📚 IB & WJEC Physics: Last-Minute Revision Notes | IB与WJEC物理考前冲刺笔记
This revision guide distils essential IB Physics (SL/HL) and WJEC Physics (AS/A2) concepts into rapid-fire notes, perfect for last-minute exam preparation. From kinematics to quantum physics, we cover the must-know equations, diagrams, and examination tricks to boost your confidence.
这本冲刺笔记浓缩了IB物理（SL/HL）与WJEC物理（AS/A2）的核心概念，力求简洁明了，非常适合考前最后一刻的复习。从运动学到量子物理，涵盖必背方程、示意图和应试技巧，助你信心满满地走入考场。
1. Measurements and Uncertainties | 测量与不确定度
Always quote a measured quantity with its absolute uncertainty, for example L = (5.0 ± 0.1) cm. The fractional uncertainty is ΔL/L and the percentage uncertainty is (ΔL/L) × 100%. If a quantity is raised to a power, multiply the percentage uncertainty by that power.
每次记录测量值时务必标注绝对不确定度，如 L = (5.0 ± 0.1) cm。分数不确定度为 ΔL/L，百分比不确定度为 (ΔL/L) × 100%。若物理量含乘方，则其百分比不确定度要乘上该乘方数。
When adding or subtracting values, simply add the absolute uncertainties: if A = B + C, then ΔA = ΔB + ΔC. For multiplication or division, add the fractional (or percentage) uncertainties: if A = B × C, then ΔA/A = ΔB/B + ΔC/C.
进行加减运算时，直接叠加绝对不确定度：若 A = B + C，则 ΔA = ΔB + ΔC。乘除运算则叠加分数（或百分比）不确定度：若 A = B × C，则 ΔA/A = ΔB/B + ΔC/C。
Always record data with the correct number of significant figures, and maintain consistency when calculating. In a final answer, the uncertainty should usually be given to one significant figure and the measurement rounded to the same decimal place.
记录数据时保留正确的有效数字，并在计算过程中保持一致性。最终答案的不确定度通常保留一位有效数字，测量值则修约至与不确定度相同的小数位。
2. Kinematics | 运动学
The four SUVAT equations describe uniform acceleration in a straight line. They link initial velocity u, final velocity v, acceleration a, time t and displacement s. The equations are:
四个 SUVAT 方程描述直线上的匀加速运动，将初速度 u、末速度 v、加速度 a、时间 t 和位移 s 联系起来。方程如下：
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
Remember to define a positive direction; quantities in the opposite direction acquire a negative sign. For free fall, replace a with g = 9.81 m·s⁻² and set the downward direction as positive if convenient.
务必先规定正方向；反方向的物理量取负号。对自由落体，用 g = 9.81 m·s⁻² 代替 a，通常取向下为正方向以简化运算。
Gradient of a displacement–time graph gives velocity, while the area under a velocity–time graph gives displacement. The gradient of a velocity–time graph gives acceleration.
位移-时间图像的斜率表示速度，速度-时间图像下的面积表示位移，而速度-时间图像的斜率表示加速度。
Projectile motion can be split into horizontal and vertical components. The horizontal velocity remains constant (if air resistance is ignored), and the vertical motion is uniformly accelerated by g.
抛体运动可分解为水平与竖直两个分量。水平速度保持不变（忽略空气阻力），竖直方向则做匀加速运动，加速度为 g。
3. Dynamics and Forces | 动力学与力
Newton’s first law: an object remains at rest or in uniform motion unless acted upon by a net external force. Newton’s second law: F = ma, where force is measured in newtons. Newton’s third law: for every action there is an equal and opposite reaction, acting on different bodies.
牛顿第一定律：不受外力作用时物体保持静止或匀速直线运动。第二定律：F = ma，力的单位是牛顿。第三定律：作用力与反作用力大小相等、方向相反，且作用在不同物体上。
Momentum p = mv is conserved in isolated systems. Impulse J = FΔt = Δp explains how forces change momentum over time. In collisions, distinguish between elastic (kinetic energy conserved) and inelastic (kinetic energy not conserved).
动量 p = mv 在孤立系统中守恒。冲量 J = FΔt = Δp 描述了力随时间改变动量的过程。碰撞中要区分弹性碰撞（动能守恒）和非弹性碰撞（动能不守恒）。
Draw free-body diagrams showing all forces acting on a point mass. Common forces include weight mg, normal reaction N, tension T, friction f ≤ μN, and spring force F = kx. Resolve forces into components when needed.
学会画受力图，标出质点所受的全部力。常见力有重力 mg、法向反力 N、张力 T、摩擦力 f ≤ μN 以及弹簧力 F = kx。必要时将力正交分解。
4. Work, Energy and Power | 功、能与功率
Work done by a force is W = Fs cosθ, where θ is the angle between force and displacement. Kinetic energy is KE = ½mv². Gravitational potential energy near the Earth’s surface is GPE = mgh.
力做的功为 W = Fs cosθ，其中 θ 是力与位移的夹角。动能为 KE = ½mv²。地表附近的重力势能为 GPE = mgh。
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. In many problems, set initial total energy equal to final total energy and include work done against friction.
能量守恒定律指出能量不能被创造或消灭，只能转移或转化。在许多题目中，令初始总能量等于末态总能量，并计入克服摩擦做的功。
Power is the rate of doing work, P = ΔW/Δt = Fv for a constant force acting parallel to velocity. Efficiency η = (useful output power)/(input power) × 100%.
功率是做功的快慢，P = ΔW/Δt；当力与速度同向时 P = Fv。效率 η = (有用输出功率)/(输入功率) × 100%。
For a stretched spring, elastic potential energy = ½kx², where k is the spring constant and x is the extension from equilibrium. This energy is recoverable when the spring returns to its natural length.
拉伸弹簧的弹性势能为 ½kx²，k 是劲度系数，x 是伸长量。弹簧恢复原长时该能量可释放出来。
5. Thermal Physics | 热物理
Temperature is a measure of the average random kinetic energy of particles. Internal energy is the sum of the total random kinetic energy and the total intermolecular potential energy of a substance. Heating increases internal energy; so does doing work on the system.
温度是分子无规则运动平均动能的量度。内能是物体内部所有分子无规则运动的动能和分子势能的总和。加热或对系统做功均可增加内能。
Specific heat capacity: Q = mcΔθ. Specific latent heat: Q = mL, where L is the latent heat of fusion or vaporization. During a phase change, the temperature remains constant even though heat is being supplied.
比热容：Q = mcΔθ。比潜热：Q = mL，L 为熔化潜热或汽化潜热。相变过程中，即使持续加热温度也保持不变。
The ideal gas law is pV = nRT, where n is the number of moles and R = 8.31 J·K⁻¹·mol⁻¹. It can also be written as pV = NkT, with N being the number of molecules and k = 1.38 × 10⁻²³ J·K⁻¹ (Boltzmann constant).
理想气体状态方程为 pV = nRT，n 为摩尔数，R = 8.31 J·K⁻¹·mol⁻¹。也可写为 pV = NkT，N 是分子数，k = 1.38 × 10⁻²³ J·K⁻¹（玻尔兹曼常数）。
The pressure of an ideal gas arises from elastic collisions of molecules with the container walls. The average kinetic energy of a molecule is (3/2)kT. The root-mean-square speed c_rms relates to pressure via p = ⅓ρ(c_rms)².
理想气体的压强源于分子与器壁的弹性碰撞。分子平均平动动能为 (3/2)kT。方均根速率 c_rms 与压强的关系为 p = ⅓ρ(c_rms)²。
6. Waves and Oscillations | 波动与振动
For any wave, speed v = fλ. Frequency f is the number of oscillations per second; period T = 1/f. Transverse waves have displacement perpendicular to propagation; longitudinal waves have displacement parallel to propagation.
任何波的波速 v = fλ。频率 f 是每秒振动次数，周期 T = 1/f。横波的振动方向垂直于传播方向，纵波的振动方向平行于传播方向。
When two waves overlap, they superpose. Constructive interference occurs when the path difference is nλ; destructive interference occurs when it is (n + ½)λ. For Young’s double-slit experiment, fringe spacing Δx = λD/d, where D is distance to screen and d is slit separation.
两列波相遇时叠加。波程差为 nλ 时发生相长干涉，波程差为 (n + ½)λ 时发生相消干涉。杨氏双缝干涉的条纹间距为 Δx = λD/d，D 为缝屏间距，d 为双缝间距。
Standing waves form when two identical waves travel in opposite directions. The fixed ends are nodes (zero displacement), and antinodes occur halfway between nodes. For a string fixed at both ends, the wavelength of the nth harmonic is 2L/n.
两列相同的波沿相反方向传播时形成驻波。固定端为波节（位移始终为零），波腹在相邻波节的中点。对于两端固定的弦，第 n 次谐波的波长为 2L/n。
Snell’s law governs refraction: n₁ sinθ₁ = n₂ sinθ₂. The refractive index n = c/v. Total internal reflection occurs when light travels from a denser to a less dense medium at an angle greater than the critical angle, given by sin C = 1/n.
折射定律遵循斯涅耳定律：n₁ sinθ₁ = n₂ sinθ₂。折射率 n = c/v。光从光密介质射向光疏介质且入射角大于临界角 C（sin C = 1/n）时发生全内反射。
The Doppler effect shifts the observed frequency when source and observer move relative to each other: f’ = f (v ± vₒ)/(v ± vₛ). Use signs logically: when they move towards each other, observed frequency increases.
多普勒效应使观测频率随波源与观察者的相对运动而变化：f’ = f (v ± vₒ)/(v ± vₛ)。合理使用符号：二者靠近时观测频率升高。
7. Electricity and Magnetism | 电学与磁学
Current I = ΔQ/Δt, measured in amperes. Ohm’s law states that V = IR for ohmic conductors at constant temperature. Resistance R can also be expressed via resistivity: R = ρL/A, where ρ depends on the material.
电流 I = ΔQ/Δt，单位为安培。欧姆定律指出当温度恒定时欧姆导体的 V = IR。电阻也可用电阻率表示：R = ρL/A，ρ 由材料决定。
In a series circuit, current is the same, voltages add up. In a parallel circuit, voltage is the same across each branch, currents add up. Kirchhoff’s laws: junction rule ΣI_in = ΣI_out; loop rule ΣV = 0 around any closed loop.
串联电路中电流相同，电压相加。并联电路中各支路电压相等，电流相加。基尔霍夫定律：节点电流 ΣI_in = ΣI_out；回路电压 ΣV = 0。
Power in electrical circuits: P = IV = I²R = V²/R. The electromotive force (emf) ε is the total energy per unit charge provided by a source. Use ε = I(R + r) where r is internal resistance.
电路中的电功率：P = IV = I²R = V²/R。电动势 ε 是电源每单位电荷提供的总能量。使用 ε = I(R + r)，其中 r 为内阻。
A current-carrying conductor in a magnetic field experiences a force F = BIL sinθ (Fleming’s left-hand rule). A moving charge in a field feels F = qvB sinθ. Magnetic flux Φ = BA cosθ, and the induced emf from Faraday’s law is ε = -N dΦ/dt.
通电导线在磁场中受力 F = BIL sinθ（左手定则）。运动电荷受力 F = qvB sinθ。磁通量 Φ = BA cosθ，法拉第电磁感应定律给出感应电动势 ε = -N dΦ/dt。
An ideal transformer obeys Vₚ/Vₛ = Nₚ/Nₛ and, for 100% efficiency, VₚIₚ = VₛIₛ. Lenz’s law gives the direction of induced current: it opposes the change causing it.
理想变压器满足 Vₚ/Vₛ = Nₚ/Nₛ，且在效率 100% 时 VₚIₚ = VₛIₛ。楞次定律给出感应电流的方向：总是阻碍引起感应电流的变化。
8. Circular Motion and Gravitation | 圆周运动与万有引力
For an object moving in a circle of radius r at constant speed v, the angular velocity ω = v/r. The period T = 2π/ω. Even though speed is constant, the velocity changes direction, giving rise to centripetal acceleration a = v²/r = ω²r.
物体在半径为 r 的圆周上以恒定速率 v 运动时，角速度 ω = v/r。周期 T = 2π/ω。虽然速率不变，但方向改变，因此存在向心加速度 a = v²/r = ω²r。
Centripetal force required is F = mv²/r = mω²r. This force is not a new kind of force but a net force caused by tension, gravity, friction, or the normal reaction pointed toward the centre.
所需的向心力为 F = mv²/r = mω²r。向心力并不是一种新的力，而是由指向圆心的张力、引力、摩擦力或法向反力等提供的合力。
Newton’s law of universal gravitation: F = GMm/r². Gravitational field strength g = F/m = GM/r². Near Earth, g ≈ 9.81 N·kg⁻¹. For satellites, gravitational force provides the centripetal force, leading to orbital speed v = √(GM/r).
万有引力定律：F = GMm/r²。引力场强度 g = F/m = GM/r²。地表附近 g ≈ 9.81 N·kg⁻¹。对人造卫星，万有引力提供向心力，可得轨道速率 v = √(GM/r)。
Kepler’s third law states that the square of the period T is proportional to the cube of the semi-major axis r: T² ∝ r³. For a satellite in a circular orbit, energy considerations show that total mechanical energy is negative, indicating a bound system.
开普勒第三定律指出 T² ∝ r³。对圆轨道卫星，能量分析表明总机械能为负值，说明系统处于束缚状态。
9. Atomic, Nuclear and Particle Physics | 原子、核物理与粒子物理
α-decay reduces the mass number by 4 and atomic number by 2. β⁻-decay turns a neutron into a proton, emitting an electron and an antineutrino. γ-decay releases energy without changing the nucleus’s composition. Balance mass numbers and atomic numbers in all nuclear equations.
α 衰变使质量数减 4，原子序数减 2。β⁻ 衰变将一个中子转变为质子，释放出一个电子和一个反中微子。γ 衰变释放能量，但不改变原子核的组成。书写核反应方程时务必配平质量数和原子序数。
The half-life T_½ = ln2/λ, where λ is the decay constant. Activity A = λN decreases exponentially: N = N₀ e^{-λt}. After n half-lives, the fraction remaining is (½)ⁿ.
半衰期 T_½ = ln2/λ，λ 是衰变常量。活度 A = λN 按指数衰减：N = N₀ e^{-λt}。经过 n 个半衰期后，剩余比例为 (½)ⁿ。
Mass–energy equivalence E = mc². Binding energy is the energy required to separate a nucleus into its constituent protons and neutrons. The mass defect Δm corresponds to this energy, giving binding energy = Δm c².
质能等价 E = mc²。结合能是将原子核分解成其组成质子和中子所需的能量。质量亏损 Δm 对应此能量，结合能 = Δm c²。
Fission splits a heavy nucleus into smaller fragments, releasing energy. Fusion combines light nuclei, such as hydrogen isotopes, to form helium, releasing even more energy per unit mass. Standard Model particles include quarks (up, down, strange, etc.), leptons (electron, muon, neutrino) and gauge bosons (photon, W, Z, gluon).
裂变使重核分裂为较轻的碎片，释放能量。聚变将轻核（如氢同位素）结合成氦，单位质量释放的能量更多。标准模型粒子包括夸克（上、下、奇异等）、轻子（电子、μ子、中微子）和规范玻色子（光子、W、Z、胶子）。
10. Quantum and Wave-Particle Duality | 量子与波粒二象性
Photoelectric effect: when light of frequency f above the threshold frequency shines on a metal surface, electrons are emitted. Energy equation: E_k max = hf – Φ, where Φ is the work function. The stopping voltage V_s satisfies eVs = E_k max.
光电效应：频率 f 高于截止频率的光照射金属表面时，会打出电子。能量方程为 E_k max = hf – Φ，Φ 是逸出功。遏止电压 V_s 满足 eVs = E_k max。
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