📚 Physics for the IB Diploma: 396 Key Concepts Explained | IB 物理：396 个核心概念解析
The IB Physics curriculum, as mapped in the widely used “Physics for the IB Diploma” textbook, covers roughly 396 critical concepts from measurements to modern physics. These concepts, spanning Standard and Higher Level, form the foundation of the entire course. From kinematic equations and thermodynamic laws to wave behaviour and quantum phenomena, mastering these core ideas is essential for tackling Paper 1, Paper 2, and the Internal Assessment. This article breaks down the key concept clusters, explains each with concise definitions and equations, and provides effective study strategies to help you ace your IB Physics exam.
IB 物理课程，正如广为使用的《Physics for the IB Diploma》教材所梳理的那样，涵盖了约 396 个从测量到现代物理的关键概念。这些概念横跨标准级与高级，构成了整个课程的基础。从运动学方程、热力学定律到波动行为和量子现象，掌握这些核心思想对于应对试卷一、试卷二和内部评估至关重要。本文将这些关键概念分门别类，用简洁的定义和方程逐一解释，并给出有效的学习策略，帮助你斩获 IB 物理高分。
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) and can be combined into derived units. A measurement without an uncertainty is meaningless; absolute uncertainty ±Δx and fractional uncertainty Δx/x must be propagated through sums, differences, products and quotients. For a function, the uncertainty is estimated using the gradient or the range of repeated readings.
所有物理量都用 SI 基本单位（kg、m、s、A、K、mol、cd）表示，并可组合成导出单位。没有不确定度的测量毫无意义；绝对不确定度 ±Δx 和相对不确定度 Δx/x 必须通过加减、乘除运算进行传播。对于函数关系，可利用斜率或多次读数的范围来估计不确定度。
Scalars possess magnitude only, while vectors have both magnitude and direction. Vectors can be added graphically (tip-to-tail) or by resolving into perpendicular components. A resultant vector R = √(A² + B²) when perpendicular; for non-perpendicular angles, components Aₓ = A cosθ and Aᵧ = A sinθ are used. In IB, stating correct significant figures and scientific notation is expected for every numerical answer.
标量只有大小，矢量既有大小又有方向。矢量可以用尾首相接的作图法相加，也可以分解为相互垂直的分量。当两矢量垂直时，合矢量大小 R = √(A² + B²)；不垂直时，使用水平分量 Aₓ = A cosθ 和竖直分量 Aᵧ = A sinθ。在 IB 考试中，每个数字答案都需要正确保留有效数字并使用科学记数法。
2. Mechanics | 力学
Kinematics describes motion with quantities displacement s, velocity v and acceleration a. The four SUVAT equations, e.g. v = u + at, s = ut + ½at² and v² = u² + 2as, apply only to constant acceleration. On a velocity–time graph, the gradient gives acceleration and the area under the curve gives displacement. Free-fall acceleration g is approximately 9.81 m s⁻² on Earth.
运动学用位移 s、速度 v 和加速度 a 描述运动。四个 SUVAT 方程，例如 v = u + at、s = ut + ½at² 和 v² = u² + 2as，仅适用于匀加速。在速度–时间图中，斜率代表加速度，曲线下面积代表位移。地球上的自由落体加速度 g 约为 9.81 m s⁻²。
Newton’s three laws form the core of dynamics: inertia (ΣF = 0 ⇒ constant velocity), ΣF = ma, and action–reaction pairs. Momentum p = mv is conserved in isolated systems. Impulse J = FΔt = Δp explains how crumple zones reduce peak force. Work done W = Fs cosθ, kinetic energy Eₖ = ½mv² and gravitational potential energy Eₚ = mgΔh lead to the work–energy principle and conservation of mechanical energy.
牛顿三定律构成了动力学的核心：惯性定律（ΣF = 0 ⇒ 速度恒定）、ΣF = ma 和作用力与反作用力。动量 p = mv 在孤立系统中守恒。冲量 J = FΔt = Δp 解释了为何溃缩区能减小峰值力。功 W = Fs cosθ、动能 Eₖ = ½mv² 和重力势能 Eₚ = mgΔh 引出了功能原理和机械能守恒。
3. Thermal Physics | 热物理学
Temperature measures the average random kinetic energy of particles; heat Q is energy transferred due to a temperature difference. Specific heat capacity c = Q/(mΔT) and specific latent heat L = Q/m quantify phase-change energies. The internal energy U of an ideal gas depends only on its temperature and is the sum of molecular kinetic energies.
温度量度粒子平均无规则动能；热量 Q 是因温度差而传递的能量。比热容 c = Q/(mΔT) 和比潜热 L = Q/m 量化相变能量。理想气体的内能 U 仅取决于其温度，是分子动能的总和。
Ideal gas laws are connected by pV = nRT = Nk_B T. For constant temperature, p ∝ 1/V; at constant pressure, V ∝ T. The kinetic model links pressure to molecular collisions: p = ⅓ (Nm/V)
理想气体定律由 pV = nRT = Nk_B T 联系在一起。恒温时 p ∝ 1/V；恒压时 V ∝ T。分子动理论将压强与分子碰撞联系起来：p = ⅓ (Nm/V)
4. Waves | 波动
A travelling wave transfers energy without net motion of matter. Key descriptors include wavelength λ, frequency f, period T = 1/f and speed v = fλ. Transverse waves (e.g. light) vibrate perpendicular to propagation; longitudinal waves (e.g. sound) vibrate parallel. Intensity I is proportional to amplitude squared, I ∝ A².
行波传递能量而不伴随物质的净移动。关键描述量包括波长 λ、频率 f、周期 T = 1/f 和波速 v = fλ。横波（如光）的振动方向与传播方向垂直；纵波（如声音）的振动方向与之平行。强度 I 与振幅的平方成正比，I ∝ A²。
Reflection, refraction, diffraction and superposition define wave behaviour. Snell’s law n₁ sinθ₁ = n₂ sinθ₂ uses refractive index n = c/v. Young’s double-slit experiment yields fringe spacing Δx = λD/d, while a diffraction grating gives maxima at nλ = d sinθ. When waves superpose, constructive and destructive interference occur, forming standing waves in pipes and on strings with nodes and antinodes. The Doppler effect shifts observed frequency: f’ = f (v ± vₒ)/(v ∓ vₛ).
反射、折射、衍射和叠加定义了波动行为。斯涅耳定律 n₁ sinθ₁ = n₂ sinθ₂ 用到折射率 n = c/v。杨氏双缝实验给出条纹间距 Δx = λD/d，而衍射光栅的极大满足 nλ = d sinθ。波叠加时产生相长和相消干涉，在管中和弦上形成具有波节和波腹的驻波。多普勒效应使观测频率变为 f’ = f (v ± vₒ)/(v ∓ vₛ)。
5. Electricity and Magnetism | 电磁学
Electric current I = Δq/Δt flows from a source of emf ε. Ohm’s law V = IR defines resistance R = ρL/A, where resistivity ρ depends on material and temperature. Kirchhoff’s junction rule (ΣI = 0) and loop rule (ΣV = 0) underpin circuit analysis. Power dissipated is P = IV = I²R = V²/R. Internal resistance r of a cell reduces terminal voltage: V = ε − Ir.
电流 I = Δq/Δt 从电动势源 ε 流出。欧姆定律 V = IR 定义了电阻 R = ρL/A，其中电阻率 ρ 取决于材料和温度。基尔霍夫节点定则（ΣI = 0）和回路定则（ΣV = 0）是电路分析的基础。耗散功率为 P = IV = I²R = V²/R。电池内阻 r 会使路端电压降低：V = ε − Ir。
Electric field strength E = F/q points from positive to negative. Potential difference V = ΔW/q, and in a uniform field, E = V/d. A capacitor stores charge Q = CV and energy ½CV². Exponential charging/discharging follows V = V₀ e⁻ᵗ/RC, where time constant τ = RC. Magnetic flux Φ = BA cosθ and Faraday’s law ε = −N dΦ/dt explain induction; Lenz’s law gives the direction of induced emf. A transformer alters voltage according to Vₚ/Vₛ = Nₚ/Nₛ.
电场强度 E = F/q 的方向从正指向负。电势差 V = ΔW/q，在匀强电场中 E = V/d。电容器储存电荷 Q = CV 和能量 ½CV²。指数式充放电遵循 V = V₀ e⁻ᵗ/RC，时间常数 τ = RC。磁通量 Φ = BA cosθ 和法拉第定律 ε = −N dΦ/dt 解释了电磁感应；楞次定律给出感应电动势的方向。变压器按 Vₚ/Vₛ = Nₚ/Nₛ 变换电压。
6. Circular Motion and Gravitation | 圆周运动与引力
Uniform circular motion has constant speed but continuous radial acceleration aₙ = v²/r = ω²r, directed to the centre. Centripetal force F = maₙ = mv²/r is required to maintain the curved path; it is not a separate force but provided by tension, gravity or friction. Period T = 2πr/v.
匀速圆周运动速度大小恒定，但有始终指向圆心的径向加速度 aₙ = v²/r = ω²r。维持曲线路径需要向心力 F = maₙ = mv²/r；它不是一种独特的力，而是由张力、引力或摩擦力提供。周期 T = 2πr/v。
Newton’s law of universal gravitation F = GMm/r² describes attraction between masses. Gravitational field strength g = F/m = GM/r². For a planet, the orbital motion obeys Kepler’s third law: T² ∝ r³. Total energy of an orbiting satellite is negative and equals −GMm/(2r). Escape velocity is v_esc = √(2GM/R).
牛顿万有引力定律 F = GMm/r² 描述了质量间的相互吸引。引力场强 g = F/m = GM/r²。行星的轨道运动遵循开普勒第三定律：T² ∝ r³。环绕卫星的总能量为负，等于 −GMm/(2r)。逃逸速度为 v_esc = √(2GM/R)。
7. Atomic, Nuclear and Particle Physics | 原子、核与粒子物理
Photon energy E = hf and momentum p = E/c. The photoelectric effect, explained by Einstein, requires f > f₀ to release electrons: KE_max = hf − Φ, where Φ is the work function. The Bohr model for hydrogen gives energy levels Eₙ = −13.6/n² eV. Spectral lines correspond to electron transitions between orbits, producing absorption and emission spectra.
光子能量 E = hf，动量 p = E/c。爱因斯坦解释的光电效应要求频率 f > f₀ 才能释放电子：KE_max = hf − Φ，其中 Φ 为逸出功。氢原子的玻尔模型给出能级 Eₙ = −13.6/n² eV。光谱线对应电子在轨道间的跃迁，产生吸收和发射光谱。
Nuclear structure involves protons Z, neutrons N and mass number A. Radioactive decay follows N = N₀ e⁻λt, with half-life T½ = ln2/λ. Alpha, beta (β⁻ and β⁺) and gamma decays change the nucleus. Mass–energy equivalence E = mc² explains binding energy and fusion/fission energy release. The Standard Model classifies leptons, quarks and exchange bosons; the Higgs boson is responsible for mass.
原子核结构包含质子数 Z、中子数 N 和质量数 A。放射性衰变遵循 N = N₀ e⁻λt，半衰期 T½ = ln2/λ。α、β（β⁻ 和 β⁺）和 γ 衰变改变原子核。质能等价 E = mc² 解释了结合能以及聚变/裂变能量的释放。标准模型将粒子分为轻子、夸克和规范玻色子；希格斯玻色子赋予粒子质量。
8. Energy Production | 能源生产
Energy sources are classified as renewable (solar, wind, hydro, tidal, geothermal, biomass) and non-renewable (fossil fuels, nuclear). The energy density and specific energy of fuels determine their practicality. Sankey diagrams display energy degradation, and efficiency is η = useful output/input. Conduction, convection and radiation transfer thermal energy.
能源分为可再生能源（太阳能、风能、水力、潮汐能、地热、生物质）和不可再生能源（化石燃料、核能）。燃料的能量密度和比能决定其实用性。桑基图展示能量贬损，效率 η = 有用输出/输入。热传导、对流和辐射传递热能。
In a nuclear reactor, controlled fission of Uranium-235 releases energy. Binding energy per nucleon peaks at iron-56, making fusion of light nuclei and fission of heavy nuclei energetically favourable. Photovoltaic cells convert solar radiation directly into electricity with a certain efficiency. The carbon cycle and greenhouse effect are also examined in the context of global energy balances.
核反应堆中，铀-235 的受控裂变释放能量。每核子结合能在铁-56 处最大，从而使轻核聚变和重核裂变在能量上有利。光伏电池以一定效率直接将太阳辐射转化为电能。在全球能量平衡的背景下，碳循环和温室效应也纳入考察。
9. Relativity (Option) | 相对论（选修）
An inertial frame moves with constant velocity. The two postulates of special relativity are: the laws of physics are the same in all inertial frames, and the speed of light in vacuum c is invariant. Time dilation Δt = γΔt₀ and length contraction L = L₀/γ, where the Lorentz factor γ = 1/√(1 − v²/c²), explain why moving clocks run slow and moving rods shorten.
惯性系作匀速直线运动。狭义相对论的两条基本假设是：物理定律在所有惯性系中相同，真空光速 c 不变。时间膨胀 Δt = γΔt₀ 以及长度收缩 L = L₀/γ，其中洛伦兹因子 γ = 1/√(1 − v²/c²)，解释了为何运动时钟变慢、运动米尺缩短。
Relativistic momentum p = γmv, total energy E = γmc², and rest energy E₀ = mc². The threshold frequency for pair production is f_min = 2mₑc²/h. In general relativity, gravity is the curvature of spacetime; gravitational lensing and black holes are consequences. These ideas are directly examined in the IB Option topic and require both qualitative and quantitative understanding.
相对论动量 p = γmv，总能量 E = γmc²，静止能量 E₀ = mc²。电子对产生的最低频率为 f_min = 2mₑc²/h。在广义相对论中，引力是时空的弯曲；引力透镜和黑洞就是其推论。这些观念在 IB 选修专题中直接考查，需要定性和定量两方面的理解。
10. Astrophysics (Option) | 天体物理（选修）
Apparent magnitude m and absolute magnitude M relate to brightness. Luminosity L of a star is a measure of its total power output. The electromagnetic spectrum from radio to gamma rays reveals stellar composition. Wien’s displacement law λ_max T = 2.9 × 10⁻³ m K and Stefan-Boltzmann law L = 4πR² σT⁴ allow astronomers to determine a star’s temperature and radius.
视星等 m 和绝对星等 M 与亮度相关。恒星的光度 L 量度其总辐射功率。从射电到伽马射线的电磁波谱揭示了恒星的成分。维恩位移定律 λ_max T = 2.9 × 10⁻³ m K 和斯特藩-玻尔兹曼定律 L = 4πR² σT⁴ 使天文学家能够确定恒星的温度和半径。
The Hertzsprung-Russell diagram plots luminosity against temperature, showing the main sequence, red giants and white dwarfs. Nuclear fusion in stellar cores proceeds through the proton-proton chain or CNO cycle, creating elements up to iron. The Hubble law v = H₀d provides evidence for the expanding Universe, and cosmic microwave background radiation supports the Big Bang model.
赫罗图将光度对温度作图，展示了主序星、红巨星和白矮星。恒星核心的核聚变通过质子-质子链或 CNO 循环进行，产生了直至铁的元素。哈勃定律 v = H₀d 为宇宙膨胀提供了证据，而宇宙微波背景辐射支持大爆炸模型。
11. How to Master the 396 Key Concepts | 如何掌握这 396 个核心概念
Break the syllabus into manageable chunks (e.g., 10 concepts per day) and use active recall: after studying a concept, close the book and explain it aloud or write a summary without looking. Practise past-paper questions that specifically test each concept, and track your mistakes in a log. Use the IB data booklet as a constant reference, ensuring you understand the origin and limitations of every formula.
将大纲分解成易于管理的模块（例如每天 10 个概念），并使用主动回忆法：学完一个概念后，合上书，大声解释或默写总结。练习直接考查每个概念的历年真题，并在错题本中记录错误。将 IB 公式手册作为常备参考，确保理解每个公式的来源和适用条件。
Diagrams and visual maps, such as mind maps linking energy, forces and fields, reinforce connections between concepts. Peer teaching also consolidates understanding; join a study group where each member presents one topic. Finally, simulate timed exam conditions frequently, because applying concepts under pressure is a skill that can only be built through practice.
图表和视觉导图，例如将能量、力和场联系起来的思维导图，可以强化概念之间的关联。同伴教学也能巩固理解；参加学习小组，每位成员讲解一个主题。最后，经常模拟限时考试环境，因为在压力下应用概念是一项唯有通过练习才能练就的技能。
12. Conclusion | 结语
The 396 concepts encapsulated in “Physics for the IB Diploma” may appear overwhelming, but they are interconnected and logical once you see the big picture. From the smallest particles to the largest cosmic structures, physics explains the universe. Consistent, structured revision of these concepts, coupled with problem-solving, will give you both deep insight and the examination technique to achieve a top grade in IB Physics.
《Physics for the IB Diploma》所提炼的 396 个概念或许看似庞杂，但一旦你把握住大框架，它们便是相互关联且逻辑清晰的。从最小的粒子到最大的宇宙结构，物理学解释着天地万物。持续、有条理地复习这些概念并辅以解题训练，将使你既获得深刻的洞见，又掌握在 IB 物理中斩获高分的应试技巧。
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