Year 12 Edexcel Physics Formula & Theorem Quick Reference Handbook | 年12 Edexcel 物理公式定理速查手册

📚 Year 12 Edexcel Physics Formula & Theorem Quick Reference Handbook | 年12 Edexcel 物理公式定理速查手册

This quick reference handbook compiles all the essential formulas, equations, and theorems covered in the Year 12 Edexcel Physics syllabus. Keep it handy to review key relationships before exams, solve numerical problems, and deepen your conceptual understanding of mechanics, materials, electricity, waves, and quantum phenomena.

这本速查手册汇总了年12 Edexcel 物理课程中所有的核心公式、方程和定理。你可以随身携带，在考试前回顾关键关系式、求解计算题，并加深对力学、材料学、电学、波动和量子现象的概念理解。

1. Kinematics & Projectile Motion | 运动学与抛体运动

For uniform acceleration in a straight line, the SUVAT equations relate displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). The same equations apply to each perpendicular component in projectile motion, where horizontal acceleration is zero and vertical acceleration is g = 9.81 m s^-2 downwards.

对于匀加速直线运动，SUVAT 方程将位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t) 联系起来。在抛体运动中，这些方程同样适用于每个相互垂直的分量，其中水平加速度为零，竖直加速度为向下的 g = 9.81 m s^-2。

v = u + at
s = ut + ½ a t²
v² = u² + 2as
s = ((u + v) / 2) t

Displacement, velocity and acceleration are vectors; sign conventions must be consistent when plugging into these formulas. For projectiles, resolve initial speed into horizontal and vertical components: u_x = u cos θ, u_y = u sin θ.

位移、速度和加速度是矢量；代入这些公式时符号规则必须一致。对于抛体，将初速度分解为水平和竖直分量：u_x = u cos θ，u_y = u sin θ。

2. Forces, Newton’s Laws & Moments | 力、牛顿定律与力矩

Newton’s three laws form the backbone of classical mechanics. The second law gives the net force as F = ma. Weight is the force of gravity on a mass: W = mg. When an object is in equilibrium, both the resultant force and the resultant moment about any point are zero.

牛顿三定律是经典力学的基石。第二定律给出合力 F = ma。重量是作用在物体上的重力：W = mg。物体处于平衡状态时，合外力与关于任意点的合力矩均为零。

F_net = ma
W = mg (g = 9.81 N kg^-1 on Earth)
Moment = F d (where d is the perpendicular distance from the pivot)
Principle of moments: sum of clockwise moments = sum of anticlockwise moments
Equilibrium conditions: ΣF = 0 and ΣM = 0

Remember that the moment of a force depends on the line of action; use trigonometry to find the perpendicular distance when the force is not at 90° to the lever arm.

请记住力矩取决于力的作用线；当力不与杠杆臂垂直时，需用三角函数求出垂直距离。

3. Work, Energy & Power | 功、能量与功率

Energy is transferred when work is done. Work done by a constant force is W = F s cosθ, where θ is the angle between force and displacement. Kinetic energy and gravitational potential energy are two key mechanical energy stores, while power measures the rate of energy transfer.

做功时能量发生转移。恒力做的功为 W = F s cosθ，其中 θ 是力与位移的夹角。动能和重力势能是两种重要的机械能储存形式，而功率衡量能量转移的快慢。

W = F s cos θ
E_k = ½ m v²
ΔE_p = m g Δh
P = W / t
For an object moving at constant speed against a force, P = F v
Efficiency = (useful energy output / total energy input) × 100%

In a closed system with no external work, total mechanical energy is conserved, but energy may be dissipated as heat due to friction.

在无外部做功的封闭系统中，总机械能守恒，但能量可能因摩擦以热的形式耗散。

4. Momentum & Impulse | 动量与冲量

Linear momentum is the product of mass and velocity, p = m v. The impulse exerted by a net force equals the change in momentum: F Δt = Δp. In the absence of external forces, total momentum in a collision or explosion is conserved.

线动量是质量与速度的乘积：p = m v。合力施加的冲量等于动量的变化量：F Δt = Δp。在无外力作用时，碰撞或爆炸过程中的总动量守恒。

p = m v
Impulse = F Δt = Δp = m v – m u
Conservation of momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
In an elastic collision, kinetic energy is also conserved.
In an inelastic collision, kinetic energy is not conserved.

Impulse can be found from the area under a force–time graph. Always treat momentum as a vector when collisions occur in two dimensions.

冲量可通过力-时间图下的面积求得。当碰撞发生在二维时，始终将动量作为矢量处理。

5. Materials: Stress, Strain & Young Modulus | 材料：应力、应变与杨氏模量

When a material is stretched or compressed, stress and strain describe the load and deformation respectively. Hooke’s law states that, up to the limit of proportionality, extension is proportional to applied force. Young modulus is a measure of a material’s stiffness and is constant for a given material up to its elastic limit.

当材料被拉伸或压缩时，应力和应变分别描述载荷与形变。胡克定律指出，在比例极限内，伸长量与施加的力成正比。杨氏模量衡量材料的刚度，在弹性极限内对给定材料为常数。

Stress = F / A (unit: Pa)
Strain = ΔL / L (no unit)
Young modulus E = stress / strain (unit: Pa)
Hooke’s law: F = k x, where k is the spring constant
Elastic potential energy stored: E = ½ F x = ½ k x²

The stress–strain graph reveals important points: limit of proportionality, elastic limit, yield point and ultimate tensile stress. Area under the force–extension graph gives work done.

应力-应变图揭示了重要特征点：比例极限、弹性极限、屈服点和极限抗拉应力。力-伸长图下的面积表示做功。

6. Electric Circuits: Ohm’s Law & Resistivity | 电路：欧姆定律与电阻率

Current I is the rate of flow of charge. Ohm’s law holds for ohmic conductors at constant temperature: V = I R. The resistance of a uniform wire depends on its length, cross-sectional area and the resistivity of the material.

电流 I 是电荷流动的速率。欧姆定律在恒温条件下适用于欧姆导体：V = I R。均匀导线的电阻取决于其长度、横截面积和材料的电阻率。

I = ΔQ / Δt
V = I R (Ohm’s law)
R = ρ L / A (resistivity equation)
Resistors in series: R_total = R₁ + R₂ + …
Resistors in parallel: 1/R_total = 1/R₁ + 1/R₂ + …

For a cell with internal resistance r, the terminal potential difference is V = ε – I r, where ε is the electromotive force (emf).

对于具有内阻 r 的电池，端电压为 V = ε – I r，其中 ε 为电动势。

7. Circuit Rules & Electrical Power | 电路法则与电功率

Kirchhoff’s laws are the tools for analysing complex circuits. Power dissipated in a component is the rate at which it transfers electrical energy. Combining these with resistance formulas allows you to handle any series–parallel network.

基尔霍夫定律是分析复杂电路的工具。元件耗散的功率是其转移电能的速率。将这些与电阻公式结合，可以处理任何串并联网络。

Kirchhoff’s current law: Σ I_in = Σ I_out at a junction
Kirchhoff’s voltage law: Σ ε = Σ I R around a closed loop
P = I V = I² R = V² / R
Total power delivered by a source: P = I ε
Power wasted in internal resistance: P_wasted = I² r
Efficiency of power transfer: (R / (R + r)) × 100% when load resistance R matches internal r for max power?

Energy transferred is calculated by E = I V t, so 1 kWh = 3.6 × 10⁶ J. Remember that resistance can change with temperature for non‑ohmic devices.

转移的能量用 E = I V t 计算，因此 1 kWh = 3.6 × 10⁶ J。请记住，非欧姆器件的电阻可能随温度变化。

8. Waves: Properties & The Wave Equation | 波：性质与波动方程

All periodic waves can be described by their frequency f, wavelength λ, amplitude A and speed v. The wave equation v = f λ links these. For a point on a wave, phase difference expresses the fraction of a cycle separating two points.

所有周期波都可以用频率 f、波长 λ、振幅 A 和波速 v 来描述。波动方程 v = f λ 将它们联系起来。对于波上的点，相位差表示两点之间相隔的周期比例。

v = f λ
f = 1 / T (T is period)
Wave speed on a string: v = √(T / μ) (T is tension, μ is mass per unit length) – this may be Year 13 but is useful for Year 12 stretching context; sometimes covered
Intensity I is proportional to amplitude squared: I ∝ A²
Phase difference (in radians) = (2π × path difference) / λ

In transverse waves, oscillations are perpendicular to the direction of energy transfer; in longitudinal waves, they are parallel. Polarisation only occurs for transverse waves.

在横波中，振动方向与能量传递方向垂直；在纵波中，振动方向与能量传递方向平行。偏振仅发生在横波中。

9. Refraction & Critical Angle | 折射与临界角

When light passes from one medium to another, its speed changes, causing refraction. Snell’s law relates the angles of incidence and refraction to the refractive indices. Total internal reflection occurs when the angle of incidence exceeds the critical angle.

当光从一种介质进入另一种介质时，其速度发生变化，引起折射。斯涅尔定律将入射角和折射角与折射率联系起来。当入射角大于临界角时，发生全内反射。

n₁ sin θ₁ = n₂ sin θ₂ (Snell’s law)
For light entering a medium from vacuum/air, n = sin i / sin r, and n = c / v
Critical angle: sin C = 1 / n (when light goes from medium to less dense medium)
Condition for total internal reflection: i > C, and the light must travel from higher to lower n.

Dispersion occurs because n varies with wavelength; shorter wavelengths (blue) are refracted more than longer wavelengths (red).

色散的产生是因为 n 随波长变化；短波长（蓝光）比长波长（红光）折射得更厉害。

10. Photoelectric Effect & Photon Model | 光电效应与光子模型

The photoelectric effect provides key evidence for the particle nature of light. Einstein’s equation uses the photon model, where each photon carries energy E = h f. A minimum (threshold) frequency is required to eject electrons.

光电效应为光的粒子性提供了重要证据。爱因斯坦方程使用光子模型，其中每个光子携带能量 E = h f。要打出电子，需要一个最低的（阈值）频率。

E = h f (photon energy, h = 6.63 × 10^-34 J s)
c = f λ (for electromagnetic waves in vacuum)
Einstein’s photoelectric equation: h f = φ + E_{k, max}
φ is the work function (minimum energy to eject an electron)
Threshold frequency f₀ = φ / h
Maximum kinetic energy: E_{k, max} = e V_s, where V_s is the stopping potential

The graph of E_{k, max} against f is a straight line with slope h and intercept on the frequency axis at f₀. Intensity only affects the rate of electron emission, not their maximum kinetic energy.

E_{k, max} 对 f 的图是一条斜率为 h 的直线，其在频率轴上的截距为 f₀。光强仅影响电子发射的速率，而不影响其最大动能。

11. Wave–Particle Duality & De Broglie Wavelength | 波粒二象性与德布罗意波长

Matter can exhibit wave‑like behaviour. The de Broglie wavelength λ = h / p links a particle’s momentum to its wavelength. Electron diffraction patterns confirm the wave nature of electrons and support the concept of wave–particle duality.

物质可以表现出波动性。德布罗意波长 λ = h / p 将粒子的动量与其波长联系起来。电子衍射图样证实了电子的波动性，并支持波粒二象性的概念。

λ = h / p = h / (m v) (de Broglie wavelength)
For electrons accelerated through a potential difference V, ½ m v² = e V, so λ = h / √(2 m e V)
Evidence: electron diffraction from crystals shows rings of constructive/destructive interference, similar to X‑ray diffraction.
Particles with larger mass have extremely short wavelengths, making their wave properties negligible in everyday scales.

The wave–particle duality is not about light or electrons changing their nature, but about using the most appropriate model – wave or particle – to explain observations.

波粒二象性并非指光或电子改变本质，而是指根据观察结果选用最合适的模型——波动模型或粒子模型。

12. Constants, Conversions & Data | 常数、换算与数据

The following constants and unit conversions are frequently needed in Year 12 Edexcel Physics calculations. Using precise values is essential for accurate numerical answers.

以下常数和单位换算在年12 Edexcel 物理计算中经常用到。使用精确数值对于获得准确的计算结果至关重要。

Constant	Symbol & Value
Acceleration of free fall	g = 9.81 m s^-2 (use 9.81 unless told otherwise)
Speed of light in vacuum	c = 3.00 × 10⁸ m s^-1
Planck constant	h = 6.63 × 10^-34 J s
Elementary charge	e = 1.60 × 10^-19 C
Electron mass	m_e = 9.11 × 10^-31 kg
Avogadro constant (useful for context)	N_A = 6.02 × 10²³ mol^-1
1 electronvolt	1 eV = 1.60 × 10^-19 J
Degrees ↔ radians	180° = π rad

Always convert units to SI before using equations: length in metres, mass in kilograms, time in seconds, force in newtons, energy in joules. Prefixes such as k (10³), M (10⁶), c (10^-2), m (10^-3), μ (10^-6) must be handled carefully.

使用方程前务必将单位转换为国际单位制：长度用米，质量用千克，时间用秒，力用牛顿，能量用焦耳。需谨慎处理词头，如 k (10³)、M (10⁶)、c (10^-2)、m (10^-3)、μ (10^-6)。

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Year 12 Edexcel Physics Formula & Theorem Quick Reference Handbook | 年12 Edexcel 物理公式定理速查手册