energy per nucleon curve explains fission and fusion. Nuclear reactions conserve nucleon number and charge.
质量亏损与结合能：E = Δm c²。比结合能曲线解释了裂变和聚变现象。核反应中核子数和电荷数守恒。
Particle physics introduces quarks, leptons and exchange bosons. Beta decay (n → p + e⁻ + ν̄ₑ) exemplifies weak interaction. Conservation rules (baryon number, lepton number, strangeness) are common exam fodder.
粒子物理部分涉及夸克、轻子和交换玻色子。β衰变（n → p + e⁻ + ν̄ₑ）是弱相互作用的实例。守恒定律（重子数、轻子数、奇异数）是考试的常见内容。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导