📚 Year 12 WJEC Physics: Formula & Theorem Quick Reference Handbook | 威尔士 WJEC 物理公式定理速查手册
This quick-reference handbook gathers the essential equations, laws, and theorems for Year 12 WJEC AS Physics. Covering topics from kinematics and materials to electricity and quantum phenomena, each entry pairs a clearly displayed formula with a concise bilingual explanation to reinforce your understanding and speed up revision.
本速查手册汇集了 WJEC 12 年级 AS 物理必须掌握的公式、定律和定理。内容涵盖运动学、材料、电学到量子现象，每个条目均以醒目的公式搭配中英双语简明解释，帮助你加深理解、高效复习。
1. Kinematics Equations | 运动学公式
For motion with constant acceleration along a straight line, the following four equations allow you to calculate displacement, velocity, time and acceleration.
对于匀加速直线运动，以下四个方程可用于计算位移、速度、时间和加速度。
v = u + a t
Relates final velocity v to initial velocity u, acceleration a and time t. Useful when displacement s is not needed.
将末速度 v 与初速度 u、加速度 a 和时间 t 联系起来。当不需要位移 s 时使用。
s = u t + ½ a t²
This expression gives the displacement s after time t. It is the most common choice when acceleration is constant and the final velocity is unknown.
此式给出时间 t 内的位移 s。当加速度恒定且末速度未知时最常用。
s = ½ (u + v) t
Calculates displacement using the average velocity. Ideal when acceleration is not directly required.
利用平均速度计算位移。当不需要直接使用加速度时非常方便。
v² = u² + 2 a s
Eliminates time t; used when the time interval is not given or is irrelevant.
消去了时间 t；当时间未知或不需要时使用。
2. Newton’s Laws and Forces | 牛顿定律与力
Newton’s three laws form the foundation of classical mechanics. The second law quantifies how a net force produces acceleration.
牛顿三定律是经典力学的基础。第二定律定量描述了合力如何产生加速度。
Fnet = m a
The net force (resultant) acting on an object equals the object’s mass multiplied by its acceleration. Remember to resolve forces into components when necessary.
作用在物体上的合力等于物体的质量乘以其加速度。必要时记得将力分解为分量。
W = m g
Weight W is the gravitational force on a mass m near the Earth’s surface, where g ≈ 9.81 m s⁻².
重量 W 是地球表面附近质量 m 所受的重力，g 取约 9.81 m s⁻²。
f ≤ μ R
The frictional force f is proportional to the normal reaction R, with maximum static friction fmax = μs R and kinetic friction fk = μk R.
摩擦力 f 与法向反作用力 R 成正比，最大静摩擦力为 fmax = μs R，动摩擦力为 fk = μk R。
3. Work, Energy and Power | 功、能与功率
Energy concepts link force and motion. Work is done when a force moves its point of application, and the rate of doing work is power.
能量概念将力和运动联系起来。力使其作用点移动时做功，做功的快慢为功率。
W = F s cos θ
Work done by a constant force F is the product of the force, displacement s, and the cosine of the angle θ between them.
恒力 F 所做的功等于力的大小、位移 s 以及力与位移夹角 θ 的余弦三者的乘积。
Ek = ½ m v²
Kinetic energy of an object of mass m moving at speed v. Always measured in joules (J).
质量为 m、速度为 v 的物体的动能。单位始终为焦耳 (J)。
ΔEp = m g Δh
Change in gravitational potential energy near Earth’s surface for a height change Δh.
地球表面附近高度变化 Δh 时的重力势能变化。
Eel = ½ k x²
Elastic potential energy stored in a spring of stiffness k stretched or compressed by x, provided Hooke’s law is obeyed.
劲度系数为 k 的弹簧在拉伸或压缩 x 时所储存的弹性势能，前提是满足胡克定律。
P = W / t = F v
Power is the rate of energy transfer. For an object moving at constant speed v against a force F, P = F v.
功率是能量转移的速率。物体以恒定速度 v 抵抗力 F 运动时，有 P = F v。
4. Momentum and Impulse | 动量与冲量
Momentum is a vector quantity conserved in all isolated systems. Impulse connects force to change in momentum.
动量是矢量，在任何孤立系统中都守恒。冲量将力与动量变化联系起来。
p = m v
Linear momentum p is mass times velocity. Direction of p matches direction of v.
线动量 p 等于质量乘以速度。p 的方向与 v 的方向一致。
F Δt = Δp
Impulse equals average force multiplied by the time interval, and also equals the change in momentum. Use this to find forces in collisions.
冲量等于平均力乘以时间间隔，也等于动量的变化。可用于求碰撞中的力。
Σpbefore = Σpafter
Principle of conservation of momentum: in the absence of external forces, total momentum before an event equals total momentum after.
动量守恒原理：在没有外力时，事件前的总动量等于事件后的总动量。
5. Materials and Young’s Modulus | 材料与杨氏模量
Understanding the strength and stiffness of materials relies on stress, strain and the elastic constants. Hooke’s law describes the linear region.
理解材料的强度和刚度需要用到应力、应变和弹性常数。胡克定律描述了线弹性区域。
F = k x
Hooke’s law: the extension x of a spring is directly proportional to the applied force F, up to the limit of proportionality. k is the spring constant.
胡克定律：在比例极限内，弹簧的伸长量 x 与施加力 F 成正比。k 为劲度系数。
Stress = F / A
Tensile or compressive stress is the force per unit cross-sectional area. Unit: pascal (Pa) or N m⁻².
拉伸或压缩应力是单位横截面积上的力。单位：帕斯卡 (Pa) 或 N m⁻²。
Strain = ΔL / L₀
Strain is the fractional extension; it has no units. ΔL is the change in length and L₀ is the original length.
应变是长度的变化率，无量纲。ΔL 为长度变化，L₀ 为原始长度。
E = stress / strain = (F/A) / (ΔL/L₀)
Young’s modulus E measures a material’s stiffness. A steep stress–strain graph indicates a large E.
杨氏模量 E 衡量材料的刚度。应力-应变曲线越陡，E 越大。
Elastic strain energy = ½ F ΔL = ½ k x²
Energy stored in a wire or spring within the elastic limit can be expressed using the work done by the average force.
弹性极限内储存在线材或弹簧中的能量可用平均力做功来表示。
6. Waves and the Wave Equation | 波与波动方程
All waves carry energy without transferring matter. The key link between speed, frequency and wavelength is universal.
所有波都传输能量而不转移物质。波速、频率和波长之间的关键关系具有普适性。
v = f λ
Wave speed v equals frequency f multiplied by wavelength λ. Applies to transverse and longitudinal waves, including light and sound.
波速 v 等于频率 f 乘以波长 λ。适用于横波和纵波，包括光和声波。
T = 1 / f
Period T is the time for one complete oscillation. It is the reciprocal of the frequency.
周期 T 是一次完整振动所需的时间，是频率的倒数。
I = P / A
Intensity I is the power per unit area incident on a surface. For a spherical wave front, intensity falls as 1/r².
强度 I 是单位面积上接收的功率。对于球面波前，强度随 1/r² 减小。
Path difference for phase
A path difference of one wavelength λ corresponds to a phase difference of 2π radians. This idea underpins interference of coherent waves.
波长 λ 的路程差对应 2π 弧度的相位差。这一思想是相干波干涉的基础。
7. Refraction and Optics | 折射与光学
When light crosses a boundary between media, its speed and direction change according to Snell’s law. Total internal reflection is crucial for fibre optics.
光穿过介质交界面时，速度和方向遵从斯涅耳定律变化。全内反射是光纤通信的关键。
n = c / v
Absolute refractive index n of a medium is the ratio of the speed of light in vacuum c to the speed v in that medium.
介质的绝对折射率 n 是真空光速 c 与介质中光速 v 之比。
n₁ sin θ₁ = n₂ sin θ₂
Snell’s law. θ₁ is the angle of incidence and θ₂ the angle of refraction, both measured from the normal.
斯涅耳定律。θ₁ 是入射角，θ₂ 是折射角，均从法线量起。
sin θc = n₂ / n₁ (n₁ > n₂)
Critical angle θc for total internal reflection: when light attempts to pass from a denser to a less dense medium at angles larger than θc, all light is reflected.
全内反射的临界角 θc：光从光密介质射向光疏介质，且入射角大于 θc 时，光全部被反射。
8. Electricity and Circuits | 电学与电路
Circuit analysis relies on Ohm’s law, Kirchhoff’s rules and power relationships. The microscopic conduction model links resistance to material and geometry.
电路分析依赖欧姆定律、基尔霍夫定律和功率关系。微观导电模型将电阻与材料和几何尺寸联系起来。
I = ΔQ / Δt
Electric current I is the rate of flow of charge. 1 A = 1 C s⁻¹.
电流 I 是电荷流动的速率。1 A = 1 C s⁻¹。
V = I R
Ohm’s law: potential difference V across a resistor is proportional to current I. R is the resistance (Ω).
欧姆定律：电阻两端的电势差 V 与电流 I 成正比。R 为电阻 (Ω)。
R = ρ L / A
Resistance of a wire depends on resistivity ρ, length L and cross-sectional area A. Resistivity is a material property.
导线的电阻取决于电阻率 ρ、长度 L 和横截面积 A。电阻率是材料属性。
P = I V = I² R = V² / R
Electrical power dissipated or transferred. Choose the form that best suits the known quantities.
电功率的耗散或传递。根据已知量选取最方便的形式。
ΣIin = ΣIout and Σε = ΣV
Kirchhoff’s first law (junction rule) states charge is conserved; the second law (loop rule) states energy is conserved. ε represents emf.
基尔霍夫第一定律（节点定律）表明电荷守恒；第二定律（回路定律）表明能量守恒。ε 表示电动势。
ε = I (R + r) and Vterminal = ε − I r
For a source with internal resistance r, terminal p.d. falls as current increases. Open-circuit voltage equals ε.
对于有内阻 r 的电源，端电压随电流增大而下降。开路电压等于 ε。
9. Quantum Phenomena | 量子现象
The photon model describes light as discrete packets of energy. Einstein’s photoelectric equation explains the emission of electrons from a metal surface.
光子模型将光视为离散的能量包。爱因斯坦的光电效应方程解释了电子从金属表面的发射。
E = h f = h c / λ
Photon energy; h is the Planck constant (6.63 × 10⁻³⁴ J s), f is frequency, c is speed of light, and λ is wavelength.
光子能量；h 为普朗克常数 (6.63 × 10⁻³⁴ J s)，f 为频率，c 为光速，λ 为波长。
h f = φ + ½ m vmax²
Einstein’s photoelectric equation: the energy of a single photon does work to overcome the work function φ, with excess energy becoming the maximum kinetic energy of the emitted electron.
爱因斯坦光电方程：单个光子的能量一部分用于克服逸出功 φ，剩余能量转化为发射电子的最大动能。
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