📚 IB & Edexcel Physics: Last-Minute Revision Notes | IB 与 Edexcel 物理：考前冲刺笔记
These last-minute revision notes condense the essential concepts, equations, and problem-solving strategies for IB and Edexcel Physics. Whether you are reviewing mechanics, waves, electricity, or modern physics, the following sections provide a clear and structured recap of the most examinable content. Each topic is presented in a concise bilingual format to help you quickly identify key relationships and avoid common pitfalls.
这份考前冲刺笔记浓缩了 IB 和 Edexcel 物理的核心概念、公式和解题策略。无论你正在复习力学、波动、电学还是现代物理，以下各节都以清晰的结构重现了最常考的内容。每个主题采用简洁的双语对照形式，帮助你快速把握关键关系，避开常见陷阱。
1. Kinematics and Motion Graphs | 运动学与运动图像
Displacement is a vector from the initial to final position; distance is a scalar. Velocity is the rate of change of displacement, while acceleration is the rate of change of velocity.
位移是从初位置指向末位置的矢量；路程是标量。速度是位移对时间的变化率，而加速度是速度对时间的变化率。
For constant acceleration in one dimension, use the SUVAT equations: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u + v)t. These require consistent signs for direction.
对于一维匀加速运动，可使用 SUVAT 方程组：v = u + at、s = ut + ½at²、v² = u² + 2as 和 s = ½(u + v)t。使用时需注意方向的正负号一致。
Motion graphs help visualise relationships: the slope of a displacement–time graph gives velocity; the slope of a velocity–time graph gives acceleration, and its area gives displacement.
运动图像有助于直观理解：位移-时间图的斜率表示速度；速度-时间图的斜率表示加速度，其面积表示位移。
For projectile motion, resolve into horizontal (constant velocity) and vertical (constant acceleration g = 9.81 m s⁻²) components. Time of flight links the two independent motions.
对于抛体运动，可分解为水平方向（匀速）和竖直方向（匀加速 g = 9.81 m s⁻²）。飞行时间是联系这两个独立运动的关键。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s first law states that an object remains at rest or in uniform motion unless acted upon by a resultant force. Inertia is the tendency to resist changes in motion.
牛顿第一定律指出，除非受到合外力作用，物体将保持静止或匀速直线运动状态。惯性是物体抵抗运动状态改变的性质。
Newton’s second law: F = ma (resultant force = mass × acceleration). Always apply this to the net force in a given direction.
牛顿第二定律：F = ma（合外力 = 质量 × 加速度）。务必对指定方向上的合外力应用此定律。
Newton’s third law: action–reaction pair forces are equal in magnitude, opposite in direction, and act on different bodies. Do not confuse them with balanced forces on a single body.
牛顿第三定律：作用力与反作用力大小相等、方向相反，且作用在不同的物体上。切勿将其与作用在同一物体上的平衡力混淆。
Weight W = mg acts downwards; normal reaction N is perpendicular to the surface. Friction f ≤ μN, where static friction adapts up to a limit, and kinetic friction is constant.
重力 W = mg 竖直向下；法向支撑力 N 垂直于接触面。摩擦力 f ≤ μN，其中静摩擦力随外力增大至最大值，动摩擦力保持恒定。
Draw free-body diagrams showing all forces as arrows from the centre of mass. Resolve inclined plane forces into parallel (mg sin θ) and perpendicular (mg cos θ) components.
画出受力示意图，用从质心出发的箭头表示所有力。在处理斜面问题时，将重力分解为沿斜面分量（mg sin θ）和垂直斜面分量（mg cos θ）。
3. Work, Energy and Power | 功、能与功率
Work done by a constant force is W = F s cos θ, where θ is the angle between force and displacement. Energy is the capacity to do work; both are scalar quantities measured in joules (J).
恒力做功为 W = F s cos θ，其中 θ 是力与位移的夹角。能量是做功的本领；两者都是标量，单位为焦耳 (J)。
Kinetic energy: Eₖ = ½mv². Gravitational potential energy near Earth’s surface: Eₚ = mgΔh. Elastic potential energy in a spring: Eₑ = ½k x², where k is the spring constant and x is the extension or compression.
动能：Eₖ = ½mv²。地表附近的重力势能：Eₚ = mgΔh。弹簧的弹性势能：Eₑ = ½k x²，其中 k 为劲度系数，x 为伸长或压缩量。
The principle of conservation of energy: energy cannot be created or destroyed, only transformed from one form to another. In many problems, total mechanical energy (KE + PE) is conserved when only conservative forces act.
能量守恒定律：能量既不能创造也不能消灭，只能从一种形式转化为另一种形式。在许多问题中，若只有保守力做功，则物体的总机械能（动能 + 势能）守恒。
Power is the rate of doing work: P = W/t or P = F v for constant force and velocity in the same direction. Efficiency = useful power output / total power input × 100%.
功率是做功的快慢：P = W/t，或当力与速度同向且恒定时 P = F v。效率 = 有用输出功率 / 总输入功率 × 100%。
4. Momentum and Collisions | 动量与碰撞
Momentum p = m v is a vector quantity. The impulse of a force equals the change in momentum: F Δt = Δp. Impulse is the area under a force–time graph.
动量 p = m v 是矢量。冲量等于动量的变化量：F Δt = Δp。冲量的大小等于力-时间图线下的面积。
The law of conservation of momentum: in a closed system with no external forces, total momentum before an interaction equals total momentum after.
动量守恒定律：在没有外力作用的封闭系统中，相互作用前的总动量等于相互作用后的总动量。
In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, momentum is conserved but kinetic energy is not; perfectly inelastic collisions result in the bodies sticking together.
在弹性碰撞中，动量和动能均守恒；在非弹性碰撞中，动量守恒但动能不守恒；完全非弹性碰撞后两物体粘在一起运动。
Rocket propulsion and explosions are explained by momentum conservation: the ejected mass gains backward momentum, so the rocket gains forward momentum.
火箭推进和爆炸现象可用动量守恒解释：喷出的物质获得向后的动量，火箭则获得向前的动量。
5. Circular Motion and Gravitation | 圆周运动与引力
An object moving in a circle at constant speed has a centripetal acceleration directed towards the centre: a = v²/r = ω²r, where ω is the angular speed (rad s⁻¹).
做匀速圆周运动的物体具有指向圆心的向心加速度：a = v²/r = ω²r，其中 ω 为角速度（rad s⁻¹）。
Centripetal force is the net force causing this acceleration: F = m v²/r = m ω² r. It is not a separate force but the resultant of real forces (tension, gravity, friction, etc.).
向心力是产生向心加速度的合外力：F = m v²/r = m ω² r。它不是某种单独的力，而是实际作用力（张力、重力、摩擦力等）的合力。
Newton’s law of gravitation: F = G M m / r². For a satellite in orbit, the gravitational force provides the centripetal force, leading to relationships between orbital speed, period, and radius.
牛顿万有引力定律：F = G M m / r²。对于沿轨道运行的卫星，万有引力充当向心力，从而可推导出轨道速度、周期与轨道半径的关系。
Kepler’s third law: T² ∝ r³ for circular orbits, where T is the orbital period and r is the orbital radius. Geostationary orbits have a period of 24 hours.
开普勒第三定律（圆轨道）：T² ∝ r³，其中 T 为轨道周期，r 为轨道半径。地球同步轨道的周期为 24 小时。
6. Thermal Physics and Ideal Gases | 热学与理想气体
Temperature is a measure of the average kinetic energy of particles. The Kelvin scale is absolute: T (K) = θ (°C) + 273.15.
温度是粒子平均动能的量度。热力学温度使用开尔文温标：T (K) = θ (°C) + 273.15。
Specific heat capacity c: Q = m c ΔT. Specific latent heat L: Q = m L (fusion or vaporisation). During a phase change, temperature remains constant while heat is absorbed or released.
比热容 c：Q = m c ΔT。比潜热 L：Q = m L（熔化或汽化）。在相变过程中，虽然持续吸热或放热，但温度保持不变。
An ideal gas obeys pV = nRT (where n is moles, R = 8.31 J mol⁻¹ K⁻¹) or pV = N k T (N particles, k Boltzmann constant). Boyle’s law (T constant: pV = constant), Charles’s law (p constant: V ∝ T), and the pressure law (V constant: p ∝ T) are special cases.
理想气体遵守 pV = nRT（n 为摩尔数，R = 8.31 J mol⁻¹ K⁻¹）或 pV = N k T（N 为粒子数，k 为玻尔兹曼常数）。玻意耳定律（T 一定，pV = 常量）、查理定律（p 一定，V ∝ T）和压力定律（V 一定，p ∝ T）是特例。
Kinetic theory links macroscopic quantities to microscopic behaviour: pV = ⅓ N m ⟨c²⟩, and average kinetic energy per particle = ³⁄₂ k T.
分子动理论将宏观量与微观行为联系起来：pV = ⅓ N m ⟨c²⟩，单个粒子的平均动能为 ³⁄₂ k T。
7. Waves and Oscillations | 波动与振动
Waves transfer energy without transferring matter. Transverse waves have oscillations perpendicular to propagation (e.g., light); longitudinal waves have oscillations parallel to propagation (e.g., sound).
波传递能量而不传递物质。横波的振动方向与传播方向垂直（如光波）；纵波的振动方向与传播方向平行（如声波）。
Key wave quantities: v = f λ, period T = 1/f. Phase difference indicates the shift between two points or waves, measured in radians or degrees.
关键波动量：v = f λ，周期 T = 1/f。相位差描述两点或两列波之间的偏移，以弧度或度为单位。
Superposition: when two waves meet, displacements add. Constructive interference occurs when path difference = nλ; destructive when path difference = (n + ½)λ.
波的叠加：两列波相遇时，位移相加。当波程差为 nλ 时产生相长干涉，波程差为 (n + ½)λ 时产生相消干涉。
Standing waves form on strings and in pipes: nodes (zero displacement) and antinodes (maximum displacement). Harmonics follow specific patterns: string fixed at both ends: λₙ = 2L/n; open pipe: λₙ = 2L/n; closed pipe: λₙ = 4L/n (odd n).
弦和管中的驻波：波节（位移为零）和波腹（位移最大）。谐频遵循特定模式：两端固定的弦：λₙ = 2L/n；开管：λₙ = 2L/n；闭管：λₙ = 4L/n（n 为奇数）。
Diffraction is the spreading of waves around obstacles or slits; significant when the gap size is comparable to the wavelength. The Doppler effect describes the change in observed frequency due to relative motion between source and observer.
衍射是波遇到障碍物或狭缝时发生的展宽现象；当缝宽与波长可比拟时衍射显著。多普勒效应描述由于波源与观察者相对运动而引起的观测频率变化。
8. Electricity and Circuits | 电学与电路
Current I = ΔQ/Δt. Potential difference V is the energy per unit charge: V = W/Q. Resistance R = V/I. Ohm’s law (V = IR) holds for ohmic conductors at constant temperature.
电流 I = ΔQ/Δt。电势差 V 是单位电荷的能量：V = W/Q。电阻 R = V/I。对于欧姆导体，在温度不变时伏安特性满足欧姆定律 V = IR。
Resistivity: R = ρ L/A, where ρ is a material property. Power in electrical circuits: P = I V = I² R = V²/R.
电阻率：R = ρ L/A，ρ 是材料特性。电路中的功率：P = I V = I² R = V²/R。
Series circuits: current is the same, voltages add, resistances add (R_total = R₁ + R₂ + …). Parallel circuits: voltage is the same, currents add; the reciprocal resistance 1/R_total = 1/R₁ + 1/R₂ + ….
串联电路：电流处处相等，电压相加，总电阻等于各电阻之和（R_总 = R₁ + R₂ + …）。并联电路：各支路电压相等，电流相加；总电阻的倒数为各电阻倒数之和（1/R_总 = 1/R₁ + 1/R₂ + …）。
Kirchhoff’s first law (junction rule): total current into a junction equals total current out. Second law (loop rule): sum of emfs equals sum of potential differences around any closed loop.
基尔霍夫第一定律（节点电流定律）：流入节点的电流之和等于流出节点的电流之和。第二定律（回路电压定律）：沿任意闭合回路，电动势的代数和等于各段电压降的代数和。
Internal resistance r of a source causes terminal voltage V = ε − I r. In potential divider circuits, the output voltage is V_out = V_in × (R₂/(R₁ + R₂)).
电源内阻 r 使得路端电压 V = ε − I r。在分压电路中，输出电压为 V_out = V_in × (R₂/(R₁ + R₂))。
9. Magnetism and Electromagnetic Induction | 磁学与电磁感应
Magnetic fields exist around magnets and current-carrying conductors. The direction of the field is given by the right-hand grip rule for a straight wire and by the right-hand rule for solenoids.
磁场存在于磁体和载流导体周围。直线电流的磁场方向由右手螺旋定则判定；螺线管的磁场方向由右手定则判定。
A charged particle moving in a magnetic field experiences a force F = q v B sin θ (Fleming’s left-hand rule). When v is perpendicular to B, the particle follows a circular path with radius r = m v/(q B).
运动电荷在磁场中受到洛伦兹力 F = q v B sin θ（弗莱明左手定则）。当 v 与 B 垂直时，粒子做圆周运动，半径为 r = m v/(q B)。
Electromagnetic induction: a changing magnetic flux induces an emf. Faraday’s law: ε = −N ΔΦ/Δt. Lenz’s law: the induced current flows in a direction that opposes the change in flux.
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/
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