📚 CIE Year 12 Physics: Formula & Theorem Quick Reference Handbook | CIE 12年级物理公式定理速查手册
This handbook provides a concise and exam-oriented summary of the key formulas and theorems covered in the Cambridge International AS Level Physics syllabus. Each formula is accompanied by definitions of symbols and brief comments to support quick revision. Use it to check your understanding and refresh your memory before tests.
本手册简明扼要地总结了剑桥国际 AS 物理课程中涉及的核心公式和定理，并附有符号说明和简要提示，适合快速复习与考前查阅。每个条目均以中英文配对呈现，助你高效巩固知识。
1. Physical Quantities and Units | 物理量与单位
All physical quantities can be expressed as a product of a numerical value and a unit. SI base units are the foundation: mass (kg), length (m), time (s), electric current (A), temperature (K), amount of substance (mol) and luminous intensity (cd).
所有物理量均可表示为数值与单位的乘积。国际基本单位是基石：质量(kg)、长度(m)、时间(s)、电流(A)、温度(K)、物质的量(mol)和发光强度(cd)。
equation must have the same base units on both sides. For example, in s = ut + ½at2, both sides have the unit m.
方程的同质性：一个正确的物理方程左右两边必须具有相同的基本单位。例如，在 s = ut + ½at2 中，两边单位都是 m。
Common prefixes: pico (p, 10-12), nano (n, 10-9), micro (μ, 10-6), milli (m, 10-3), centi (c, 10-2), kilo (k, 103), mega (M, 106), giga (G, 109).
常用词头：皮(p, 10-12)、纳(n, 10-9)、微(μ, 10-6)、毫(m, 10-3)、厘(c, 10-2)、千(k, 103)、兆(M, 106)、吉(G, 109)。
measured value. When adding/subtracting, add absolute uncertainties; when multiplying/dividing, add fractional uncertainties.
不确定度：绝对不确定度是误差的大小；相对不确定度 = 绝对不确定度 / 测量值。加减运算时，绝对不确定度相加；乘除运算时，相对不确定度相加。
2. Kinematics | 运动学
Kinematics describes motion without considering its causes. The equations of uniformly accelerated motion are used when acceleration is constant.
运动学描述运动而不涉及原因。当加速度恒定时，使用匀加速运动方程组。
v = u + at. Final velocity = initial velocity + acceleration × time.
v = u + at。末速度 = 初速度 + 加速度 × 时间。
s = ut + ½; at2. Displacement = initial velocity × time + half acceleration × time squared.
s = ut + ½; at2。位移 = 初速度 × 时间 + 加速度的一半 × 时间的平方。
v2 = u2 velocity squared = initial velocity squared + 2 × acceleration × displacement.
v2 = u2 + 2as。末速度的平方 = 初速度的平方 + 2 × 加速度 × 位移。
s = (u+v)t / 2. Average velocity × time for uniform acceleration.
s = (u+v)t / 2。匀加速运动中平均速度乘以时间。
Gradient of displacement-time graph gives velocity; gradient of velocity-time graph gives acceleration; area under velocity-time graph gives displacement.
位移-时间图梯度为速度；速度-时间图梯度为加速度；速度-时间图下方面积为位移。
3. Dynamics | 动力学
Dynamics links force to motion. Newton's laws are fundamental.
动力学将力与运动联系起来。牛顿定律是基础。
Newton's second law: F = ma. Net force equals mass times acceleration.
牛顿第二定律：F = ma。合力等于质量乘以加速度。
Weight: W = mg. Weight is the gravitational force on a mass.
重力：W = mg。重力是作用在质量上的引力。
Momentum: p = mv. Momentum is mass times velocity; it is a vector.
动量：p = mv。动量 = 质量 × 速度，是矢量。
Impulse: Impulse = F×t = Δp. The impulse of a force equals change in momentum.
冲量：冲量 = F×t = Δp。力的冲量等于动量的变化量。
: In an isolated system, total momentum before collision = total momentum after collision.
动量守恒：在孤立系统中，碰撞前总动量 = 碰撞后总动量。
4. Forces, Density and Pressure | 力、密度与压强
This section deals with types of forces, equilibrium, turning effect and pressure in fluids.
本节讨论力的种类、平衡、转动效应以及流体中的压强。
f a force: Torque = F × d. The product of force and perpendicular distance to pivot.
力矩：力矩 = F × d。力与到转轴的垂直距离的乘积。
iple of moments: For equilibrium, sum of clockwise moments = sum of anticlockwise moments.
力矩原理：平衡时，顺时针力矩之和 = 逆时针力矩之和。
Density: ρ = m / V. Mass per unit volume.
密度：ρ = m / V。单位体积的质量。
Pressure: P = F / A. Force per unit area.
压强：P = F / A。单位面积上的力。
Hydrostatic pressure: P = ρ g h. Pressure due to a fluid column of height h.
液体压强：P = ρ g h。高度为 h 的液柱产生的压强。
Upthrust: Archimedes' principle - upthrust equals weight of fluid displaced.
浮力：阿基米德原理——浮力等于排开流体的重量。
5. Work, Energy and Power | 功、能与功率
Energy can be transferred between stores via work, heating or radiation. These definitions are central to problem-solving.
能量可通过做功、热传递或辐射在储存器之间转移。以下定义是解决问题的核心。
d cosθ. Work is the product of force and displacement in the direction of the force.
做功：W = F d cosθ。功等于力与沿力方向位移的乘积。
Gravitational potential energy: Ep = m g h. Change in GPE when height changes.
重力势能：Ep = m g h。高度变化时重力势能的变化量。
Kinetic energy: Ek = ½ m v2. Energy due to motion.
动能：Ek = ½ m v2。因运动而具有的能量。
Power: P = W / t = F v. Rate of work done; for constant force and velocity.
功率：P = W / t = F v。做功的快慢；适用于恒力和恒速度情况。
Efficiency = (useful output power) / (input power) × 100%.
效率 = (有用输出功率) / (输入功率) × 100%.
Principle of conservation of energy: Energy cannot be created or destroyed, only transferred or transformed.
能量守恒原理：能量不能被创造或消灭，只能被转移或转化。
6. Deformation of Solids | 固体的形变
Materials deform under applied forces. Elastic behaviour is described by Hooke's law and Young modulus.
材料在外力作用下发生形变。弹性行为用胡克定律和杨氏模量描述。
Hooke's law: F = k x. Force proportional to extension within the elastic limit.
胡克定律：F = k x。在弹性限度内，力与伸长量成正比。
Elastic potential energy stored in a stretched spring: E = ½ F x = ½ k x2.
弹簧储存的弹性势能：E = ½ F x = ½ k x2。
Stress: σ = F / A. Tensile or compressive stress.
应力：σ = F / A。拉伸或压缩应力。
Strain: ε = ΔL / L. Extension per unit original length.
应变：ε = ΔL / L。单位原长的伸长量。
Young modulus: E = stress / strain = (F/A) / (ΔL/L). A measure of stiffness.
杨氏模量：E = 应力 / 应变 = (F/A) / (ΔL/L)。衡量材料刚度的量。
7. Waves | 波
Waves transfer energy without bulk movement of matter. The wave equation links speed, frequency and wavelength.
波传递能量而不伴随物质的整体迁移。波动方程将波速、频率和波长联系在一起。
Wave speed: v = f λ. Speed = frequency × wavelength.
波速：v = f λ。波速 = 频率 × 波长。
Frequency and period: f = 1 / T. Frequency is the reciprocal of period.
频率与周期：f = 1 / T。频率是周期的倒数。
Intensity: I = Power / Area. For a spherical wave, I ∝ 1/r2.
强度：I = 功率 / 面积。对于球面波，I ∝ 1/r2。
on a wave have phase difference Δφ = 2π × (path difference / λ).
相位差：波上两点间的相位差 Δφ = 2π × (路程差 / 波长)。
Polarisation: Only transverse waves can be polarised; it confirms the transverse nature.
偏振：只有横波才能被偏振；偏振证实了波的横波特性。
8. Superposition and Interference | 叠加与干涉
Superposition states that when two or more waves meet, the resultant displacement is the vector sum of individual displacements. Interference patterns from coherent sources enable wavelength measurement.
叠加原理指出，当两个或多个波相遇时，合位移为各分位移的矢量和。相干光源产生的干涉图样可用于测量波长。
Constructive interference: path difference = nλ (n = 0, 1, 2...).
相长干涉：路程差 = nλ (n = 0, 1, 2...)。
Destructive interference: path difference = (n + ½)λ.
相消干涉：路程差 = (n + ½)λ。
Young' ambda; D / d. Fringe separation = wavelength × distance to screen / slit separation.
杨氏双缝实验：Δx = λ D / d。条纹间距 = 波长 × 屏距 / 缝间距。
Diffraction grating: d sinθ = nλ. d is grating spacing, n is order number.
衍射光栅：d sinθ = nλ。d 为光栅常数，n 为级数。
identical waves travelling in opposite directions. Node-antinode separation = λ/4.
驻波：由两列相同、传播方向相反的波叠加形成。波节-波腹间距 = λ/4。
9. Electricity | 电流基础知识
Electricity focuses on current, potential difference, resistance and their relationships. Ohm's law is central for metallic conductors at constant temperature.
电学重点关注电流、电势差、电阻及其关系。在恒温下，欧姆定律是金属导体的核心规律。
Current: I = ΔQ / Δt. Rate of flow of charge.
电流：I = ΔQ / Δt。电荷流动的速率。
Potential difference: V = W / Q. Energy transferred per unit charge.
电势差：V = W / Q。单位电荷所转移的能量。
Ohm's law: V = I R for a constant resistance.
欧姆定律：V = I R（适用于恒定电阻）。
stivity: R = ρ L / A. Resistance depends on material, length and cross-sectional area.
电阻与电阻率：R = ρ L / A。电阻取决于材料、长度和横截面积。
Power: P = I V = I2 R = V2 / R.
电功率：P = I V = I2 R = V2 / R。
Kirchhoff's current law: Sum of currents entering a junction = sum leaving.
基尔霍夫电流定律：流入节点的电流之和 = 流出节点的电流之和。
Kirchhoff's voltage law: In a closed loop, sum of e.m.f.s = sum of p.d.s.
基尔霍夫电压定律：在闭合回路中，电动势之和 = 电势差之和。
10. D.C. Circuits | 直流电路
Components in circuits can be connected in series or parallel. Understanding equivalent resistance and potential dividers is essential.
电路元件可以串联或并联。理解等效电阻和分压器至关重要。
Resistors in series: Rtotal = R1 + R2 + ... Same current through each.
串联电阻：R总 = R1 + R2 + ...。各电阻电流相等。
Resistors in parallel: 1 / Rtotal = 1 / R1 + 1 / R2 + ... Same p.d. across each branch.
并联电阻：1 / R总 = 1 / R1 + 1 / R2 + ...。各支路两端电势差相等。
Potential divider: Vout = Vin × R2 / (R1 + R2). Used to obtain a fraction of the input voltage.
分压器：Vout = Vin × R2 / (R1 + R2)。用于从输入电压中获取一定比例的电压。
Internal resistance: V = E - I r. Terminal p.d. drops when current flows.
内阻：V = E - I r。有电流流过时，端电压下降。
Power in external load is maximum when load resistance = internal resistance.
当负载电阻等于内阻时，外部负载上获得的功率最大。
11. Particle and Nuclear Physics | 粒子与核物理
This topic covers the structure of atoms, radioactivity, and fundamental particles. Quantum ideas like photon energy and the photoelectric effect are introduced.
本主题涵盖原子结构、放射性以及基本粒子。介绍了光子能量和光电效应等量子概念。
Photon energy: E = h f. h is Planck constant (6.63×10-34 J s).
光子能量：E = h f。h 为普朗克常数 (6.63×10-34 J s)。
Photoelectric effect: h f = φ + Ek max. Work function φ is the minimum energy to release an electron.
光电效应：h f = φ + Ek max。逸出功 φ 是释放电子的最小能量。
Wave-particle duality: λ = h / p. de Broglie wavelength of a particle.
波粒二象性：λ = h / p。粒子的德布罗意波长。
Radioactive decay law: N = N0 e-λt or A = A0 e-λt. λ is decay constant.
放射性衰变规律：N = N0 e-λt 或 A = A0 e-λt。λ 为衰变常数。
Half-life: T½ = ln 2 / λ. Time for half the nuclei to decay.
半衰期：T½ = ln 2 / λ。一半原子核发生衰变所需的时间。
Mass-energy equivalence: E = m c2. Binding energy and mass defect are related.
质能方程：E = m c2。结合能与质量亏损相关联。
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