📚 Quick Revision Handbook for Year 12 Cambridge Physics: Formulas and Theorems | Year 12 Cambridge 物理：公式定理速查手册
This concise handbook gathers the essential formulas, laws and theorems required for the Year 12 Cambridge AS Level Physics course. Each section pairs an English explanation with its Chinese translation to help you consolidate understanding quickly and prepare effectively for examinations.
本速查手册汇集了 Year 12 剑桥 AS 阶段物理课程的核心公式、定律和定理。每个要点均配有中英双语解释，帮助你快速巩固理解，有效备考。
1. Physical Quantities and Units | 物理量与单位
All physical quantities are expressed as a numerical value multiplied by a unit. The SI base units are metre (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for temperature, mole (mol) for amount of substance and candela (cd) for luminous intensity.
所有物理量都表示为数值乘以单位。SI 基本单位有：米(m)表示长度，千克(kg)表示质量，秒(s)表示时间，安培(A)表示电流，开尔文(K)表示温度，摩尔(mol)表示物质的量以及坎德拉(cd)表示发光强度。
Derived units are obtained by combining base units. For example, the newton (N) is equivalent to kg m s⁻², and the joule (J) is kg m² s⁻². Checking the homogeneity of equations using base units helps to verify their validity.
导出单位由基本单位组合而成。例如，牛顿(N)等同于 kg m s⁻²，焦耳(J)等同于 kg m² s⁻²。利用基本单位检验方程的同质性有助于验证公式的正确性。
Prefixes are used to express very large or very small multiples: p (pico, 10⁻¹²), n (nano, 10⁻⁹), µ (micro, 10⁻⁶), m (milli, 10⁻³), c (centi, 10⁻²), d (deci, 10⁻¹), k (kilo, 10³), M (mega, 10⁶), G (giga, 10⁹), T (tera, 10¹²).
词头用于表示极大或极小的倍数：p(皮可, 10⁻¹²), n(纳诺, 10⁻⁹), µ(微, 10⁻⁶), m(毫, 10⁻³), c(厘, 10⁻²), d(分, 10⁻¹), k(千, 10³), M(兆, 10⁶), G(吉咖, 10⁹), T(太拉, 10¹²)。
2. Kinematics | 运动学
For an object moving with constant acceleration a along a straight line, the following equations link initial velocity u, final velocity v, displacement s and time t:
对于以恒定加速度 a 沿直线运动的物体，以下方程将初速度 u、末速度 v、位移 s 和时间 t 联系起来：
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
tical components are treated independently: the horizontal velocity remains constant (aₓ = 0), while the vertical motion experiences acceleration due to gravity g = 9.81 m s⁻².
这些方程仅在加速度恒定且运动沿直线时成立。对于抛体运动，水平分量和竖直分量独立处理：水平速度保持不变(aₓ = 0)，而竖直运动受重力加速度 g = 9.81 m s⁻² 影响。
of magnitude V at an angle θ to the horizontal has components Vₓ = V cosθ and Vᵧ = V sinθ.
矢量分解至关重要：大小为 V、与水平方向夹角为 θ 的矢量，其分量为 Vₓ = V cosθ 和 Vᵧ = V sinθ。
3. Dynamics | 动力学
Newton's first law states that an object remains at rest or in uniform motion in a straight line unless acted upon by a resultant external force. Newton's second law links resultant force, mass and acceleration:
牛顿第一定律指出，除非受到合外力的作用，物体将保持静止或匀速直线运动状态。牛顿第二定律将合力、质量和加速度联系在一起：
F = ma
Weight is the gravitational force on a mass: W = mg. Newton' s that if body A exerts a force on body B, then B exerts an equal and opposite force on A.
重量是作用于质量上的重力：W = mg。牛顿第三定律指出，若物体 A 对物体 B 施加力，则 B 同时对 A 施加大小相等、方向相反的力。
city: p = mv. The impulse of a force F acting for a time Δt equals the change in momentum:
线动量 p 定义为质量与速度的乘积：p = mv。力 F 在时间 Δt 内的冲量等于动量的变化：
FΔt = Δp
The principle of conservation of momentum states that in a closed system with no external forces, the total momentum before an interaction equals the total momentum after the interaction.
动量守恒定律指出，在没有外力的封闭系统中，相互作用前的总动量等于相互作用后的总动量。
4. Work, Energy and Power | 功、能量与功率
Work done W by a constant force F is the product of the force component in the direction of displacement s:
恒力 F 所做的功 W 是力在位移 s 方向上的分量与位移的乘积：
W = F s cosθ
where θ is the angle between the force and the displacement. Kinetic energy Ek and gravitational potential energy Ep are given by:
其中 θ 是力与位移的夹角。动能 Ek 和重力势能 Ep 为：
Eₖ = ½mv²
Eₚ = mgh
The work-energy principle states that the net work done on an object equals its change in kinetic energy. Elastic potential energy stored in a spring obeying Hooke's law is:
功能原理指出，对物体所做的净功等于其动能的变化。符合胡克定律的弹簧储存的弹性势能为：
Eₑ = ½kx²
be written as P = Fv. Efficiency is the ratio of useful output power to total input power.
功率 P 是做功的快慢：P = W / t。对于以速度 v 运动的物体受恒力作用时，功率也可写为 P = Fv。效率是有用输出功率与总输入功率之比。
5. Momentum and Collisions | 动量与碰撞
In any collision or explosion, total momentum is conserved as long as no external resultant force acts. For two objects of masses m₁ and m₂ with initial velocities u₁ and u₂, and final velocities v₁ and v₂:
在任何碰撞或爆炸中，只要没有合外力作用，总动量就守恒。对于质量分别为 m₁ 和 m₂、初速度为 u₁ 和 u₂、末速度为 v₁ 和 v₂ 的两个物体：
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
In a perfectly elastic collision, kinetic energy is conserved and the relative speed of approach equals the relative speed of separation:
在完全弹性碰撞中，动能守恒，且接近前的相对速度等于分离后的相对速度：
u₁ - u₂ = -(v₁ - v₂)
In a perfectly inelastic collision, the objects stick together and move with a common final velocity; kinetic energy is not conserved but momentum is conserved. Explosions can be treated as an inelastic collision in reverse, with the initial total momentum zero.
在完全非弹性碰撞中，物体粘在一起并以共同速度运动；动能不守恒但动量守恒。爆炸可视为反过来的非弹性碰撞，初始总动量为零。
6. Deformation of Solids | 固体的形变
Hooke's law states that within the elastic limit, the extension x of a spring is directly proportional to the applied force F:
胡克定律指出，在弹性限度内，弹簧的伸长量 x 与施加的力 F 成正比：
F = kx
where k is the spring constant. The elastic limit is the point beyond which the material does not return to its original shape.
其中 k 为劲度系数。弹性限度是材料不再恢复原状的临界点。
Stress σ and strain ε are used to describe the deformation of materials: stress is the force per unit cross-sectional area, and strain is the extension per unit original length.
应力 σ 和应变 ε 用于描述材料的形变：应力是单位横截面积上所受的力，应变是单位原长上的伸长量。
σ = F / A
ε = x / L
The Young modulus E is a measure of stiffness, defined as the ratio of stress to strain within the limit of proportionality:
杨氏模量 E 是刚度的量度，定义为比例限度内应力与应变之比：
E = σ / ε = (F / A) / (x / L)
The area under a force-extension graph equals the work done in stretching, which becomes elastic potential energy when the deformation is reversible.
力 - 伸长图下的面积等于拉伸过程中做的功，当形变可逆时该功转化为弹性势能。
7. Waves | 波
A wave transfers energy without transferring matter. The relationship between wave speed v, frequency f and wavelength λ is fundamental:
波传递能量而不传递物质。波速 v、频率 f 与波长 λ 之间的基本关系为：
v = fλ
se waves, the oscillations are perpendicular to the direction of energy transfer; for longitudinal waves, they are parallel.
周期 T 是一次完整振动所需的时间：T = 1 / f。横波的振动方向垂直于能量传递方向；纵波的振动方向则与之平行。
The intensity I of a wave is proportional to the square of its amplitude A: I ∝ A². Intensity decreases with distance from a point source according to the inverse square law.
波的强度 I 与振幅 A 的平方成正比：I ∝ A²。点源发出的波，强度随距离按平方反比规律减弱。
Phase difference φ between two points on a wave is measured in radians or degrees. A path difference of one wavelength corresponds to a phase difference of 2π rad.
波上两点间的相位差 φ 以弧度或度来度量。路程差为一个波长时，对应的相位差为 2π 弧度。
8. Superposition and Interference | 叠加与干涉
When two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements. This is the principle of superposition.
当两个或多个波在一点相遇时，合位移是各单独位移的矢量和，这就是叠加原理。
Coherent sources have a constant phase difference and the same frequency. Young's double-slit experiment demonstrates constructive and destructive interference. The fringe separation Δx on a screen placed at distance D from two slits separated by d is:
相干光源具有恒定的相位差和相同的频率。杨氏双缝实验展示了相长干涉和相消干涉。屏幕上干涉条纹间距 Δx 与双缝间距 d 及屏幕距离 D 的关系为：
Δx = λD / d
For a diffraction grating with slit spacing d, maxima occur when the path difference equals an integer number of wavelengths:
对于缝间距为 d 的衍射光栅，当光程差等于波长的整数倍时出现亮纹：
d sinθ = nλ
where n is the order number. A stationary wave is formed when two identical waves travel in opposite directions along the same line. Nodes are points of zero displacement and antinodes are points of maximum amplitude.
其中 n 为级次。两列完全相同的波沿同一直线反向传播时形成驻波。波节是位移始终为零的点，波腹是振幅最大的点。
9. Electric Fields and Current | 电场与电流
Two point charges exert a force on each other described by Coulomb's law:
两个点电荷相互施加的力由库仑定律描述：
F = kQq / r²
uniform field between two parallel plates, E = V / d, where V is the potential difference and d the plate separation.
其中 k = 1/(4πε₀)，ε₀ 为真空介电常数。电场强度 E 定义为单位正电荷所受的力：E = F / q。在平行板间的匀强电场中，E = V / d，V 为电势差，d 为板间距离。
onductor can also be expressed in terms of the microscopic properties of the charge carriers:
电流 I 是电荷流动的速率：I = ΔQ / Δt。导体中的电流也可用载流子的微观属性表示：
I = nAve
where n is the number density of charge carriers, A the cross-sectional area, v the mean drift velocity and e the elementary charge.
其中 n 为载流子数密度，A 为横截面积，v 为平均漂移速度，e 为元电荷。
10. D.C. Circuits | 直流电路
Ohm's law states that for a metallic conductor at constant temperature, the potential difference V across it is proportional to the current I through it:
欧姆定律指出，对于恒温下的金属导体，其两端的电势差 V 与通过的电流 I 成正比：
V = IR
where R is the resistance. Resistance depends on the material's resistivity ρ, length L and cross-sectional area A:
其中 R 为电阻。电阻取决于材料的电阻率 ρ、长度 L 和横截面积 A：
R = ρL / A
resistors in series, the total resistance Rₜ = R₁ + R₂ + ... . For resistors in parallel:
串联电阻的总电阻 Rₜ = R₁ + R₂ + ... 。并联电阻满足：
1/Rₜ = 1/R₁ + 1/R₂ + ...
Kirchhoff's laws govern circuit analysis: the current law states that the sum of currents entering a junction equals the sum leaving it; the voltage law states that the sum of e.m.f.s around any closed loop equals the sum of potential differences.
基尔霍夫定律是电路分析的基础：电流定律指出，流入节点的电流之和等于流出电流之和；电压定律指出，沿任意闭合回路的电动势之和等于电势降之和。
A real cell has internal resistance r, so the terminal potential difference V is less than the electromotive force ε when current flows:
实际电池具有内阻 r，有电流时端电压 V 小于电动势 ε：
V = ε - Ir
Electrical power dissipated in a component is given by P = IV = I²R = V²/R.
元件消耗的电功率由 P = IV = I²R = V²/R 给出。
11. Particle and Nuclear Physics | 粒子与核物理
Rutherford's gold foil experiment revealed that an atom consists of a small, dense, positively charged nucleus surrounded by electrons. The nucleus contains protons and neutrons, collectively called nucleons.
卢瑟福金箔实验揭示出原子由一个微小、致密、带正电的原子核及周围电子组成。原子核包含质子和中子，统称为核子。
The number of protons defines the atomic number Z; the total number of nucleons is the mass number A. Isotopes have the same Z but different A.
质子数决定原子序数 Z；核子总数是质量数 A。同位素具有相同的 Z 但不同的 A。
Radioactive decay involves the emission of alpha (⁴₂He), beta minus (electron) or gamma (photon) radiation. Beta minus decay is the transformation of a neutron into a proton, an electron and an anti-electron-neutrino; at the quark level, a down quark changes into an up quark via the weak interaction.
放射性衰变涉及发射 α 粒子(⁴₂He)、β⁻ 粒子(电子)或 γ 射线(光子)。β⁻ 衰变是中子转变为质子、电子和反电子中微子的过程；在夸克层次，一个下夸克通过弱相互作用转变成上夸克。
e is measured in becquerels (Bq) and decreases exponentially. The half-life t₁/₂ is the time taken for the number of undecayed nuclei to halve. Einstein' ounts for the energy released in nuclear reactions and the binding energy that holds the nucleus together.
放射源的活度 A 以贝克勒尔(Bq)为单位，并呈指数衰减。半衰期 t₁/₂ 是未衰变核数目减半所需的时间。爱因斯坦质能方程 E = mc² 解释了核反应中释放的能量以及将原子核结合在一起的结合能。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图