IB Physics: End-of-Term Revision Checklist | IB 物理：期末复习提纲

📚 IB Physics: End-of-Term Revision Checklist | IB 物理：期末复习提纲

A well-structured revision plan is the key to succeeding in your IB Physics end-of-term examination. This checklist breaks down the core topics into manageable sections, highlights essential formulas, common pitfalls, and strategies to help you review efficiently. Use it alongside your syllabus guide and past paper questions for maximum impact.

一个结构清晰的复习计划是在 IB 物理期末考试中取得成功的关键。本提纲将核心主题分解为易于掌握的模块，突出重要公式、常见错误以及高效复习的策略。请结合课程指南和历年真题使用，以获得最佳效果。

1. Measurements and Uncertainties | 测量与不确定度

All physical quantities are expressed in SI base units (kg, m, s, A, K, mol, cd). Be comfortable converting derived units and using scientific notation to avoid calculation errors under pressure.

所有物理量均用国际单位制基本单位（kg、m、s、A、K、mol、cd）表示。要熟练转换导出单位并使用科学记数法，以避免在压力下出现计算错误。

Uncertainties must be reported to an appropriate number of significant figures. Absolute uncertainty is the ± value in the measurement, while fractional (relative) uncertainty is absolute uncertainty divided by the measured value, often expressed as a percentage.

不确定度必须以适当有效数字报告。绝对不确定度是测量值中的 ± 数值，而分数（相对）不确定度是绝对不确定度除以测量值，通常以百分比表示。

Key formulas:

关键公式：

• Absolute uncertainty: ± Δx

  绝对不确定度：± Δx

• Fractional uncertainty: Δx / x

  分数不确定度：Δx / x

• Percentage uncertainty: (Δx / x) × 100%

  百分比不确定度：(Δx / x) × 100%

When combining measurements, add absolute uncertainties for addition/subtraction and add fractional (or percentage) uncertainties for multiplication/division.

当组合测量值时，加减运算应将绝对不确定度相加，乘除运算应将分数（或百分比）不确定度相加。

2. Kinematics | 运动学

Kinematics describes motion without considering its causes. The four SUVAT equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t) for uniformly accelerated motion in a straight line.

运动学描述运动而不考虑其成因。四个运动学方程联系了匀加速直线运动中的位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t)。

v = u + at

s = ut + ½at²

v² = u² + 2as

s = (u + v)/2 × t

Remember to define a positive direction from the start. For projectile motion, treat horizontal and vertical components independently. The horizontal velocity remains constant, while vertical motion follows free-fall kinematics with a = g = 9.81 m s⁻² (downwards).

请记住从一开始就规定正方向。对于抛体运动，应独立处理水平和竖直分量。水平速度保持不变，而竖直运动遵循自由落体运动学，加速度 a = g = 9.81 m s⁻²（向下）。

Displacement–time, velocity–time, and acceleration–time graphs give instantaneous values, gradients, and areas under curves. A common exam trick is to ask for the distance travelled from a velocity–time graph, not the displacement—check for areas below the axis.

位移–时间、速度–时间和加速度–时间图像可得出瞬时值、斜率和曲线下的面积。一个常见的考题陷阱是要求从速度–时间图像中求出运动的路程，而非位移——需检查坐标轴下方的面积。

3. Forces and Dynamics | 力与动力学

Newton’s three laws are the bedrock of mechanics. The first law defines inertia; the second law gives F = ma; the third law states that forces come in equal and opposite pairs acting on different bodies.

牛顿三定律是力学的基石。第一定律定义了惯性；第二定律给出 F = ma；第三定律指出力成对出现，大小相等、方向相反且作用在不同物体上。

Free-body diagrams are essential. Draw all forces as arrows from the center of mass, and never include the net force or components of forces on the same diagram. Balance forces for equilibrium or apply F = ma in the direction of net force.

受力分析图至关重要。将所有力从质心用箭头画出，切勿在同一图上画出合力或力的分量。对于平衡情况，使力相互平衡；否则在合力方向上应用 F = ma。

Friction is modeled by f ≤ μₛR (static) and f = μₖR (kinetic), where R is the normal reaction. Fluid resistance (drag) increases with speed and leads to terminal velocity when drag equals weight.

摩擦力模型为 f ≤ μₛR（静摩擦）和 f = μₖR（动摩擦），其中 R 为法向反作用力。流体阻力（拖曳力）随速度增大，当阻力等于重力时将出现终极速度。

Momentum p = mv is conserved in isolated systems. Impulse equals change in momentum: FΔt = Δp. Collisions can be elastic (kinetic energy conserved) or inelastic. Always apply conservation of momentum before energy when analyzing collisions.

动量 p = mv 在孤立系统中守恒。冲量等于动量变化：FΔt = Δp。碰撞可分为弹性碰撞（动能守恒）和非弹性碰撞。分析碰撞时，应始终先应用动量守恒再考虑能量。

4. Work, Energy and Power | 功、能量与功率

Work done by a force is W = F s cosθ, where θ is the angle between the force and displacement. Energy is the capacity to do work. Kinetic energy Eₖ = ½mv²; gravitational potential energy Eₚ = mgΔh (valid only near Earth’s surface).

力所做的功为 W = F s cosθ，其中 θ 为力与位移的夹角。能量是做功的能力。动能 Eₖ = ½mv²；重力势能 Eₚ = mgΔh（仅在地球表面附近有效）。

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed. In problems involving friction, some mechanical energy is dissipated as heat. Power is the rate of doing work or transferring energy: P = W/t = Fv (for constant force and velocity in same direction).

能量守恒定律指出，能量既不能创造也不能消灭，只能转化。在涉及摩擦的问题中，部分机械能将耗散为热。功率是做功或传递能量的速率：P = W/t = Fv（适用于恒力且速度方向与力相同的情况）。

Efficiency = useful output energy / total input energy, or useful power out / total power in. Always expressed as a percentage less than or equal to 100%.

效率 = 有用输出能量 / 总输入能量，或有用输出功率 / 总输入功率。总以小于或等于 100% 的百分比表示。

5. Thermal Physics | 热物理

Temperature T (in kelvin) is proportional to the average random kinetic energy of particles. Convert between Celsius and Kelvin using T (K) = θ (°C) + 273. The mole is the unit of amount of substance containing 6.02 × 10²³ particles.

温度 T（开尔文）与粒子的平均无规则动能成正比。摄氏与开尔文之间的转换为 T (K) = θ (°C) + 273。摩尔是物质的量的单位，包含 6.02×10²³ 个粒子。

Internal energy is the sum of random kinetic energy and intermolecular potential energy. During phase changes, temperature remains constant even though internal energy changes significantly—this is the latent heat effect.

内能是无规则动能与分子间势能之和。在相变过程中，即使内能发生显著变化，温度却保持不变——这就是潜热的效应。

Ideal gas laws:

理想气体定律：

• Boyle’s law: p ∝ 1/V at constant T

  玻意耳定律：p ∝ 1/V（恒温条件）

• Charles’s law: V ∝ T at constant p

  查理定律：V ∝ T（恒压条件）

• Pressure law: p ∝ T at constant V

  压力定律：p ∝ T（恒容条件）

The equation of state for an ideal gas is pV = nRT, where R = 8.31 J K⁻¹ mol⁻¹. Assumptions of the kinetic model: particles have negligible volume, no intermolecular forces (except during collisions), and collisions are elastic.

理想气体状态方程为 pV = nRT，其中 R = 8.31 J K⁻¹ mol⁻¹。分子动理论的假设：粒子体积可忽略，无分子间作用力（碰撞瞬间除外），碰撞为弹性碰撞。

6. Oscillations and Waves | 振动与波

Simple harmonic motion (SHM) requires a restoring force proportional to displacement: F = −kx, giving a = −(k/m)x = −ω²x. Solutions are sinusoidal: x = A sin(ωt) or x = A cos(ωt). Period T = 2π/ω; for a mass–spring system T = 2π√(m/k); for a simple pendulum T = 2π√(L/g).

简谐运动要求恢复力与位移成正比：F = −kx，从而 a = −(k/m)x = −ω²x。其解为正弦形式：x = A sin(ωt) 或 x = A cos(ωt)。周期 T = 2π/ω；弹簧振子 T = 2π√(m/k)；单摆 T = 2π√(L/g)。

Energy in SHM continually converts between kinetic and potential, but total energy remains constant. Damping reduces amplitude over time; critical damping returns the system to equilibrium in the shortest time without oscillation.

简谐运动中的能量在动能与势能之间不断转换，但总能量保持不变。阻尼会使振幅随时间减小；临界阻尼可在最短时间内使系统回到平衡位置而不发生振动。

Traveling waves transfer energy without net movement of matter. Transverse waves (e.g., light, water ripples) oscillate perpendicular to propagation; longitudinal waves (e.g., sound) oscillate parallel. Key relationships: v = f λ and T = 1/f.

行波传递能量而不伴随物质的净移动。横波（如光、水波涟漪）的振动方向与传播方向垂直；纵波（如声波）的振动方向与传播方向平行。关键关系式：v = f λ 和 T = 1/f。

Superposition leads to constructive or destructive interference. Standing waves form when two identical waves travel in opposite directions, characterized by nodes (zero amplitude) and antinodes (maximum amplitude). For a string fixed at both ends, the harmonic wavelengths are λₙ = 2L/n.

叠加原理导致相长干涉或相消干涉。当两列相同的波沿相反方向传播时会形成驻波，其特征为波节（振幅为零）和波腹（振幅最大）。对于两端固定的弦，谐波波长为 λₙ = 2L/n。

Single-slit diffraction produces a central bright fringe of width proportional to λ/a, where a is the slit width. Double-slit interference yields equally spaced fringes with separation Δy = λD/d. Thin film interference depends on path difference and phase change at boundaries.

单缝衍射产生中央亮纹，其宽度与 λ/a 成正比，a 为缝宽。双缝干涉产生等间距条纹，条纹间距 Δy = λD/d。薄膜干涉取决于光程差及边界的相位突变。

7. Electricity | 电学

Current I = Δq/Δt, measured in amperes (A). conventional current flows from positive to negative. Electron flow is opposite. Potential difference V = W/q, and resistance R = V/I. Ohm’s law holds for ohmic conductors at constant temperature.

电流 I = Δq/Δt，单位为安培 (A)。常规电流方向由正到负，电子流动方向与之相反。电势差 V = W/q，电阻 R = V/I。欧姆定律在恒温条件下适用于欧姆导体。

Resistivity ρ relates to resistance via R = ρL/A. Resistivity increases with temperature in metals (positive temperature coefficient) but can decrease in semiconductors. Superconductors have zero resistivity below a critical temperature.

电阻率 ρ 与电阻的关系为 R = ρL/A。金属的电阻率随温度升高而增大（正温度系数），但在半导体中可能减小。超导体在临界温度以下电阻率为零。

Circuit rules:

电路规则：

• Series: I is same; V = V₁ + V₂; Rₜₒₜ = R₁ + R₂

  串联：电流处处相等；V = V₁ + V₂；Rₜₒₜ = R₁ + R₂

• Parallel: V is same; I = I₁ + I₂; 1/Rₜₒₜ = 1/R₁ + 1/R₂

  并联：电压处处相等；I = I₁ + I₂；1/Rₜₒₜ = 1/R₁ + 1/R₂

Ammeters are connected in series (low internal resistance), voltmeters in parallel (high internal resistance). Ideal meters do not affect the circuit. Kirchhoff’s junction law (ΣI = 0) and loop law (ΣV = 0) are fundamental for complex networks.

电流表串联接入（低内阻），电压表并联接入（高内阻）。理想电表不影响电路。基尔霍夫节点定律 (ΣI = 0) 和回路定律 (ΣV = 0) 是分析复杂网络的基础。

Electrical power: P = VI = I²R = V²/R. Energy dissipated as heat in a resistor: E = Pt = VIt = I²Rt. Pay attention to kWh vs J when calculating energy bills.

电功率：P = VI = I²R = V²/R。电阻上耗散为热的能量：E = Pt = VIt = I²Rt。在计算电费时注意区分千瓦时 (kWh) 与焦耳 (J)。

8. Magnetism and Electromagnetic Induction | 磁学与电磁感应

Magnetic fields are created by moving charges and permanent magnets. Field lines point from north to south outside magnets. A current-carrying conductor in a magnetic field experiences a force: F = BIL sinθ (Lorentz force on wire). The direction is given by Fleming’s left-hand rule.

磁场由运动电荷和永磁体产生。磁感线在磁体外部由 N 极指向 S 极。载流导体在磁场中受到安培力：F = BIL sinθ（导线所受洛伦兹力）。方向由弗莱明左手定则确定。

A charged particle moving through a magnetic field experiences a centripetal force qvB = mv²/r, leading to circular motion of radius r = mv/(qB). Note that magnetic forces do no work because they are always perpendicular to velocity.

运动电荷在磁场中受到向心力 qvB = mv²/r，从而作半径为 r = mv/(qB) 的圆周运动。注意，由于磁力始终与速度垂直，磁力不做功。

Electromagnetic induction: a changing magnetic flux induces an emf. Faraday’s law: ε = −N ΔΦ/Δt. Lenz’s law (the negative sign) states that the induced current flows in a direction that opposes the change in flux. Motional emf across a moving conductor: ε = B L v.

电磁感应：变化的磁通量产生感应电动势。法拉第定律：ε = −N ΔΦ/Δt。楞次定律（负号的意义）指出感应电流的方向总是阻碍磁通量的变化。运动导体的动生电动势：ε = B L v。

Transformers change voltages for AC: Vₛ/Vₚ = Nₛ/Nₚ, and for ideal transformers Pₚ = Pₛ, so IₚVₚ = IₛVₛ. Real transformers have eddy current and hysteresis losses.

变压器可改变交流电压：Vₛ/Vₚ = Nₛ/Nₚ，对于理想变压器 Pₚ = Pₛ，因此 IₚVₚ = IₛVₛ。实际变压器存在涡流和磁滞损耗。

9. Circular Motion and Gravitation | 圆周运动与引力

Uniform circular motion requires a centripetal acceleration a = v²/r = ω²r and centripetal force F = mv²/r = mω²r, directed towards the centre. Period T = 2π/ω.

匀速圆周运动需要向心加速度 a = v²/r = ω²r 和向心力 F = mv²/r = mω²r，方向指向圆心。周期 T = 2π/ω。

Newton’s law of gravitation: F = G M m / r², where G = 6.67×10⁻¹¹ N m² kg⁻². For a satellite in circular orbit, gravitational force provides the centripetal force, leading to v = √(GM/r) and T² ∝ r³ (Kepler’s third law).

牛顿万有引力定律：F = G M m / r²，其中 G = 6.67×10⁻¹¹ N m² kg⁻²。对于在圆形轨道上的卫星，引力提供向心力，可得 v = √(GM/r) 以及 T² ∝ r³（开普勒第三定律）。

Gravitational field strength g = F/m = GM/r². Near Earth’s surface g ≈ 9.81 N kg⁻¹. Gravitational potential V = −GM/r (HL) and potential energy U = −GMm/r.

引力场强度 g = F/m = GM/r²。地球表面附近 g ≈ 9.81 N kg⁻¹。引力势 V = −GM/r（HL）和引力势能 U = −GMm/r。

10. Atomic, Nuclear and Particle Physics | 原子、核与粒子物理

The nuclear atom consists of a small, dense nucleus of protons and neutrons, surrounded by electrons in discrete energy levels. Atomic notation: ᴬ₂X, where Z is the atomic number, A is the mass number.

原子核模型由质子和中子组成的致密原子核以及处于分立能级的电子构成。原子符号：ᴬ₂X，其中 Z 为原子序数，A 为质量数。

Radioactive decay is a random, spontaneous process. Alpha decay reduces Z by 2 and A by 4; beta-minus decay increases Z by 1 with emission of an electron and antineutrino; beta-plus decay decreases Z by 1 with a positron and neutrino. Gamma decay releases excess energy without a change in composition.

放射性衰变是随机且自发的过程。α 衰变使 Z 减 2，A 减 4；β⁻ 衰变使 Z 增 1，同时发射电子与反中微子；β⁺ 衰变使 Z 减 1，放出正电子与中微子。γ 衰变仅释放多余能量而不改变核素组成。

Activity A = −dN/dt = λN, and decay follows N = N₀ e⁻ˡᵗ. Half-life T₁/₂ = ln 2 / λ. Always use consistent units and remember that background radiation must be subtracted in measurements.

活度 A = −dN/dt = λN，衰变遵循 N = N₀ e⁻ˡᵗ。半衰期 T₁/₂ = ln 2 / λ。始终使用一致的单位，并牢记测量中必须扣除本底辐射。

Mass–energy equivalence ΔE = Δm c² underpins nuclear reactions. The binding energy per nucleon curve peaks around iron-56, indicating maximum stability. Fusion combines light nuclei; fission splits heavy nuclei.

质能方程 ΔE = Δm c² 是核反应的基础。每个核子的结合能曲线在铁-56 附近达到峰值，表明该核素最稳定。聚变使轻核合并；裂变使重核分裂。

In the Standard Model, hadrons (baryons and mesons) are composed of quarks; leptons (e.g., electrons, neutrinos) are fundamental. Conservation laws include charge, baryon number, lepton number, and strangeness (where applicable).

在标准模型中，强子（重子和介子）由夸克组成；轻子（如电子、中微子）是基本粒子。守恒律包括电荷、重子数、轻子数和奇异数（在适用情况下）守恒。

11. Energy Production | 能源生产

Primary energy sources include fossil fuels, nuclear, solar, wind, tidal, hydroelectric, and geothermal. Sankey diagrams illustrate energy transformations and losses, with arrow widths proportional to energy flow. Overall efficiency is (useful output / total input).

一次能源包括化石燃料、核能、太阳能、风能、潮汐能、水电和地热等。桑基图展示了能量转换与损失，箭头宽度与能量流成正比。总效率为（有用输出 / 总输入）。

Solar power depends on intensity I = power/area. Albedo (reflectivity) and atmospheric absorption limit usable power. Photovoltaic cells convert sunlight directly to electricity with typical efficiencies 15–20%.

太阳能功率取决于强度 I = 功率/面积。反射率（反照率）和大气吸收限制了可用功率。光伏电池直接将太阳光转化为电能，典型效率为 15–20%。

Nuclear reactors use controlled fission. The moderator slows neutrons to thermal speeds; control rods absorb neutrons to regulate the chain reaction; the coolant removes heat. Safety issues include meltdown, waste disposal, and proliferation.

核反应堆利用受控裂变。慢化剂将中子减速至热中子速度；控制棒吸收中子以调节链式反应；冷却剂带走热量。安全问题包括熔毁、废物处理和核扩散。

Wind and hydroelectric turbines convert kinetic energy of fluids into electrical energy. The maximum theoretical efficiency for a wind turbine is given by the Betz limit (≈59%). Pumped storage systems act as gravitational batteries during peak demand.

风力和水力涡轮机将流体的动能转化为电能。风力涡轮机的最大理论效率由贝茨极限给出（约为 59%）。抽水蓄能系统在用电高峰时充当重力蓄电池。

12. Exam Strategies and Common Pitfalls | 应试策略与常见陷阱

Read the stem of data-based questions carefully—underline command terms such as “state,” “explain,” “calculate,” or “discuss.” “State” requires a short answer without justification; “explain” demands a reason or mechanism.

仔细阅读基于数据的题目题干——在指令词下方划线，如“陈述 (state)”、“解释 (explain)”、“计算 (calculate)”或“讨论 (discuss)”。“陈述”要求简短回答，无需解释；“解释”则需要给出原因或机制。

Be mindful of unit conversions: grams to kilograms, cm to m, hours to seconds. Always write final answers with appropriate units and to the correct number of significant figures, typically matching the least precise data given.

注意单位换算：克转千克、厘米转米、小时转秒。最终答案务必附上适当单位，并使用正确的有效数字位数，通常应与题目所给数据中最不精确的位数匹配。

When plotting graphs, label axes with quantities and units, use sensible scales, and draw a best-fit line or curve. If calculating a gradient, use a large triangle and show your working clearly. For linearization, identify the equation of the form y = mx + c, then relate the slope and intercept to the physical quantities involved.

绘图时应在坐标轴上标出物理量和单位，使用合理的比例，并画出最佳拟合线或曲线。计算斜率时应使用大三角形并清晰展示计算过程。对于线性化处理，先确定 y = mx + c 形式的方程，然后将斜率和截距与所涉及的物理量联系起来。

In extended-response questions, structure your answer logically: state the relevant law or principle, apply it to the specific situation, and discuss any assumptions or limitations. Avoid vague statements; use precise physics vocabulary.

在论述题中，逻辑清晰地组织答案：陈述相关的定律或原理，将其应用于具体情境，并讨论任何假设或局限性。避免含糊其辞，要使用精确的物理术语。

Finally, practice past papers under timed conditions. After completing a paper, spend at least the same amount of time reviewing the mark scheme—this is where the deepest learning occurs. Focus on the questions that you found most difficult, and you will turn weaknesses into strengths.

最后，在限时条件下练习历年真题。完成一份卷子后，至少花同样多的时间研读评分方案——这是产生最深入学习的环节。集中攻克你最感困难的题目，就能将弱点转化为强项。

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