📚 IB and Edexcel Physics: Summary of High-Frequency Exam Topics | IB Edexcel 物理：高频考点总结
Both IB Physics and Edexcel A Level Physics share a core set of principles that appear again and again in exams. This article distills the most frequently tested topics, offering key formulas, common pitfalls, and conceptual links to help you prepare efficiently. Reviewing these high-yield areas will strengthen your understanding and boost your confidence for both multiple-choice and structured questions.
IB 物理和 Edexcel A Level 物理共享一套核心原理，这些原理在考试中反复出现。本文提炼了最高频的考点，提供关键公式、常见陷阱和概念联系，帮助你高效备考。复习这些高回报领域将加强你的理解，并提高你在选择题和结构化题目中的信心。
1. Kinematics and Projectile Motion | 运动学与抛体运动
The kinematic equations (SUVAT) are a staple in Mechanics. Remember they only apply when acceleration is constant. In projectile problems, resolve motion into horizontal and vertical components: horizontal velocity is constant, while vertical motion experiences free-fall acceleration g = 9.81 m/s². Always set a clear sign convention for up/down directions before substituting values.
运动学方程（SUVAT）是力学中的基本工具。要记住它们仅在加速度恒定时适用。在抛体问题中，将运动分解为水平与竖直分量：水平速度不变，竖直方向则受自由落体加速度 g = 9.81 m/s² 影响。代入数值前务必为向上/向下设定清晰的符号约定。
v = u + at s = ut + ½at² v² = u² + 2as s = ½(u+v)t
A classic exam trick is to ask for the time of flight or range of a projectile launched at an angle. Always find time from the vertical motion first, then use horizontal distance = uₓ × t. Do not mix up sin θ and cos θ; draw a triangle and label the components clearly.
一个经典考题技巧是求抛体的飞行时间或射程。始终先从竖直运动求出时间，再用水平距离 = uₓ × t。不要混淆 sin θ 和 cos θ；画出三角形并清楚标出分量。
2. Newton’s Laws and Free-Body Diagrams | 牛顿定律与受力分析
Newton’s three laws underpin all force analysis. The second law, F = ma, is an equation of vector sums. Always draw a free-body diagram showing all forces acting on the object, then resolve along perpendicular axes. For inclined planes, the weight component down the slope is mg sin θ, and the normal reaction is mg cos θ. Watch out for friction that can act either up or down the slope depending on the direction of impending motion.
牛顿三大定律是所有受力分析的基础。第二定律 F = ma 是矢量求和方程。务必画出物体所受全部力的受力图，然后沿垂直轴分解。对于斜面，沿斜面向下的重力分量为 mg sin θ，法向反作用力为 mg cos θ。注意摩擦力方向可能沿斜面向上或向下，取决于运动趋势。
Elevator problems and connected particles (pulley systems) are very common. In pulleys, treat each mass separately and link them through the tension T and inextensible string conditions. Remember that the magnitude of acceleration is the same for both masses if the string remains taut.
电梯问题和连接体（滑轮系统）非常常见。在滑轮问题中，分别处理每个物体，并通过张力 T 和不可伸长绳的条件将它们联系起来。如果绳子保持绷紧，两物体的加速度大小相等。
3. Work, Energy, and Power | 功、能与功率
The work done by a force is F s cos θ, where θ is the angle between the force and displacement. The work–energy theorem states that the net work done equals the change in kinetic energy. Gravitational potential energy is mgh, but only valid near the Earth’s surface. In isolated systems, total mechanical energy is conserved if only conservative forces (gravity, springs) act. When non-conservative forces like friction do work, mechanical energy is not conserved, and energy is dissipated as heat.
力做的功为 F s cos θ，其中 θ 是力与位移的夹角。功能原理指出：合力所做的功等于动能的变化量。重力势能为 mgh，但仅在地表附近有效。在孤立系统中，如果只有保守力（重力、弹簧）做功，则总机械能守恒。当摩擦力等非保守力做功时，机械能不守恒，能量转化为内能。
P = F v (for constant force and velocity in same direction)
Power is the rate of energy transfer. In vehicle problems, the driving force can be found via P = F v for a given power output. Note that maximum speed occurs when the driving force equals the total resistive force. Efficiency as the ratio of useful output power to total input power is also tested.
功率是能量转化的速率。在车辆问题中，可由 P = F v 根据给定功率求出牵引力。注意最大速度出现在牵引力等于总阻力时。效率即有用输出功率与总输入功率之比，也是考点。
4. Momentum and Impulse | 动量与冲量
Momentum p = m v is a vector. The impulse exerted on an object equals the change in momentum, Δp = F Δt. In collisions and explosions, if no external net force acts, total momentum is conserved. Be careful with direction: set a positive axis and assign signs to velocities before and after.
动量 p = m v 是矢量。施加在物体上的冲量等于动量变化，Δp = F Δt。在碰撞和爆炸中，若无合外力作用，总动量守恒。务必注意方向：设定正方向，并给前后速度赋予正负号。
Elastic collisions conserve kinetic energy as well as momentum; inelastic collisions do not. The coefficient of restitution e is not explicitly required in all syllabi but appears in Edexcel Mathematics Mechanics links; for IB, perfectly inelastic collisions (objects stick together) are more common. Always check if kinetic energy is lost and be ready to calculate it.
弹性碰撞既守恒动量又守恒动能；非弹性碰撞不守恒动能。恢复系数 e 并非所有大纲都明确要求，但在 Edexcel 数学力学中出现；对 IB 而言，完全非弹性碰撞（粘在一起）更常见。务必检查动能是否损失，并准备好计算损失量。
5. Circular Motion and Gravitation | 圆周运动与万有引力
An object moving in a circle at constant speed experiences a centripetal acceleration a = v²/r = ω²r, directed towards the centre. The centripetal force is F = m v²/r = m ω²r. This is not a distinct force but a resultant provided by tension, friction, gravity, or normal reaction. Banked tracks, vertical circles, and conical pendulums are favourite exam scenarios.
匀速圆周运动的物体具有向心加速度 a = v²/r = ω²r，方向指向圆心。向心力 F = m v²/r = m ω²r。这不是一种独立的力，而是由张力、摩擦力、重力或法向反作用力提供的合力。倾斜弯道、竖直圆环和锥摆是常见的考题情境。
F = G M m / r² and g = G M / r²
Newton’s law of gravitation is universal. For satellites, equate gravitational force to centripetal force to find orbital speed v = √(GM/r). Kepler’s third law T² ∝ r³ can be derived from this. Geostationary orbits have period T = 24 hours and lie in the equatorial plane. Understand how gravitational field strength g varies with altitude and inside the Earth.
万有引力定律是普适的。对于卫星，令万有引力等于向心力可求得轨道速率 v = √(GM/r)。由此可推导开普勒第三定律 T² ∝ r³。地球同步轨道周期 T = 24 小时且位于赤道平面。理解重力场强 g 如何随高度和地球内部变化。
6. Simple Harmonic Motion (SHM) | 简谐运动
SHM occurs when acceleration is proportional to displacement from equilibrium and directed opposite to it: a = -ω²x. The defining equation leads to solutions x = A sin(ωt) or x = A cos(ωt). Velocity is v = ± ω √(A² – x²). Period of a mass-spring system: T = 2π √(m/k); for a simple pendulum: T = 2π √(l/g). Energy in SHM interchanges between kinetic and potential, but total energy = ½ m ω² A² remains constant (for undamped).
当加速度与相对于平衡位置的位移成正比且方向相反时，物体做简谐运动：a = -ω²x。这一方程的解为 x = A sin(ωt) 或 x = A cos(ωt)。速度表达式为 v = ± ω √(A² – x²)。弹簧振子周期：T = 2π √(m/k)；单摆周期：T = 2π √(l/g)。简谐运动的能量在动能和势能之间转化，但总能量 = ½ m ω² A² 保持不变（无阻尼情况下）。
Forced oscillations and resonance are linked: when driving frequency equals natural frequency, amplitude becomes very large. Damping reduces amplitude and shifts the resonant peak to a slightly lower frequency. Be able to sketch amplitude–frequency graphs for light, heavy, and critical damping. Also, phase difference between displacement, velocity, and acceleration is often tested: velocity leads displacement by π/2, acceleration leads by π.
受迫振动与共振相关联：当驱动频率等于固有频率时，振幅急剧增大。阻尼会减小振幅并使共振峰向略低频率方向移动。要能勾画轻阻尼、重阻尼和临界阻尼下的幅频曲线。此外，位移、速度与加速度间的相位差也常考：速度领先位移 π/2，加速度领先 π。
7. Waves, Superposition, and Interference | 波、叠加与干涉
The general wave equation v = f λ links speed, frequency, and wavelength. For waves on a string, v = √(T/μ), where μ is linear density. Sound, water, and electromagnetic waves each have their own characteristics. Pay close attention to phase and path difference: constructive interference when path difference = nλ, destructive when = (n + ½)λ.
波动普遍方程 v = f λ 关联波速、频率和波长。弦上波速 v = √(T/μ)，其中 μ 是线密度。声波、水波和电磁波各有特性。要高度重视相位差和波程差：波程差为 nλ 时发生相长干涉，为 (n + ½)λ 时发生相消干涉。
Young’s double-slit experiment measures fringe spacing Δy = λD/d, where D is screen distance and d slit separation. Diffraction gratings give sharp maxima at d sin θ = nλ. Single-slit diffraction produces a central maximum of angular width 2λ/a (a is slit width). Be ready to compare patterns and explain how slit separation or wavelength affects fringe width.
杨氏双缝实验测量条纹间距 Δy = λD/d，其中 D 为屏幕距离，d 为缝距。衍射光栅在 d sin θ = nλ 处产生锐利的极大值。单缝衍射产生角宽度为 2λ/a 的中央明纹（a 为缝宽）。要准备好比较图样，并解释缝距或波长如何影响条纹宽度。
Standing waves form when two progressive waves of the same frequency travel in opposite directions. Nodes are points of zero displacement, antinodes of maximum displacement. For pipes and strings, remember the boundary conditions: fixed end → node, free end → antinode. Calculate harmonic frequencies: for a string fixed at both ends, f = n v/(2L); for an open pipe, f = n v/(2L); for a closed pipe, f = (2n-1) v/(4L).
驻波由两列相同频率、相向传播的行波叠加而成。波节是位移为零的点，波腹是位移最大的点。对于管和弦乐器，记住边界条件：固定端→波节，自由端→波腹。计算谐频：两端固定的弦 f = n v/(2L)；开管 f = n v/(2L)；闭管 f = (2n-1) v/(4L)。
8. Electricity and Circuits | 电学与电路
Ohm’s law V = IR applies to ohmic conductors at constant temperature. Resistivity ρ links resistance to geometry: R = ρL/A. Series circuits share current, sum p.d.; parallel circuits share p.d., sum currents. The internal resistance r of a cell causes terminal p.d. V = ε – I r. Precisely, ε = I(R + r). A common experiment is to plot V vs I and find ε and r from the intercept and gradient.
欧姆定律 V = IR 适用于恒温下的欧姆导体。电阻率 ρ 将电阻与几何形状关联：R = ρL/A。串联电路电流相同、电势差相加；并联电路电势差相同、电流相加。电源内阻 r 使端电压 V = ε – I r。准确地说，ε = I(R + r)。一个常见实验是绘制 V-I 图，从截距和斜率求出 ε 和 r。
Potential dividers: Vₒᵤₜ = Vᵢₙ × R₂/(R₁+R₂). This is often used with sensors (LDR, thermistor) to change output voltage. Kirchhoff’s two laws are essential for complex circuits. Use the junction rule (Σ I = 0) and loop rule (Σ ε = Σ IR) methodically, assigning consistent directions.
分压器：Vₒᵤₜ = Vᵢₙ × R₂/(R₁+R₂)。这常与传感器（光敏电阻、热敏电阻）结合以改变输出电压。基尔霍夫两条定律对复杂电路至关重要。系统地使用节点电流定律 (Σ I = 0) 和回路电压定律 (Σ ε = Σ IR)，并保持一致的电流方向。
9. Electric and Magnetic Fields | 电场与磁场
Electric fields: E = F/q, and for a uniform field between parallel plates, E = V/d. The force on a charge q in a field is F = qE. Coulomb’s law for point charges: F = k Q₁Q₂/r². Be familiar with field line patterns for point charges and parallel plates. A charged particle moving through a uniform electric field follows a parabolic path, analogous to a projectile in a gravitational field.
电场：E = F/q，匀强电场（如平行板间）E = V/d。场中电荷 q 受力 F = qE。点电荷间库仑定律：F = k Q₁Q₂/r²。要熟悉点电荷和平行板的电场线图样。带电粒子在匀强电场中运动轨迹为抛物线，类似于引力场中的抛体运动。
Magnetic fields exert a force on moving charges: F = q v B sin θ, with direction given by Fleming’s left-hand rule. For a current-carrying wire, F = B I L sin θ. Charged particles move in circular paths in uniform magnetic fields; equate q v B = m v²/r to find radius r = m v/(q B). The Hall effect and cyclotron frequency are advanced but examinable. Magnetic flux density B is measured in tesla.
磁场对运动电荷施加力：F = q v B sin θ，方向由弗莱明左手定则确定。载流导线受力 F = B I L sin θ。带电粒子在匀强磁场中做圆周运动，令 q v B = m v²/r 得半径 r = m v/(q B)。霍尔效应和回旋频率属进阶但有考的可能。磁通密度 B 的单位是特斯拉。
Electromagnetic induction: Faraday’s law, ε = -N ΔΦ/Δt, and Lenz’s law determining the direction of induced current. Flux Φ = B A cos θ. Transformer equation: Nₛ/Nₚ = Vₛ/Vₚ (ideal). Generators and moving rod in B-field are common applied questions.
电磁感应：法拉第定律 ε = -N ΔΦ/Δt，以及楞次定律确定感应电流的方向。磁通量 Φ = B A cos θ。变压器公式：Nₛ/Nₚ = Vₛ/Vₚ（理想情况）。发电机和导体棒在磁场中的运动是常见应用题。
10. Quantum and Nuclear Physics | 量子与核物理
The photoelectric effect demonstrates the particle nature of light. The key equation: h f = Φ + Eₖₘₐₓ, where Φ is the work function. Stopping potential Vₛ is related by e Vₛ = Eₖₘₐₓ. Threshold frequency f₀ = Φ/h. Observations that cannot be explained by wave theory: instantaneous emission, existence of threshold frequency, and independence of intensity on maximum kinetic energy.
光电效应证实了光的粒子性。关键公式：h f = Φ + Eₖₘₐₓ，其中 Φ 为逸出功。遏止电势 Vₛ 满足 e Vₛ = Eₖₘₐₓ。截止频率 f₀ = Φ/h。波动理论无法解释的现象：瞬时发射、截止频率的存在、最大动能与光强无关。
Atomic energy levels: electrons can only occupy discrete energy levels. When an electron transitions between levels, a photon is emitted or absorbed with ΔE = h f. Emission and absorption spectra provide experimental evidence. Understand the hydrogen spectrum and the series (Lyman, Balmer) and their UV/visible regions.
原子能级：电子只能占据分立的能级。当电子在能级间跃迁时，会发射或吸收光子，且 ΔE = h f。发射光谱和吸收光谱提供了实验证据。理解氢原子光谱及线系（赖曼系、巴耳末系）及其所在紫外/可见光区。
Nuclear physics: Radioactive decay law N = N₀ e⁻λt, half-life T₁/₂ = ln 2/λ. Activity A = λ N. Alpha, beta, and gamma radiation have different ionising and penetrating abilities. Mass defect and binding energy: E = Δm c². Fission and fusion both release energy because binding energy per nucleon peaks near iron. Be able to sketch and interpret the N-Z curve and explain why unstable nuclei undergo specific decay modes.
核物理：放射性衰变定律 N = N₀ e⁻λt，半衰期 T₁/₂ = ln 2/λ。放射性活度 A = λ N。α、β、γ 射线具有不同的电离能力和穿透能力。质量亏损和结合能：E = Δm c²。裂变和聚变都能释放能量，因为比结合能在铁附近达到峰值。要能够勾画并解释 N-Z 曲线，说明不稳定核为何采取特定的衰变方式。
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