📚 IB Physics: High-Frequency Exam Topic Summary | IB 物理：高频考点总结
IB Physics examinations consistently test a core set of principles across the syllabus, and understanding these high-frequency topics is the most efficient way to boost your score. This article consolidates the most commonly examined concepts, formulas, and pitfalls in both Standard Level and Higher Level, enabling targeted revision.
IB 物理考试始终从大纲中提炼一套核心原理进行考查，掌握这些高频考点是提高分数最有效的方法。本文汇总了标准水平和高水平最常见的概念、公式及易错点，帮助你有针对性地复习。
1. Measurements and Uncertainties | 测量与不确定度
Every IB Physics paper includes questions on uncertainties. You must be able to calculate absolute, fractional, and percentage uncertainties, and combine them correctly for sums/differences (add absolute uncertainties) and products/quotients (add fractional uncertainties).
每份 IB 物理试卷都会出现不确定度相关题目。你必须能够计算绝对不确定度、相对不确定度和百分比不确定度，并针对加减运算（绝对不确定度相加）和乘除运算（相对不确定度相加）正确合成。
ty of 3 Ω, the fractional uncertainty is 3/150 = 0.02, and the percentage uncertainty is 2 % tainty in P is twice the percentage uncertainty in V plus the percentage uncertainty in R.
如果一个电阻 R 测量值为 150 Ω，绝对不确定度为 3 Ω，那么相对不确定度为 3/150 = 0.02，百分比不确定度为 2 %。当 R 用于电路中通过 P = V²/R 计算功率时，P 的百分比不确定度等于 V 百分比不确定度的两倍加上 R 的百分比不确定度。
Vector quantities (displacement, velocity, acceleration, force, momentum) must be added with attention to direction. Always resolve vectors into perpendicular components when necessary.
矢量（位移、速度、加速度、力、动量）相加时必须注意方向。必要时总要将矢量分解为互相垂直的分量。
2. Mechanics: Kinematics and Dynamics | 力学：运动学与动力学
The suvat equations are the backbone of kinematics, applicable only when acceleration is constant. Remember the four forms and select the one that does not involve the missing variable.
匀变速运动方程是运动学的基石，仅适用于加速度恒定的情况。熟记四个方程，并选择不含未知量的那个进行求解。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = (u+v)t/2
Newton's second law, Fnet and write the net force equation clearly for each axis. Static and kinetic friction (f ≤ μsN and f = μkN) are frequent distractors.
牛顿第二定律 Fnet = ma 必须结合受力图使用。画出所有力，将有角度的力分解，并分别写出各轴的合力方程。静摩擦力和动摩擦力（f ≤ μsN 和 f = μkN）是常见的干扰项。
Terminal velocity occurs when air resistance balances weight. At this point, net force is zero and acceleration becomes zero, giving a constant maximum speed.
当空气阻力与重力平衡时达到终极速度。此时合力为零，加速度为零，速度保持恒定的最大值。
3. Work, Energy and Power | 功、能量与功率
along the displacement and the displacement itself: W = F s cos θ. The area under a force–displacement graph represents work done.
功等于力沿位移方向的分量与位移的乘积：W = F s cos θ。力-位移图下的面积代表做功的多少。
Kinetic energy (Ek = ½mv²) and gravitational potential energy (Ep = mgh) are linked by the work– ation of energy. In the absence of friction, the total mechanical energy remains constant.
动能 (Ek = ½mv²) 和重力势能 (Ep = mgh) 通过功-能定理和能量守恒联系起来。在没有摩擦的情况下，总机械能保持不变。
ut energy (or power). Power is the rate of doing work: P = W/t = F v, where v is velocity.
效率是有用输出能量（或功率）与总输入能量（或功率）的比值。功率是做功的快慢：P = W/t = F v，其中 v 是速度。
ing down a frictionless incline, which is best solved using energy conversion: mgh = ½mv².
常见题目要求计算物体沿无摩擦斜面下滑后的速度，最佳解法是用能量转化：mgh = ½mv²。
4. Momentum and Impulse | 动量与冲量
Momentum p = mv is a vector; impulse J = F Δt = Δp. The area under a force– In collisions and explosions, momentum is conserved in the absence of external net forces.
动量 p = mv 是矢量；冲量 J = F Δt = Δp。力-时间图下的面积表示冲量。在没有外合力的碰撞和爆炸过程中，动量守恒。
so conserves kinetic energy. In inelastic collisions, kinetic energy is not conserved, but momentum is always conserved.
对于两体碰撞，m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。弹性碰撞还同时满足动能守恒。非弹性碰撞中，动能不守恒，但动量总是守恒的。
Relative speed of approach equals relative speed of separation for perfectly elastic collisions in one dimension. This relationship simplifies solving for final velocities.
对于一维完全弹性碰撞，接近的相对速度等于分离的相对速度。这个关系可以简化末速度的求解。
5. Circular Motion and Gravitation | 圆周运动与万有引力
Remember that centripetal force is not a separate force; it is provided by tension, gravity, friction, or normal reaction.
向心加速度 a = v²/r = ω²r 始终指向圆心，向心力 F = mv²/r = mω²r。注意向心力并不是一个独立的力；它由拉力、重力、摩擦力或法向反作用力提供。
Newton' ular orbit, gravitational force provides centripetal force: GMm/r² = mv²/r, leading to v = √GM/r and T² ∝ r³.
牛顿万有引力定律：F = G M m / r²。对于做圆周运动的卫星，引力提供向心力：GMm/r² = mv²/r，由此可得 v = √GM/r 并且 T² ∝ r³。
/R². Apparent weightlessness in orbiting spacecraft is due to free-fall, not zero gravity.
引力场强度 g = F/m，在行星表面有 g = GM/R²。轨道飞行器中的表观失重是由于自由下落，而非重力为零。
6. Thermal Physics | 热学
Temperature measures the average random kinetic energy of particles. Internal energy is the sum of random kinetic energy and intermolecular potential energy. During a phase change, temperature remains constant while potential energy changes.
温度量度粒子随机热运动的平均动能。内能是随机动能和分子间势能的总和。在相变过程中，温度保持不变，但势能发生变化。
y interpret heating curves and distinguish between latent heat of fusion and vaporisation.
比热容公式 Q = m c ΔT，比潜热公式 Q = m L。要能正确解读加热曲线，并区分熔化潜热和汽化潜热。
The ideal gas laws are linked to the kinetic model: p ∝ T (at constant V), V ∝ t p), and p V = constant (at constant T). The absolute temperature in Kelvin must be used.
理想气体定律与分子动理论模型相联系：p ∝ T（恒容），V ∝ T（恒压），p V = 常数（恒温）。必须使用开尔文温标。
The ideal gas equation pV = nRT and its kinetic form pV = ⅓ N m
理想气体状态方程 pV = nRT 及其动力论形式 pV = ⅓ N m
7. Waves and Oscillations | 波与振动
T. At maximum displacement, velocity is zero and acceleration is maximum; at equilibrium, velocity is maximum and acceleration is zero.
简谐运动要求恢复力与位移成正比：F = -k x，从而 a = -ω²x。关键关系：T = 1/f，ω = 2πf = 2π/T。在最大位移处，速度为零、加速度最大；在平衡位置，速度最大、加速度为零。
c and potential, but total energy remains constant and equals ½mω²A². The period of a mass–spring system is T = 2π√m/k; for a simple pendulum, T = 2π√l/g.
简谐运动中的能量在动能和势能之间转换，但总能量保持不变，为 ½mω²A²。弹簧振子的周期 T = 2π√m/k；单摆的周期 T = 2π√l/g。
rence. Transverse waves (light) can be polarised; longitudinal waves (sound) cannot. Superposition, standing waves, and diffraction are examined frequently.
波的性质：v = f λ，波上两点之间的相位差可以用 (2π/λ) × 路程差表示。横波（光）可以偏振；纵波（声）不能。叠加、驻波和衍射是常考内容。
nterference occurs when d sin θ = n λ. Path difference and phase difference are closely tested.
单缝衍射产生中央亮纹，极小条件为 b sin θ = n λ。双缝干涉中，当 d sin θ = n λ 时出现加强干涉。路程差和相位差是重点考查对象。
8. Electricity and Magnetism | 电与磁
Ohm' d cross-sectional area: R = ρ L / A. Potential dividers are essential for sensor circuits.
欧姆定律 V = IR 适用于恒温下的欧姆导体。电阻取决于电阻率、长度和横截面积：R = ρ L / A。分压器在传感器电路中至关重要。
of a cell causes terminal pd V = ε - I r. The emf ε can be found from the intercept of a V–I graph; r is the negative gradient.
电池内阻 r 使得路端电压 V = ε - I r。电动势 ε 可以从 V-I 图的截距求得；内阻 r 为负斜率。
v B sin θ. For a current-carrying wire: F = B I L sin θ. The direction is given by Fleming' perpendicular to a uniform magnetic field follows a circular path with radius r = mv/(Bq).
运动电荷在磁场中受力：F = q v B sin θ。载流导线受力：F = B I L sin θ。方向由左手定则判定。带电粒子垂直于均匀磁场运动时，做半径为 r = mv/(Bq) 的圆周运动。
Electromagnetic induction: induced emf ε = -N ΔΦ/Δt. Magnetic flux Φ = B A cos θ. Faraday's law and Lenz' transformers. An alternating current is produced when a coil rotates in a magnetic field.
电磁感应：感应电动势 ε = -N ΔΦ/Δt。磁通量 Φ = B A cos θ。法拉第定律和楞次定律可以解释发电机和变压器的工作原理。线圈在磁场中转动时会产生交流电。
9. Atomic, Nuclear and Particle Physics | 原子、核与粒子物理学
tomic mass unit u is defined as 1/12 of the mass of a carbon-12 atom; 1 u = 931.5 MeV c⁻².
原子结构：质子、中子、电子；Z 为质子数，A 为核子数。同位素具有相同的 Z，不同的 A。统一原子质量单位 u 定义为碳-12 原子质量的 1/12；1 u = 931.5 MeV c⁻²。
Radioactive decay follows the exponential law N = N₀ e-λ t us, and gamma decays must be balanced in terms of atomic and mass numbers. Neutrino emission accompanies beta decay.
放射性衰变遵循指数规律 N = N₀ e-λ t，半衰期 T₁/₂ = ln2 / λ。活度 A = λ N。α 衰变、β⁻ 衰变、β⁺ 衰变和 γ 衰变必须满足原子序数和质量数守恒。β 衰变伴随着中微子的发射。
Mass defect and binding energy: the mass of a nucleus is less than the sum of its constituent nucleons. Binding energy per nucleon peaks at iron-56, explaining fusion and fission energy release. Nuclear reactions must be written with conservation of nucleon number and charge.
质量亏损和结合能：原子核的质量小于其组成核子质量之和。比结合能在铁-56 附近达到峰值，这解释了聚变和裂变的能量释放。书写核反应方程时要确保核子数和电荷守恒。
Particle physics introduces quarks, leptons, and exchange particles. Protons are uud, neutrons are udd. The strong force is mediated by gluons, the weak force by W and Z bosons. Conservation rules (baryon number, lepton number, strangeness) dictate allowed interactions.
粒子物理学引入了夸克、轻子和交换粒子。质子由 uud 组成，中子由 udd 组成。强力由胶子传递，弱力由 W 和 Z 玻色子传递。守恒律（重子数、轻子数、奇异数）决定了允许的反应。
10. Energy Production and Global Warming | 能源生产与全球变暖
agrams illustrate energy transfers; the width of each arrow is proportional to the amount of energy.
需要比较燃料的能量密度和比能量：能量密度 = 单位体积能量；比能量 = 单位质量能量。桑基图用于表示能量传递；每条箭头的宽度与能量大小成正比。
Power generation from fossil fuels, nuclear fission, wind, solar, hydroelectric, and pumped storage is evaluated in terms of efficiency, cost, and environmental impact. The greenhouse effect is enhanced by CO₂ and methane, leading to global warming.
化石燃料、核裂变、风能、太阳能、水力发电和抽水蓄能等发电方式需从效率、成本和环境影响等方面进行评价。二氧化碳和甲烷加剧了温室效应，从而导致全球变暖。
on. Black-body radiation curves peak at shorter wavelengths as temperature increases (Wien's displacement law: λₘₐₓ T = constant). The solar constant is about 1360 W m⁻².
反照率是反射辐射与入射辐射的比值。黑体辐射曲线随着温度升高，峰值波长变短（维恩位移定律：λₘₐₓ T = 常数）。太阳常数约为 1360 W m⁻²。
Simple models of the energy balance for the Earth often appear, requiring you to calculate equilibrium temperature considering albedo and emissivity. These connect thermal physics to real-world energy issues.
常出现地球能量平衡的简化模型，要求结合反照率和发射率计算平衡温度。这就将热学与现实能源议题联系了起来。
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