📚 AQA Year 12 Physics: Formula & Theorem Quick Reference Manual | AQA物理公式定理速查手册
This quick reference guide collects every essential formula, constant and theorem you need for Year 12 AQA Physics. Use it to revise core topics from particles and quantum phenomena to mechanics, materials, waves and electricity. Each section presents the key relationships with concise explanations, enabling fast recall before your exams.
这本速查手册汇集了 Year 12 AQA 物理所需的所有核心公式、常数和定理。从粒子物理与量子现象到力学、材料、波及电学，每部分都给出关键关系式并配有简明说明，助你在考前快速回顾。
1. Particles, Antiparticles and Photons | 粒子、反粒子与光子
Every particle has a corresponding antiparticle with the same rest mass but opposite charge. Annihilation occurs when a particle meets its antiparticle, converting their total mass into two gamma photons. Pair production is the reverse process, where a photon with sufficient energy transforms into a particle–antiparticle pair.
每种粒子都有对应的反粒子，静质量相同但电荷相反。一个粒子与其反粒子相遇时发生湮灭，总质量转化为两个伽马光子。对产生是逆过程，能量足够高的光子可以转化成一个粒子–反粒子对。
The energy of a photon is directly proportional to its frequency. This relationship underpins all photon interactions.
光子的能量与其频率成正比，这一关系是所有光子相互作用的基础。
E = h f or E = h c / λ
In annihilation, the minimum photon energy released equals the rest energy of one particle. For an electron–positron pair, each photon receives at least 0.511 MeV.
在湮灭中，释放的最小光子能量等于一个粒子的静能。对于电子–正电子对，每个光子至少得到 0.511 MeV。
E₀ = m c²
2. Quantum Phenomena: Photoelectric Effect and Energy Levels | 量子现象：光电效应与能级
Einstein’s photoelectric equation explains the emission of electrons from a metal surface when illuminated by light above a threshold frequency. The kinetic energy of the emitted electrons depends on the photon energy minus the work function of the metal.
爱因斯坦光电方程解释了当光频率高于阈值时金属表面发射电子的现象。逸出电子的最大动能等于光子能量减去金属的逸出功。
Ek max = h f − φ
The stopping potential Vs is related to the maximum kinetic energy by e Vs = Ek max. The work function φ is the minimum energy needed to remove an electron from the surface.
遏止电势差 Vs 满足 e Vs = Ek max。逸出功 φ 是从金属表面移去一个电子所需的最小能量。
Electrons in atoms can only exist in discrete energy levels. When an electron drops from a higher level E₂ to a lower level E₁, a photon is emitted with energy equal to the difference.
原子中的电子只能处于分立能级。电子从高能级 E₂ 跃迁到低能级 E₁ 时会放出光子，其能量等于能级差。
ΔE = E₂ − E₁ = h f
Excitation can occur by absorbing a photon of exactly the right energy or by collision with a free electron that carries sufficient kinetic energy.
激发可通过吸收能量恰好匹配的光子，或通过与具有足够动能的自由电子碰撞实现。
3. Waves: Fundamentals and Interference | 波动基础与干涉
ve waves, the phase difference between two points separated by distance x is Δφ = (2πx)/λ.
波动方程联系了所有行波的波速、频率和波长。对行波而言，相距 x 的两点间相位差为 Δφ = (2πx)/λ。
v = f λ
Young’s double-slit experiment produces an interference pattern of bright and dark fringes. The fringe spacing w for slits separated by s and a screen at distance D is given by the following relation (small‑angle approximation).
杨氏双缝实验产生明暗相间的干涉条纹。缝间距为 s、屏幕距离为 D 时，条纹间距 w 由下式给出（小角度近似）。
w = λ D / s
For a diffraction grating with line spacing d, maxima occur when the path difference is an integer number of wavelengths. The grating equation is essential for spectroscopy.
对于光栅间距为 d 的衍射光栅，当光程差等于波长的整数倍时出现极大。光栅方程是光谱分析的核心。
d sinθ = n λ
4. Refraction and Total Internal Reflection | 折射与全内反射
The absolute refractive index of a medium is the ratio of the speed of light in a vacuum to the speed in the medium. Snell’s law describes the relationship between the angles of incidence and refraction at a boundary.
介质的绝对折射率是真空中的光速与介质中光速的比值。斯涅尔定律描述边界上入射角和折射角的关系。
n₁ sinθ₁ = n₂ sinθ₂
The critical angle C for a boundary from a denser medium to a less dense one is reached when the angle of refraction is 90°. For light incident at angles greater than the critical angle, total internal reflection occurs.
从光密介质到光疏介质时，当折射角为 90° 时对应的入射角即为临界角 C。入射角大于临界角时发生全内反射。
sin C = 1 / n (for n₁ = n, n₂ = 1)
5. Stationary Waves | 驻波
Stationary waves are formed by the superposition of two progressive waves of equal frequency travelling in opposite directions. The fundamental frequency of a string fixed at both ends depends on the string length L, tension T and mass per unit length μ.
驻波由两列频率相同、传播方向相反的行波叠加形成。两端固定弦的基频取决于弦长 L、张力 T 和线密度 μ。
f₁ = (1 / 2L) √T / μ
For a pipe open at both ends, the harmonic series contains all integer multiples of the fundamental. For a pipe closed at one end, only odd harmonics are present.
两端开口管中，谐波序列包含基频的所有整数倍。一端闭口管则只存在奇数倍谐波。
fn = n v / 2L (open–open)
fn = n v / 4L (closed–open, n odd)
6. Kinematics: Motion in a Straight Line | 运动学：直线运动
For uniform acceleration a, the four SUVAT equations link initial velocity u, final velocity v, displacement s and time t. These equations apply only when acceleration is constant.
对于匀加速度 a，四个 SUVAT 方程将初速度 u、末速度 v、位移 s 和时间 t 联系起来。这些方程仅适用于加速度恒定的情形。
v = u + a t
s = u t + ½ a t²
s = ½ (u + v) t
v² = u² + 2 a s
For projectile motion, the horizontal and vertical components are treated independently. The horizontal velocity remains constant, while the vertical motion follows constant acceleration due to gravity g.
抛体运动中，水平和竖直分量独立处理。水平速度保持不变，竖直运动遵循重力加速度 g 的匀变速规律。
x = u cosθ t
y = u sinθ t − ½ g t²
7. Forces, Equilibrium and Moments | 力、平衡与力矩
Newton' rate of change of momentum, which simplifies to mass × acceleration when mass is constant.
牛顿第二定律指出，物体所受合力等于其动量变化率。在质量不变的情况下，简化为质量乘以加速度。
F = m a
For an object in equilibrium, the vector sum of forces is zero and the sum of clockwise moments about any pivot equals the sum of anticlockwise moments. The moment of a force is the product of force and perpendicular distance from the pivot.
处于平衡状态的物体，合外力为零，且对任意支点的顺时针力矩之和等于逆时针力矩之和。力矩是力与支点到力作用线垂直距离的乘积。
M = F d
The maximum static friction is proportional to the normal reaction, fmax = μs R. Kinetic friction acts when surfaces slide relative to each other.
最大静摩擦力与法向反力成正比，fmax = μs R。当表面间相对滑动时，动摩擦力起作用。
8. Energy, Work and Power | 能量、功与功率
Work done by a constant force is the product of force and displacement in the direction of the force. Kinetic energy and gravitational potential energy are the two main mechanical energy stores in Year 12.
恒力做功等于力与沿力方向位移的乘积。动能和重力势能是 Year 12 中最主要的两种机械能形式。
W = F s cosθ
Ek = ½ m v²
Ep = m g h
onstant force moving at speed v, the power delivered can be expressed as force × velocity.
功率是能量转移的速率。对于以恒定速度 v 运动的物体，恒力提供的功率可以表示为力与速度的乘积。
P = W / t = F v
Efficiency measures useful output as a proportion of input energy or power. It is always less than unity due to dissipative forces.
效率衡量有用输出能量或功率占输入的比例。由于耗散力的存在，效率始终小于 1。
9. Momentum and Impulse | 动量与冲量
Linear momentum is the product of mass and velocity. In a closed system, total momentum is conserved before and after any collision or explosion.
线动量是质量与速度的乘积。在一个封闭系统中，碰撞或爆炸前后的总动量守恒。
p = m v
The impulse exerted on an object equals its change in momentum and is given by the area under a force–time graph. For a constant force, this reduces to F Δt.
作用在物体上的冲量等于其动量的变化，数值上等于力–时间图线下的面积。对恒力，简化为 F Δt。
Impulse = F Δt = Δp
In perfectly elastic collisions, kinetic energy is conserved alongside momentum. The relative speed of approach equals the relative speed of separation.
在完全弹性碰撞中，动能与动量同时守恒，接近相对速率等于分离相对速率。
10. Materials: Stress, Strain and Young Modulus | 材料：应力、应变与杨氏模量
Stress is the internal force per unit cross‑sectional area, while strain is the extension per unit original length. The Young modulus characterises the stiffness of a material in the linear elastic region.
应力是单位横截面积上的内力，应变是单位原长的伸长量。杨氏模量表征材料在线性弹性区的刚度。
σ = F / A
ε = ΔL / L
E = σ / ε
The elastic strain energy stored in a stretched spring or wire can be calculated from the area under the force–extension graph. For a Hooke’s law material, it equals half the product of final force and extension.
拉伸的弹簧或金属线中储存的弹性应变能可由力–伸长图线下的面积求得。对于胡克定律材料，它等于最终力与伸长量乘积的一半。
Elastic potential energy = ½ F ΔL = ½ k ΔL²
11. Current Electricity: Charge, Potential Difference and Resistance | 电流：电荷、电势差与电阻
Electric current is the rate of flow of charge. Potential difference is the work done per unit charge moved between two points.
电流是电荷流动的速率。电势差是将单位电荷从一点移动到另一点所做的功。
I = ΔQ / Δt
V = W / Q
Ohm’s law states that, for an ohmic conductor at constant temperature, the current is directly proportional to the potential difference, giving a constant resistance R.
欧姆定律指出，对于恒定温度下的欧姆导体，电流与电势差成正比，电阻 R 为定值。
R = V / I
Resistivity ρ links the resistance of a uniform conductor to its length and cross‑sectional area. Superconductors are materials that have zero resistivity below a critical temperature.
电阻率 ρ 将均匀导体的电阻与其长度和横截面积联系起来。超导体是在临界温度以下电阻率为零的材料。
R = ρ L / A
12. Circuits: EMF, Internal Resistance and Potential Dividers | 电路：电动势、内阻与分压器
Kirchhoff’s first law states that the sum of currents entering a junction equals the sum leaving it. His second law states that in any closed loop the algebraic sum of the EMFs equals the sum of the p.d.s across the components.
基尔霍夫第一定律：流入节点的电流之和等于流出节点的电流之和。第二定律：在任一闭合回路中，电动势的代数和等于各元件上电压降的代数和。
l p.d. is lower than its EMF when current flows. The relationship is given by V = ε − I r.
对于具有内阻 r 的实际电池，在有电流时端电压低于电动势。关系式为 V = ε − I r。
ε = I (R + r)
A potential divider produces a fraction of the input voltage. For two resistors in series, the output voltage across R₂ is determined by their ratio.
分压器输出一个比例的输入电压。对于两个电阻串联，R₂ 两端的输出电压由它们的比值决定。
Vout = Vin × R₂ / (R₁ + R₂)
Resistors in series add directly; for parallel resistors, the reciprocal of total resistance equals the sum of reciprocals.
电阻串联时总阻值直接相加；并联时总电阻的倒数等于各电阻倒数之和。
Series: RT = R₁ + R₂ + …
Parallel: 1/RT = 1/R₁ + 1/R₂ + …
13. Measurements, Uncertainties and Errors | 测量、不确定度与误差
Every measurement has an associated uncertainty, which can be expressed as an absolute uncertainty or a percentage uncertainty. When measurements are combined, uncertainties propagate according to simple rules.
每次测量都带有不确定度，可以用绝对不确定度或百分比不确定度表示。当测量值组合时，不确定度按简单规则传播。
For addition or subtraction of quantities, absolute uncertainties add. For multiplication or division, percentage uncertainties add.
对于量的加减，绝对不确定度相加；对于乘除，百分比不确定度相加。
If R = a + b, then ΔR = Δa + Δb
If R = a × b, then %UR = %Ua + %Ub
Always record readings to the precision of the instrument and, where possible, repeat measurements to reduce random errors.
始终根据仪器精度记录读数，并尽可能重复测量以减少随机误差。
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