📚 A-Level WJEC Physics: Exam Revision Notes | A-Level WJEC 物理：考前冲刺笔记
Welcome to your last-minute revision guide for the WJEC A-Level Physics exam. This article focuses on the core concepts, essential formulas, and common mistakes so you can walk into the exam hall with confidence. Whether you need a quick refresher or a structured recap, the following notes will help you secure top marks.
欢迎阅读WJEC A-Level物理考前冲刺笔记。本文聚焦核心概念、必备公式和常见误区，帮助你在走进考场时胸有成竹。无论你是需要快速复习还是系统性回顾，下面的笔记都将助你冲击高分。
1. SI Units and Dimensional Analysis | 国际单位制与量纲分析
Mastering base and derived units is crucial for tackling calculation questions. The seven SI base units are kilogram (kg), metre (m), second (s), ampere (A), kelvin (K), mole (mol) and candela (cd). Every other physical quantity can be expressed in terms of these, and checking the homogeneity of an equation by comparing units on both sides will instantly reveal algebraic mistakes.
掌握基本单位和导出单位是解决计算题的关键。七个SI基本单位是千克(kg)、米(m)、秒(s)、安培(A)、开尔文(K)、摩尔(mol)和坎德拉(cd)。所有其他物理量都可以用这些基本单位表示，通过比较方程两边的单位来检验量纲一致性，可以迅速发现代数错误。
Always write derived units as products of base units when asked to show base units. For example, the newton (N) is equivalent to kg m s⁻², and the volt (V) is equivalent to kg m² s⁻³ A⁻¹. Practise converting common quantities such as energy (J → kg m² s⁻²) and resistance (Ω → kg m² s⁻³ A⁻²).
当题目要求用基本单位表示时，一定要将导出单位写成基本单位的乘积。例如，牛顿(N)等价于kg m s⁻²，伏特(V)等价于kg m² s⁻³ A⁻¹。练习转换常见物理量，如能量(J → kg m² s⁻²)和电阻(Ω → kg m² s⁻³ A⁻²)。
2. Kinematics Equations | 运动学方程
The four equations for uniformly accelerated motion are the toolkit for any projectile or straight-line motion problem. Memorise them in their standard forms, and always define your positive direction before substituting values.
匀加速运动的四个方程是解决任何抛体或直线运动问题的工具。牢记它们的标准形式，并在代入数值前始终定义好正方向。
v = u + at
s = ut + ½ at²
v² = u² + 2as
s = ½ (u + v)t
Here, u is initial velocity, v is final velocity, a is constant acceleration, t is time and s is displacement. When tackling two-dimensional projectile motion, split the velocity into horizontal and vertical components. The horizontal motion has constant velocity (a = 0), while the vertical motion has a = g = 9.81 m s⁻² downwards.
这里u是初速度，v是末速度，a是恒定加速度，t是时间，s是位移。处理二维抛体运动时，将速度分解为水平分量和竖直分量。水平方向速度恒定(a = 0)，竖直方向则受向下、大小为g = 9.81 m s⁻²的加速度影响。
3. Newton’s Laws and Free-Body Diagrams | 牛顿定律与受力图
Always start dynamics problems with a clear free-body diagram showing all forces acting on the object. Newton’s second law, F = ma, is a vector equation, so apply it independently in perpendicular directions. Common forces include weight (mg), normal reaction, tension, friction and applied forces.
解动力学问题时，始终要从画出清晰的受力图开始，显示物体所受的所有力。牛顿第二定律F = ma是矢量方程，应沿垂直方向独立应用。常见的力包括重力(mg)、法向反作用力、张力、摩擦力和外加力。
The third law reminds us that forces come in action–reaction pairs of the same type acting on different bodies. A classic error is to include forces that an object exerts on its surroundings in its own free-body diagram—only the forces acting on the object should appear.
第三定律提醒我们，力以相同类型、作用在不同物体上的作用力–反作用力对的形式出现。一个经典错误是将物体施加给周围环境的力画在它自己的受力图中——只有作用在该物体上的力才应当出现。
4. Work, Energy and Power | 功、能与功率
The principle of conservation of energy is a powerful problem-solving tool. Work done by a constant force is W = Fd cosθ, where θ is the angle between the force and the displacement. Kinetic energy is KE = ½ mv², and gravitational potential energy near Earth’s surface is GPE = mgh.
能量守恒原理是强大的解题工具。恒力做功的公式为W = Fd cosθ，其中θ是力与位移的夹角。动能为KE = ½ mv²，地球表面附近的重力势能为GPE = mgh。
Power is the rate of energy transfer: P = W/t. For an object moving at constant speed against a force F, useful forms are P = Fv. Be careful to apply this only when the velocity is parallel to the force; otherwise, the scalar product is needed.
功率是能量转移的速率：P = W/t。对于抵抗一个力F、以恒定速度运动的物体，P = Fv是一种有用的形式。注意只有在速度与力平行时才适用此式；否则需要用标量积。
5. Momentum and Impulse | 动量与冲量
Linear momentum is defined as p = mv, and the impulse of a force equals the change in momentum: FΔt = Δp. The area under a force–time graph gives the impulse. In WJEC exams, you are often asked to use the law of conservation of momentum for collisions and explosions.
线动量定义为p = mv，力的冲量等于动量的变化量：FΔt = Δp。力–时间图下的面积表示冲量。在WJEC考试中，经常要求用动量守恒定律处理碰撞和爆炸问题。
In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not. For objects that stick together (perfectly inelastic), the common final velocity can be found directly from momentum conservation.
在弹性碰撞中，动量和动能都守恒。在非弹性碰撞中，动量守恒而动能不守恒。对于粘在一起的物体（完全非弹性碰撞），可直接从动量守恒求出共同末速度。
6. Circular Motion | 圆周运动
An object moving in a circle at constant speed is not in equilibrium, because the direction of its velocity is continuously changing. The centripetal acceleration is a = v²/r = ω²r, and the resultant force towards the centre is F = ma = mv²/r = mω²r.
匀速圆周运动的物体并不处于平衡态，因为速度方向一直在变。向心加速度为a = v²/r = ω²r，指向圆心的合力为F = ma = mv²/r = mω²r。
The angular speed ω is related to the period T by ω = 2π/T = 2πf, and to the linear speed by v = ωr. Always draw a diagram and indicate the radial direction; the centripetal force is provided by tension, friction, gravity or a normal reaction, depending on the scenario.
角速度ω与周期T的关系为ω = 2π/T = 2πf，与线速度的关系为v = ωr。始终要画图并标明径向；向心力可以由张力、摩擦力、重力或法向反作用力提供，取决于具体情境。
7. Simple Harmonic Motion | 简谐运动
SHM is defined by a restoring force or acceleration that is proportional to displacement and directed towards equilibrium: a = -ω²x. The minus sign is essential. From this definition, two standard solutions for displacement are x = A cos(ωt) and x = A sin(ωt), depending on the initial conditions.
简谐运动的定义是回复力或加速度与位移成正比且指向平衡位置：a = -ω²x。负号至关重要。由这一定义可得到位移的两个标准解：x = A cos(ωt) 和 x = A sin(ωt)，取决于初始条件。
The period T = 2π/ω is independent of amplitude, which is a key feature of SHM. For a mass–spring system, T = 2π√(m/k); for a simple pendulum with small amplitude, T = 2π√(L/g). Energy continuously alternates between kinetic and potential forms, but the total energy E = ½ mω²A² remains constant.
周期T = 2π/ω与振幅无关，这是简谐运动的关键特征。对于弹簧振子，T = 2π√(m/k)；对于小振幅单摆，T = 2π√(L/g)。能量在动能和势能之间连续转换，但总能量E = ½ mω²A²保持恒定。
8. Gravitational Fields | 引力场
Newton’s law of universal gravitation gives the force between two point masses: F = Gm₁m₂/r², where G = 6.67 × 10⁻¹¹ N m² kg⁻². The gravitational field strength at a distance r from a point mass M is g = GM/r², and it points towards the mass.
万有引力定律给出两个质点间的引力：F = Gm₁m₂/r²，其中G = 6.67 × 10⁻¹¹ N m² kg⁻²。距质点M为r处的引力场强为g = GM/r²，方向指向该质点。
Gravitational potential V_g = -GM/r is the work done per unit mass to bring a test mass from infinity to that point. In a radial field, the magnitude of g equals the negative gradient of the potential. For satellites, equate centripetal force to gravitational force to derive orbital speed v = √(GM/r) and period relationships.
引力势V_g = -GM/r是把单位质量从无穷远移到该点所做的功。在径向场中，g的大小等于势的负梯度。对于卫星，令向心力等于引力，可推导出轨道速率v = √(GM/r)以及周期关系。
9. Electric Fields and Capacitance | 电场与电容
Coulomb’s law for two point charges is F = kQ₁Q₂/r², where k = 1/(4πε₀). Electric field strength E = F/q, and for a uniform field between parallel plates, E = V/d. Remember that field lines point from positive to negative, and the force on a negative charge is opposite to the field direction.
两点电荷的库仑定律为F = kQ₁Q₂/r²，其中k = 1/(4πε₀)。电场强度E = F/q，对于平行板间的匀强电场，E = V/d。记住电力线从正电荷指向负电荷，负电荷所受电场力与场强方向相反。
Capacitance C = Q/V, and for a parallel-plate capacitor C = εA/d. The energy stored in a capacitor is ½ QV = ½ CV². The time constant for an RC circuit is τ = RC; during charging or discharging, the p.d. varies exponentially with a characteristic time τ.
电容C = Q/V，对于平行板电容器C = εA/d。电容器储存的能量为½ QV = ½ CV²。RC电路的时间常数为τ = RC；充放电过程中，电势差随时间按指数规律变化，特征时间为τ。
10. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
A current-carrying conductor in a magnetic field experiences a force F = BIL sinθ, where θ is the angle between the current and the field. Use Fleming’s left-hand rule to determine the direction of the force. For a moving charge, the magnetic force is F = Bqv sinθ, which is always perpendicular to velocity and field, causing circular motion.
磁场中的载流导体受到力F = BIL sinθ的作用，其中θ是电流与磁场的夹角。用左手定则判断力的方向。对于运动电荷，磁力为F = Bqv sinθ，它始终垂直于速度和磁场，能使电荷做圆周运动。
Faraday’s law states that the induced e.m.f. in a coil equals the negative rate of change of magnetic flux linkage: ε = -N ΔΦ/Δt. Lenz’s law gives the direction: the induced current opposes the change that produced it. Use the right-hand grip rule to relate current, field and induced e.m.f.
法拉第定律指出，线圈中的感应电动势等于磁链变化率的负值：ε = -N ΔΦ/Δt。楞次定律给出方向：感应电流总是阻碍引起感应电流的变化。用右手螺旋定则确定电流、磁场和感应电动势的关系。
11. Quantum Phenomena | 量子现象
The photoelectric effect demonstrates that light consists of photons of energy E = hf, where h = 6.63 × 10⁻³⁴ J s. The work function φ is the minimum energy needed to release an electron. Einstein’s photoelectric equation, hf = φ + Eₖ_max, links photon energy, work function and the maximum kinetic energy of emitted electrons.
光电效应表明光由能量为E = hf的光子组成，其中h = 6.63 × 10⁻³⁴ J s。功函数φ是释放一个电子所需的最小能量。爱因斯坦光电方程hf = φ + Eₖ_max将光子能量、功函数与出射电子的最大动能联系起来。
The threshold frequency f₀ = φ/h gives the minimum frequency for emission. The de Broglie wavelength λ = h/p shows the wave nature of particles, while electron diffraction provides evidence for this. Energy level transitions in atoms produce emission and absorption spectra; the photon energy equals the difference between two energy levels.
截止频率f₀ = φ/h给出产生光发射的最低频率。德布罗意波长λ = h/p揭示了粒子的波动性，电子衍射为其提供了证据。原子中的能级跃迁产生发射光谱和吸收光谱；光子能量等于两个能级的能量差。
12. Nuclear Physics | 核物理
Radioactive decay is a random process described by the activity A = λN, where λ is the decay constant. The number of undecayed nuclei follows N = N₀ e^(⁻λt), and half-life t₁/₂ = ln 2 / λ. In WJEC structured questions, you may need to work with mass–energy equivalence: E = mc².
放射性衰变是一种随机过程，用活度A = λN描述，其中λ是衰变常量。未衰变的原子核数目遵循N = N₀ e^(⁻λt)，半衰期t₁/₂ = ln 2 / λ。在WJEC的结构题中，你可能需要运用质能等价关系：E = mc²。
Nuclear fission involves splitting a heavy nucleus into two lighter fragments, releasing energy and neutrons; nuclear fusion combines light nuclei into a heavier one, releasing even greater energy per unit mass. Binding energy per nucleon peaks near iron-56, providing the energetic rationale for both processes.
核裂变是将重核分裂为两个较轻的碎片，释放能量和中子；核聚变将轻核结合成较重的核，单位质量释放的能量更大。平均结合能在铁-56附近达到峰值，这为两种过程提供了能量依据。
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