📚 Year 12 Edexcel Physics: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This is your go-to reference for all the essential equations and principles covered in the Year 12 Edexcel Physics syllabus. Each entry is explained briefly to help you recall its meaning and application under exam pressure.
这是你在 Year 12 Edexcel 物理课程中所有核心公式与定理的速查手册。每条内容都附有简要解释，帮助你在考试压力下快速回忆其含义与用法。
1. Kinematics Equations | 运动学方程
The four equations of motion for constant acceleration in a straight line link displacement, initial velocity, final velocity, acceleration and time.
匀加速直线运动的四个运动方程将位移、初速度、末速度、加速度和时间联系起来。
v = u + at
This gives final velocity v after time t for initial velocity u and constant acceleration a.
此式给出在初速度 u 和恒定加速度 a 下经过时间 t 后的末速度 v。
s = ½ (u + v) t
Displacement s is average velocity multiplied by time.
位移 s 等于平均速度乘以时间。
s = ut + ½ at²
This expresses displacement directly in terms of initial velocity, acceleration and time.
该式直接用初速度、加速度和时间表示位移。
v² = u² + 2as
Use this when time is not given.
当问题中未给出时间时使用此式。
2. Forces & Newton’s Laws | 力与牛顿定律
Newton’s three laws of motion form the foundation of classical mechanics. Together with free-body diagrams they allow analysis of all force systems.
牛顿三大运动定律构成经典力学的基础。结合受力分析图，它们可以用来分析所有力系。
ΣF = ma
The net force acting on a body equals its mass times acceleration (Newton’s second law). This is the single most important equation in dynamics.
作用在物体上的合力等于质量乘以加速度（牛顿第二定律）。这是动力学中最重要的方程。
Weight is the force due to gravity: W = mg, where g = 9.81 m s⁻² on Earth.
重力是由于引力而产生的力：W = mg，其中在地球表面 g = 9.81 m s⁻²。
Tension, normal reaction, friction and drag must be considered. Static friction obeys F ≤ μsR, and kinetic friction F = μkR where R is the normal reaction force.
必须考虑张力、法向反作用力、摩擦力和阻力。静摩擦力满足 F ≤ μsR，滑动摩擦力满足 F = μkR，其中 R 为法向反作用力。
3. Energy, Work & Power | 能量、功与功率
Energy is conserved in all processes. The principle of conservation of energy states that energy can be transferred, stored or dissipated but never created or destroyed.
能量在所有过程中守恒。能量守恒定律指出，能量可以转移、储存或耗散，但不会凭空产生或消失。
Kinetic energy: Ek = ½ mv²
This is the energy a body possesses due to its motion.
这是物体因运动而具有的能量。
Gravitational potential energy: ΔEp = mgΔh
Change in GPE depends on vertical height change Δh near the Earth’s surface.
重力势能的变化取决于地球表面附近的竖直高度变化 Δh。
Work done: W = Fd cos θ
Work is the product of the force component along the direction of displacement and the displacement magnitude. θ is the angle between force and displacement vectors.
功是沿位移方向的力分量与位移大小的乘积。θ 是力与位移矢量之间的夹角。
Power: P = W/t = Fv
Power is the rate of doing work. For a constant force acting on an object moving at speed v, instantaneous power is Fv.
功率是做功的快慢。对于作用在以速度 v 运动的物体上的恒定力，瞬时功率为 Fv。
4. Momentum & Impulse | 动量与冲量
The momentum of an object is the product of its mass and velocity. In a closed system, total momentum is conserved in all collisions and explosions.
物体的动量是其质量与速度的乘积。在封闭系统中，所有碰撞和爆炸过程中总动量守恒。
p = mv
Momentum is a vector quantity with unit kg m s⁻¹.
动量是矢量，单位为 kg m s⁻¹。
Impulse = Δp = FΔt
The impulse imparted by a force equals the change in momentum of the object. This is Newton’s second law in its most general form.
力施加的冲量等于物体动量的变化。这是牛顿第二定律最普遍的形式。
In a perfectly elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not; some kinetic energy is converted to other forms.
在完全弹性碰撞中，动量和动能均守恒。在非弹性碰撞中，动量守恒但动能不守恒；部分动能转化为其他形式的能量。
5. Moments & Equilibrium | 力矩与平衡
A body is in static equilibrium when the resultant force and the resultant moment about any point are both zero.
当作用在物体上的合外力以及对任意点的合力矩均为零时，物体处于静力平衡状态。
Moment = F × d (perpendicular distance from pivot)
The moment of a force measures its turning effect. It is taken as positive if it causes clockwise rotation, or vice versa depending on convention.
力矩衡量力的转动效应。通常规定使物体顺时针转动的力矩为正，或根据约定取相反符号。
For a uniform rod, its weight acts through the geometrical centre. The principle of moments states that for an object in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about any pivot.
对于匀质杆，重力作用在几何中心。力矩原理指出，处于转动平衡的物体，关于任意支点的顺时针力矩之和等于逆时针力矩之和。
6. Materials: Stress, Strain & Young Modulus | 材料：应力、应变与杨氏模量
The mechanical properties of materials are quantified by stress, strain and the Young modulus. These define how materials deform under load.
材料的力学性能由应力、应变和杨氏模量来量化，这些量描述了材料在载荷作用下如何变形。
Stress: σ = F/A
Stress is the force applied per unit cross‑sectional area. Unit: Pa (N m⁻²).
应力是单位横截面积上施加的力。单位：Pa (N m⁻²)。
Strain: ε = ΔL/L
Strain is the extension per unit original length; it is dimensionless.
应变是单位原始长度的伸长量，无量纲。
Young modulus: E = σ/ε
The Young modulus is a measure of stiffness of a material within its elastic limit. Gradient of stress‑strain graph in the linear region.
杨氏模量是衡量材料在弹性极限内刚度的量，是应力‑应变图线性区域的斜率。
Hooke’s law for springs: F = kΔx, where k is the spring constant. Elastic strain energy = ½ FΔx = ½ k(Δx)².
弹簧的胡克定律：F = kΔx，其中 k 为劲度系数。弹性势能 = ½ FΔx = ½ k(Δx)²。
7. Waves: Basics & the Wave Equation | 波动基础与波动方程
Waves transfer energy without transferring matter. Transverse waves (e.g. light, water ripples) have oscillations perpendicular to the direction of energy transfer; longitudinal waves (e.g. sound) have oscillations parallel to it.
波传递能量而不传递物质。横波（如光、水波）的振动方向与能量传递方向垂直；纵波（如声波）的振动方向与能量传递方向平行。
v = fλ
The wave speed v equals frequency f multiplied by wavelength λ. This applies to all waves.
波速 v 等于频率 f 乘以波长 λ。这适用于所有波。
Phase difference Δφ is measured in radians or degrees; two points separated by λ have a phase difference of 2π rad (360°).
相位差 Δφ 以弧度或度来衡量；相距 λ 的两点相位差为 2π rad (360°)。
Intensity ∝ amplitude². For a point source, intensity ∝ 1/r².
强度与振幅的平方成正比。对于点波源，强度与 1/r² 成正比。
8. Refraction, Reflection & Total Internal Reflection | 折射、反射与全内反射
When a wave meets a boundary between two media, part is reflected and part transmitted, usually with a change in direction (refraction).
当波遇到两种介质的边界时，部分被反射，部分透射，通常伴有方向的变化（折射）。
Snell’s law: n₁ sin θ₁ = n₂ sin θ₂
Here n is the refractive index and θ the angle measured relative to the normal. If light enters an optically denser medium, it bends towards the normal.
这里 n 是折射率，θ 是相对于法线的角度。光进入光密介质时会向法线方向偏折。
Critical angle θc occurs when θ₂ = 90°. Then sin θc = n₂/n₁ (with n₁ > n₂). For angles of incidence greater than θc, total internal reflection occurs.
当 θ₂ = 90° 时对应的入射角为临界角 θc。则 sin θc = n₂/n₁（其中 n₁ > n₂）。入射角大于临界角时发生全内反射。
9. Superposition, Interference & Stationary Waves | 叠加、干涉与驻波
The principle of superposition: when two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements.
叠加原理：当两个或多个波在某点相遇时，合位移等于各分位移的矢量和。
For double-slit interference (Young’s experiment):
双缝干涉（杨氏实验）：
λ = ax/D
where a is slit separation, x is fringe spacing, D is the distance from slits to screen. This gives the wavelength of coherent light.
其中 a 为双缝间距，x 为条纹间距，D 为双缝到屏幕的距离。此式用于求相干光的波长。
For a diffraction grating: nλ = d sin θ, where d = 1/N is the grating spacing and n is the order number.
衍射光栅：nλ = d sin θ，其中 d = 1/N 为光栅常数，n 为级数。
Stationary waves form when two identical waves travelling in opposite directions superpose. Nodes are points of zero displacement; antinodes have maximum amplitude. λ = 2L for the fundamental frequency on a string fixed at both ends.
驻波由两列相同但反向传播的波叠加形成。波节是位移始终为零的点；波腹振幅最大。对于两端固定的弦，基频满足 λ = 2L。
10. Electric Current, Charge & Potential Difference | 电流、电荷与电势差
Electric current is the rate of flow of charge. In a metal, it is carried by electrons.
电流是电荷流动的速率。在金属中，电荷载体是电子。
I = ΔQ/Δt
Unit: ampere (A). 1 A = 1 C s⁻¹.
单位：安培 (A)。1 A = 1 C s⁻¹。
Potential difference (p.d.) between two points is the energy transferred per unit charge moved.
两点间的电势差是单位电荷移动时转移的能量。
V = W/Q
Electromotive force (e.m.f.) of a source is the energy converted from other forms to electrical energy per unit charge passing through the source.
电源的电动势是单位电荷通过电源时从其他形式转换成电能的能量。
Ohm’s law: for a metallic conductor at constant temperature, V = IR.
欧姆定律：对于温度恒定的金属导体，V = IR。
Resistance depends on geometry and material: R = ρL/A, where ρ is resistivity.
电阻取决于几何形状和材料：R = ρL/A，其中 ρ 为电阻率。
11. Circuits: Series & Parallel Rules | 电路：串联与并联规则
Understanding how components combine in circuits is essential for analysis.
理解元件在电路中的组合方式对于电路分析至关重要。
| Quantity | Series | Parallel |
|---|---|---|
| Current | I constant | Itotal = I₁ + I₂ + … |
| Potential difference | Vtotal = V₁ + V₂ + … | V constant |
| Resistance | Rtotal = R₁ + R₂ + … | 1/Rtotal = 1/R₁ + 1/R₂ + … |
The power dissipated in a resistor can be expressed as P = IV, P = I²R or P = V²/R.
电阻消耗的功率可以用 P = IV、P = I²R 或 P = V²/R 表示。
A potential divider is used to obtain a variable voltage. For two resistors R₁ and R₂ in series across supply Vs,
分压器用于获得可变电压。对于串联在电源 Vs 上的两个电阻 R₁ 和 R₂，
Vout = Vs × (R₂/(R₁+R₂))
Internal resistance r of a cell reduces the terminal p.d.: V = ε − Ir.
电池的内阻 r 会降低路端电压：V = ε − Ir。
12. Quantum Physics: Photons & the Photoelectric Effect | 量子物理：光子与光电效应
Light behaves as both a wave and a particle. A photon is a quantum of electromagnetic energy.
光同时表现出波动性和粒子性。光子是电磁能的量子。
E = hf
where h is Planck’s constant (6.63×10⁻³⁴ J s). Photon energy is directly proportional to frequency.
其中 h 为普朗克常量 (6.63×10⁻³⁴ J s)。光子能量与频率成正比。
The photoelectric effect demonstrates the particle nature of light. Electrons are emitted from a metal surface when incident light frequency exceeds the threshold frequency f₀.
光电效应证明了光的粒子性。当入射光频率超过截止频率 f₀ 时，电子从金属表面逸出。
hf = φ + Kmax
Einstein’s photoelectric equation: photon energy = work function φ + maximum kinetic energy of emitted electron. The work function is the minimum energy required to liberate an electron from the metal surface.
爱因斯坦光电方程：光子能量 = 逸出功 φ + 发射电子的最大动能。逸出功是从金属表面释放一个电子所需的最小能量。
Threshold frequency f₀ = φ/h. Stopping potential Vs is related to Kmax by Kmax = eVs, where e is the elementary charge (1.60×10⁻¹⁹ C).
截止频率 f₀ = φ/h。遏止电势 Vs 与 Kmax 的关系为 Kmax = eVs，其中 e 为元电荷 (1.60×10⁻¹⁹ C)。
The electronvolt (eV) is a unit of energy: 1 eV = 1.60×10⁻¹⁹ J. Use it conveniently for photon energies and work functions.
电子伏特 (eV) 是能量单位：1 eV = 1.60×10⁻¹⁹ J。在处理光子能量和逸出功时使用它很方便。
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