📚 Pre-U WJEC Physics Formula & Theorem Quick Reference Handbook | Pre-U WJEC 物理公式定理速查手册
A compact yet comprehensive reference of the essential formulae and theorems required for the Pre-U WJEC Physics examination. Understanding when and how to apply each relationship is just as vital as memorising them – use this handbook to reinforce your conceptual grasp and problem-solving speed.
一份简洁而全面的Pre-U WJEC物理考试必备公式定理速查手册。理解每个关系式适用条件与使用方式与记住它们同样重要——用这本手册巩固概念理解与解题速度。
1. Kinematics and Dynamics | 运动学与动力学
The SUVAT equations describe uniformly accelerated motion in a straight line. They are valid only when acceleration a is constant.
SUVAT方程组描述匀加速直线运动，仅在加速度a恒定时适用。
v = u + at s = ut + ½at² v² = u² + 2as s = ½(u + v)t
Newton’s second law relates resultant force to the rate of change of momentum: F = dp/dt, and for constant mass it simplifies to F = ma.
牛顿第二定律将合力与动量变化率联系起来：F = dp/dt，对恒定质量简化为F = ma。
Momentum is conserved in isolated systems: Σp_before = Σp_after. Impulse equals change in momentum: J = Δp = F_avg Δt.
孤立系统动量守恒：Σp_before = Σp_after。冲量等于动量变化：J = Δp = F_avg Δt。
2. Work, Energy and Power | 功、能量和功率
Work done by a constant force: W = Fs cosθ, where θ is the angle between force and displacement. The work–energy theorem states that the net work done equals the change in kinetic energy.
恒力做功：W = Fs cosθ，其中θ为力与位移的夹角。功-能定理指出合力做的净功等于动能的变化量。
Kinetic energy: Eₖ = ½mv². Gravitational potential energy near Earth’s surface: Eₚ = mgh.
动能：Eₖ = ½mv²。地表附近的重力势能：Eₚ = mgh。
Power is the rate of doing work: P = W/t = Fv cosθ. Efficiency = useful power output / total power input.
功率是做功的速率：P = W/t = Fv cosθ。效率 = 有用输出功率 / 总输入功率。
3. 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 is ω = dθ/dt = v/r. The centripetal acceleration is a = v²/r = ω²r, directed towards the centre.
物体以恒定速率v做半径为r的圆周运动时，角速度ω = dθ/dt = v/r。向心加速度a = v²/r = ω²r，方向指向圆心。
Centripetal force: F = mv²/r = mω²r. Newton’s law of gravitation: F = Gm₁m₂ / r², where G = 6.67 × 10⁻¹¹ N m² kg⁻².
向心力：F = mv²/r = mω²r。牛顿万有引力定律：F = Gm₁m₂ / r²，G = 6.67 × 10⁻¹¹ N m² kg⁻²。
For orbital motion, gravitational force provides centripetal force: GmM / r² = mv²/r, leading to v² = GM/r and Kepler’s third law T² = (4π²/GM) r³.
对于轨道运动，引力提供向心力：GmM / r² = mv²/r，导出v² = GM/r以及开普勒第三定律T² = (4π²/GM) r³。
4. Oscillations and Waves | 振动与波
Simple harmonic motion (SHM) occurs when acceleration is directly proportional to displacement from equilibrium and directed towards it: a = −ω²x. The solution is x = A sin(ωt + φ) or x = A cos(ωt + φ).
简谐运动(SHM)发生条件是加速度与位移成正比且指向平衡位置：a = −ω²x。解为x = A sin(ωt + φ)或x = A cos(ωt + φ)。
Maximum speed v_max = ωA, maximum acceleration a_max = ω²A. Period of a mass–spring system: T = 2π√(m/k); simple pendulum: T = 2π√(L/g).
最大速度v_max = ωA，最大加速度a_max = ω²A。弹簧振子周期：T = 2π√(m/k)；单摆周期：T = 2π√(L/g)。
Wave speed: v = fλ. Intensity is proportional to amplitude squared: I ∝ A². For two-source interference, constructive maxima occur when path difference = nλ; destructive minima when path difference = (n + ½)λ.
波速：v = fλ。强度与振幅平方成正比：I ∝ A²。双源干涉中，光程差 = nλ 时出现相长极大，光程差 = (n + ½)λ 时出现相消极小。
5. Electric Fields | 电场
Coulomb’s law: force between two point charges F = k Q₁Q₂ / r², where k = 1/(4πε₀), ε₀ = 8.85 × 10⁻¹² F m⁻¹.
库仑定律：两点电荷间的作用力 F = k Q₁Q₂ / r²，k = 1/(4πε₀)，ε₀ = 8.85 × 10⁻¹² F m⁻¹。
Electric field strength E = F/q. For a point charge, E = kQ / r². In a uniform field between parallel plates, E = V/d.
电场强度 E = F/q。点电荷电场：E = kQ / r²。平行板间的匀强电场：E = V/d。
Potential difference: work done per unit charge. Electric potential due to a point charge: V = kQ / r. The force on a charge q in an electric field: F = qE.
电势差：移动单位电荷所做的功。点电荷的电势：V = kQ / r。电荷q在电场中受力：F = qE。
6. Capacitance | 电容
Capacitance is defined as C = Q / V. For a parallel-plate capacitor, C = ε₀εᵣ A / d, where εᵣ is the relative permittivity of the dielectric.
电容定义为 C = Q / V。平行板电容器电容：C = ε₀εᵣ A / d，εᵣ 是介质的相对介电常数。
Energy stored in a capacitor: E = ½QV = ½CV² = ½ Q²/C. Capacitor charging/discharging follows exponential equations: Q = Q₀ (1 − e^{-t/RC}) for charging, Q = Q₀ e^{-t/RC} for discharging, with time constant τ = RC.
电容器储存的能量：E = ½QV = ½CV² = ½ Q²/C。电容充放电遵循指数方程：充电 Q = Q₀ (1 − e^{-t/RC})，放电 Q = Q₀ e^{-t/RC}，时间常数 τ = RC。
7. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
Force on a moving charge in a magnetic field: F = qvB sinθ (Lorentz force). Force on a current-carrying conductor: F = BIL sinθ, where θ is the angle between the conductor and the field.
运动电荷在磁场中受力：F = qvB sinθ（洛伦兹力）。载流导体受力：F = BIL sinθ，θ为导体与磁场的夹角。
Magnetic flux density B is measured in tesla. Magnetic flux: Φ = BA cosθ. Faraday’s law of induction: induced e.m.f. equals the rate of change of flux linkage: ε = −d(NΦ)/dt.
磁感应强度B的单位是特斯拉。磁通量：Φ = BA cosθ。法拉第电磁感应定律：感应电动势等于磁链变化率：ε = −d(NΦ)/dt。
For a conductor of length L moving perpendicular to a uniform field B with speed v, the induced e.m.f. is ε = BLv. Lenz’s law states that the induced current opposes the change in flux that produced it, giving the negative sign in Faraday’s law.
长度为L的导体以速度v垂直切割均匀磁场B时，感生电动势为ε = BLv。楞次定律表明感应电流总是阻碍引起感应的磁通量变化，这解释了法拉第定律中的负号。
8. Thermal Physics | 热物理
Temperature is proportional to the average kinetic energy of particles. The ideal gas equation: pV = nRT, where R = 8.31 J mol⁻¹ K⁻¹. Alternatively, pV = NkT, with k = 1.38 × 10⁻²³ J K⁻¹.
温度与粒子的平均动能成正比。理想气体状态方程：pV = nRT，R = 8.31 J mol⁻¹ K⁻¹。也可写为pV = NkT，k = 1.38 × 10⁻²³ J K⁻¹。
Kinetic theory links pressure to molecular motion: p = ⅓ ρ
分子动理论将压强与分子运动联系起来：p = ⅓ ρ
First law of thermodynamics: ΔU = Q + W, where ΔU is the change in internal energy, Q is heat added to the system, and W is work done on the system. (Work done by system = −W).
热力学第一定律：ΔU = Q + W，ΔU为内能变化，Q为系统吸热，W为外界对系统做的功。（系统对外做功 = −W）。
9. Quantum Physics | 量子物理
Photon energy: E = hf = hc / λ, where h = 6.63 × 10⁻³⁴ J s. The photoelectric effect is explained by hf = Φ + Eₖ_max, where Φ is the work function. Stopping potential relates to maximum kinetic energy: eV_s = Eₖ_max.
光子能量：E = hf = hc / λ，h = 6.63 × 10⁻³⁴ J s。光电效应由hf = Φ + Eₖ_max解释，Φ为逸出功。遏制电势与最大动能关系：eV_s = Eₖ_max。
De Broglie wavelength: λ = h / p, where p = mv is momentum. Electron diffraction confirms the wave nature of particles. Energy levels in atoms are quantised; a photon is emitted when an electron transitions from a higher to a lower energy level: ΔE = hf.
德布罗意波长：λ = h / p，p = mv为动量。电子衍射证实了粒子的波动性。原子能级是量子化的；电子从高能级跃迁到低能级时辐射光子：ΔE = hf。
10. Nuclear Physics | 核物理
The nucleus is described by atomic number Z and mass number A. Radius of a nucleus: R = r₀ A^{1/3}, with r₀ ≈ 1.2 fm. This implies constant nuclear density.
原子核由原子序数Z和质量数A描述。核半径：R = r₀ A^{1/3}，r₀ ≈ 1.2 fm。这表明核密度为常数。
Mass defect and binding energy: E = Δm c², where Δm is the difference between the total mass of separate nucleons and the mass of the nucleus. Binding energy per nucleon is a measure of nuclear stability.
质量亏损和结合能：E = Δm c²，Δm是分散核子总质量与原子核质量之差。平均结合能（每核子结合能）是核稳定性的量度。
Radioactive decay follows exponential law: N = N₀ e^{-λt}, half-life T_{½} = ln2 / λ. Activity A = λN. In α decay, A decreases by 4 and Z by 2. In β⁻ decay, a neutron changes to a proton, emitting an electron and an antineutrino; Z increases by 1. In β⁺ decay, a proton changes to a neutron, emitting a positron and a neutrino; Z decreases by 1.
放射性衰变遵循指数规律：N = N₀ e^{-λt}，半衰期T_{½} = ln2 / λ。活度 A = λN。α衰变中，A减少4，Z减少2。β⁻衰变中，中子转变为质子，释放电子与反中微子，Z增加1。β⁺衰变中，质子转变为中子，释放正电子与中微子，Z减少1。
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