📚 IB CIE Physics: Last-Minute Revision Notes | IB CIE 物理：考前冲刺笔记
As the exam approaches, a concise set of last-minute revision notes can sharpen your recall of critical IB and CIE Physics topics. This guide summarises definitions, key formulas, and conceptual pitfalls across mechanics, thermal physics, waves, electricity, magnetism, and modern physics. Use it to check your understanding and avoid common mistakes.
临考之际，一份精炼的冲刺笔记能帮你快速回顾IB和CIE物理关键考点。本指南总结力学、热学、波动、电学、磁学和近代物理的定义、核心公式和常见误区，助你排查疏漏，稳拿基础分。
1. Kinematics and Motion | 运动学
Motion is described by displacement, velocity, and acceleration. The SUVAT equations apply only when acceleration is constant. Always define a positive direction and stick to it.
运动由位移、速度和加速度描述。SUVAT方程仅在加速度恒定时适用。务必规定正方向并保持一致。
v = u + at | s = ut + ½at² | v² = u² + 2as | s = ½(u + v)t
Here v = final velocity, u = initial velocity, a = constant acceleration, t = time, s = displacement. The first equation lacks s, the second lacks v, the third lacks t, and the fourth lacks a.
其中 v = 末速度，u = 初速度，a = 恒定加速度，t = 时间，s = 位移。第一个方程不含 s，第二个不含 v，第三个不含 t，第四个不含 a。
In a displacement–time graph, the gradient gives velocity. In a velocity–time graph, the gradient gives acceleration and the area under the curve gives displacement. For projectile motion, split into constant horizontal velocity and vertical motion under gravity (g = 9.81 m s⁻²). Time of flight is determined solely by the vertical component.
位移–时间图中，斜率表示速度。速度–时间图中，斜率表示加速度，曲线下面积表示位移。抛体运动分解为水平匀速和竖直方向重力加速度（g = 9.81 m s⁻²）运动。飞行时间仅由竖直分量决定。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s First Law: an object remains at rest or in uniform motion unless acted upon by a net external force. Newton’s Second Law: F = ma, and Newton’s Third Law: forces come in action–reaction pairs acting on different bodies.
牛顿第一定律：物体在不受外力时保持静止或匀速直线运动。牛顿第二定律：F = ma。牛顿第三定律：作用力与反作用力大小相等、方向相反，作用在不同物体上。
Free-body diagrams are essential for resolving forces. Common forces: weight (W = mg), normal reaction, tension, friction (f ≤ μR), and air resistance. Equilibrium means net force = 0 and net torque = 0.
受力分析图至关重要。常见力：重力（W = mg）、法向反作用力、张力、摩擦力（f ≤ μR）和空气阻力。平衡意味着合外力为零且合外力矩为零。
Friction always opposes relative motion. Limit of static friction: fₘₐₓ = μₛR; kinetic friction: fₖ = μₖR, where R is the normal reaction. When a body is on an incline, resolve weight into mg sin θ (down the slope) and mg cos θ (into the slope).
摩擦力总是阻碍相对运动。最大静摩擦：fₘₐₓ = μₛR；动摩擦：fₖ = μₖR，其中 R 为法向作用力。物体在斜面上时，将重力分解为 mg sin θ（沿斜面）和 mg cos θ（垂直于斜面）。
3. Work, Energy and Power | 功、能量与功率
Work done (W) = F s cos θ, where θ is the angle between force and displacement. Energy is the capacity to do work. Kinetic energy: KE = ½mv²; gravitational potential energy near Earth’s surface: GPE = mgh.
功 W = F s cos θ，θ 是力与位移的夹角。能量是做功的本领。动能：KE = ½mv²；地表附近重力势能：GPE = mgh。
The work–energy principle: net work done = change in kinetic energy. In a closed system, energy is conserved and may transform between forms (kinetic, potential, thermal, etc.). Power is the rate of doing work: P = W/t or P = Fv for an object moving at constant velocity.
功能原理：合外力做功等于动能的变化量。封闭系统内能量守恒，可在不同形式间转化（动能、势能、内能等）。功率是做功的快慢：P = W/t，物体匀速运动时 P = Fv。
Efficiency = (useful output energy)/(total input energy) × 100%. For inclined planes, pulley systems, or motors, always account for energy dissipated as heat.
效率 =（有用输出能量）/（总输入能量）× 100%。对于斜面、滑轮组或电动机，务必计入耗散的热能。
4. Momentum and Collisions | 动量与碰撞
Momentum p = mv, a vector quantity. The impulse delivered by a force is J = FΔt = Δp. The area under a force–time graph equals impulse. In collisions and explosions, total momentum is conserved if no external force acts.
动量 p = mv，为矢量。冲量 J = FΔt = Δp。力–时间图下的面积等于冲量。无外力时，碰撞与爆炸过程中总动量守恒。
Elastic collisions: kinetic energy is conserved. Inelastic collisions: kinetic energy is not conserved, but momentum is still conserved. For a perfectly inelastic collision, the bodies stick together.
弹性碰撞：动能守恒。非弹性碰撞：动能不守恒，但动量仍守恒。完全非弹性碰撞中，两物体粘合在一起。
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Note: assign a positive direction and use signs consistently. For 2D collisions, resolve momentum into perpendicular components.
注意：规定正方向并带上正负号。对二维碰撞，将动量分解到相互垂直的两个方向分别守恒。
5. Circular Motion and Gravitation | 圆周运动与引力
An object in uniform circular motion has a constant speed but changing velocity, hence a centripetal acceleration directed toward the centre: a = v²/r = ω²r. Centripetal force F = mv²/r = mω²r.
物体做匀速圆周运动时速率不变但速度方向时刻变化，因此存在指向圆心的向心加速度：a = v²/r = ω²r。向心力 F = mv²/r = mω²r。
The centripetal force is not a new kind of force; it is provided by gravity, tension, friction, or the normal reaction. Always ask what physically provides the centripetal component.
向心力并非新类型的力，而是由引力、张力、摩擦力或法向反作用力等充当。需明确谁提供了向心力。
Newton’s law of universal gravitation: F = G M m / r². Gravitational field strength g = F/m = GM/r². For circular orbits: v = √(GM/r) and T² ∝ r³ (Kepler’s third law).
万有引力定律：F = G M m / r²。重力场强度 g = F/m = GM/r²。对圆形轨道：v = √(GM/r)，周期 T² ∝ r³（开普勒第三定律）。
6. Thermal Physics | 热物理
Temperature is a measure of the average random kinetic energy of particles. The Celsius and kelvin scales are related by T(K) = θ(°C) + 273.15. The Kelvin scale is used in gas laws.
温度是分子平均平动动能的量度。摄氏温标与开氏温标换算：T(K) = θ(°C) + 273.15。气体定律必须使用开氏温标。
Specific heat capacity c: Q = mcΔθ. Specific latent heat L: Q = mL (fusion or vaporisation at constant temperature). Internal energy is the sum of random kinetic and potential energies of all particles.
比热容 c：Q = mcΔθ。比潜热 L：Q = mL（在恒定温度下熔化或汽化）。内能是所有分子无规则动能与分子间势能的总和。
Ideal gas equation: pV = nRT, where n is the amount in moles, R = 8.31 J mol⁻¹ K⁻¹. Boyle’s law (pV = constant at fixed T), Charles’s law (V/T = constant at fixed p), Pressure law (p/T = constant at fixed V). The average kinetic energy of a gas molecule is (3/2)kT, where k is Boltzmann’s constant.
理想气体状态方程：pV = nRT，n 为摩尔数，R = 8.31 J mol⁻¹ K⁻¹。波义耳定律（等温下 pV = 常数）、查理定律（等压下 V/T = 常数）、压强定律（等容下 p/T = 常数）。气体分子平均动能 (3/2)kT，k 为玻尔兹曼常数。
7. Wave Phenomena | 波动现象
Waves transfer energy without transferring matter. Transverse waves (e.g., light, water waves) vibrate perpendicular to propagation; longitudinal waves (e.g., sound) vibrate parallel. Key properties: amplitude (A), frequency (f), period (T = 1/f), wavelength (λ), wave speed (v = fλ).
波传播能量而不传播物质。横波（如光、水波）振动方向与传播方向垂直；纵波（如声波）振动方向与传播方向平行。主要物理量：振幅 A、频率 f、周期 T = 1/f、波长 λ、波速 v = fλ。
Reflection, refraction, diffraction, and interference are fundamental wave behaviours. Phase difference Δφ = (2π/λ) × path difference. Constructive interference occurs when path difference = nλ; destructive when (n + ½)λ.
反射、折射、衍射和干涉是基本的波动行为。相位差 Δφ = (2π/λ) × 程差。当程差等于 nλ 时产生相长干涉，(n + ½)λ 时产生相消干涉。
For standing waves, nodes are points of zero displacement, antinodes are points of maximum amplitude. The distance between adjacent nodes (or antinodes) is λ/2. Harmonics on a string: fₙ = n(v/2L) for both ends fixed.
驻波中，波节处位移始终为零，波腹处振幅最大。相邻波节或波腹间距为 λ/2。两端固定的弦上的谐频：fₙ = n(v/2L)。
8. Electric Fields and Circuits | 电场与电路
Electric field strength E = F/q (unit N C⁻¹ or V m⁻¹). Between parallel plates: E = V/d. The direction of an electric field is the force on a positive test charge. Coulomb’s law: F = k Q₁ Q₂ / r².
电场强度 E = F/q（单位 N C⁻¹ 或 V m⁻¹）。平行板间匀强电场：E = V/d。电场方向为正检验电荷所受电场力方向。库仑定律：F = k Q₁ Q₂ / r²。
Current I = ΔQ/Δt. Ohm’s law: V = IR for an ohmic conductor at constant temperature. Resistance R = ρL/A, where ρ is resistivity. Power dissipated in a resistor: P = IV = I²R = V²/R.
电流 I = ΔQ/Δt。欧姆定律：对恒定温度下的欧姆导体有 V = IR。电阻 R = ρL/A，ρ 为电阻率。电阻耗散功率：P = IV = I²R = V²/R。
Series: Rₜₒₜₐₗ = R₁ + R₂ + … ; same current through all. Parallel: 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + … ; same p.d. across all. Kirchhoff’s current law: sum of currents into a junction equals sum out. Kirchhoff’s voltage law: sum of emfs = sum of pds in any closed loop.
串联：Rₜₒₜₐₗ = R₁ + R₂ + …，电流处处相等。并联：1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + …，各支路电压相等。基尔霍夫电流定律：流入节点的电流总和等于流出总和。基尔霍夫电压定律：任意闭合回路中电动势升等于电压降之和。
Potential divider: Vₒᵤₜ = Vᵢₙ × [R₂/(R₁ + R₂)]. A potentiometer can measure emf by comparing potential differences without drawing current. Internal resistance r of a cell: V = ℰ − Ir.
分压器：Vₒᵤₜ = Vᵢₙ × [R₂/(R₁ + R₂)]。电位差计可通过比较电位差来测量电动势而不产生电流。电池内阻 r：端电压 V = ℰ − Ir。
9. Magnetic Fields and Electromagnetism | 磁场与电磁学
Magnetic field lines emerge from north to south poles. A moving charge in a magnetic field experiences a force F = q v B sin θ. Use Fleming’s left-hand rule: thumb = force, forefinger = field, middle finger = current (+ charge velocity).
磁感线从N极指向S极。运动电荷在磁场中受力 F = q v B sin θ。使用弗莱明左手定则：拇指—受力方向，食指—磁场方向，中指—电流方向（正电荷运动方向）。
For a current-carrying wire: F = B I L sin θ, where L is the length of wire in the field. The force is perpendicular to both B and I. This allows the definition of the tesla: 1 T = 1 N A⁻¹ m⁻¹.
对通电导线：F = B I L sin θ，L 为导线在磁场中的长度。安培力方向垂直于 B 和 I。由此定义特斯拉：1 T = 1 N A⁻¹ m⁻¹。
Electromagnetic induction: an emf is induced when the magnetic flux linking a circuit changes. Faraday’s law: ℰ = −N ΔΦ/Δt. Lenz’s law: the induced current opposes the change in flux. For a moving conductor: ℰ = B L v. Generators and transformers rely on induction.
电磁感应：穿过电路的磁通量发生变化时产生感应电动势。法拉第定律：ℰ = −N ΔΦ/Δt。楞次定律：感应电流的磁场阻碍磁通量的变化。对于切割磁感线的导体：ℰ = B L v。发电机和变压器均基于电磁感应。
For an ideal transformer: Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ (100% efficiency). Real transformers lose energy through eddy currents and hysteresis, so step-up transformers lower current in transmission lines to reduce I²R losses.
理想变压器：Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ（100%效率）。实际变压器有涡流和磁滞损耗。升压变压器在输电线路上提高电压、降低电流以减少 I²R 损耗。
10. Quantum and Nuclear Physics | 量子与核物理
Photon energy E = hf = hc/λ. The photoelectric effect: electrons are emitted from a metal surface when photons with frequency above the threshold frequency f₀ strike it. Maximum kinetic energy of photoelectrons: Kₘₐₓ = hf − Φ, where Φ is the work function. Intensity determines the number of photons, not the kinetic energy.
光子能量 E = hf = hc/λ。光电效应：频率高于截止频率 f₀ 的光子照射金属表面，会使电子逸出。光电子最大动能：Kₘₐₓ = hf − Φ，Φ 为逸出功。光的强度影响光子数目，而非光电子动能。
Emission and absorption spectra provide evidence for discrete electron energy levels in atoms. Energy released when an electron drops from level Eₕᵢ₉ₕ to Eₗₒₒ is ΔE = hf.
发射光谱和吸收光谱证明了原子中存在分立的能级。电子从高能级 Eₕᵢ₉ₕ 跃迁到低能级 Eₗₒₒ 释放的光子能量 ΔE = hf。
Nuclear structure: A = mass number = protons + neutrons, Z = atomic number = protons. Isotopes have same Z but different A. Radioactive decay: alpha (α – ⁴₂He), beta minus (β⁻ – electron, a neutron becomes proton), beta plus (β⁺ – positron), gamma (γ – electromagnetic). Activity A = λN, decay law N = N₀ e^{-λt} and half-life T_{½} = ln2/λ.
原子核结构：质量数 A = 质子数+中子数，原子序数 Z = 质子数。同位素的 Z 相同、A 不同。放射性衰变：α 衰变（⁴₂He），β⁻ 衰变（中子转变为质子并放出电子），β⁺ 衰变（正电子），γ 衰变（电磁辐射）。活度 A = λN，衰变律 N = N₀ e^{-λt}，半衰期 T_{½} = ln2/λ。
Mass defect and binding energy: the total mass of a nucleus is less than the sum of its individual nucleons. The energy equivalent is E = Δm c². Binding energy per nucleon peaks around iron-56, determining stability. Nuclear fission and fusion release energy by moving toward higher binding energy per nucleon.
质量亏损与结合能：原子核的总质量小于其所有核子单独存在时的质量和，能量等价 E = Δm c²。比结合能在铁-56附近达到峰值，决定核的稳定性。核裂变与核聚变都通过向更高比结合能方向变化释放能量。
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