📚 Year 12 CCEA Physics: Formula & Theorem Quick Reference Handbook | CCEA 物理：公式定理速查手册
This handy reference collects the essential formulae, constants and theorems required for the Year 12 CCEA Physics course. Each section presents a core topic with clearly stated equations and concise explanations to support quick revision and exam preparation.
这本速查手册汇集了 Year 12 CCEA 物理课程必备的公式、常数和定理。每个小节围绕一个核心主题，列出关键方程并配以简明解释，帮助你快速复习和备考。
1. Mechanics: Equations of Motion | 力学：运动方程
For uniform acceleration in a straight line, four key equations relate displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t).
对于匀加速直线运动，四个关键方程将位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t) 联系起来。
v = u + a t
This gives the final velocity after time t.
此式给出时间 t 后的末速度。
s = u t + ½ a t²
Displacement when initial velocity and acceleration are known.
已知初速度和加速度时的位移。
v² = u² + 2 a s
Linking velocity and displacement without time.
不涉及时间，将速度与位移联系起来。
s = ½ (u + v) t
Displacement as average velocity multiplied by time.
位移等于平均速度乘以时间。
2. Newton’s Laws and Forces | 牛顿定律与力
Newton’s three laws form the foundation of classical mechanics.
牛顿三定律构成了经典力学的基础。
ΣF = m a
Newton’s Second Law: the resultant force on an object equals its mass multiplied by its acceleration.
牛顿第二定律：作用在物体上的合力等于物体质量乘以加速度。
Weight is given by W = m g, where g = 9.81 m s⁻² on Earth.
重力由 W = m g 给出，地表 g = 9.81 m s⁻²。
The coefficient of friction μ relates frictional force to normal reaction: F_friction = μ R.
摩擦系数 μ 将摩擦力与法向反作用力联系起来：F_friction = μ R。
Equilibrium occurs when the vector sum of forces is zero.
当力的矢量和为零时，物体处于平衡状态。
3. Momentum and Impulse | 动量与冲量
Momentum (p) is the product of mass and velocity: p = m v. It is a vector quantity.
动量 (p) 是质量与速度的乘积：p = m v，它是一个矢量。
The impulse exerted by a force equals the change in momentum:
力产生的冲量等于动量的变化：
Impulse = F Δt = Δp = m v – m u
In a closed system, total momentum is conserved: Σp_before = Σp_after.
在封闭系统中，总动量守恒：碰撞前的总动量等于碰撞后的总动量。
For elastic collisions, kinetic energy is also conserved; for inelastic collisions, kinetic energy is not conserved but momentum always is.
对于弹性碰撞，动能也守恒；对于非弹性碰撞，动能不守恒，但动量始终守恒。
4. Work, Energy and Power | 功、能量与功率
Work done by a constant force: W = F s cosθ, where θ is the angle between the force and displacement.
恒力做的功：W = F s cosθ，θ 为力与位移之间的夹角。
Kinetic energy: KE = ½ m v².
动能：KE = ½ m v²。
Gravitational potential energy: GPE = m g h (near Earth’s surface).
重力势能：GPE = m g h（地表附近）。
Principle of conservation of energy: energy cannot be created or destroyed, only converted from one form to another.
能量守恒原理：能量既不能创造也不能消灭，只能从一种形式转化为另一种形式。
Power is the rate of doing work: P = W / t or P = F v for a constant force moving at constant speed v.
功率是做功的速率：P = W / t；对于恒力作用下以恒定速率 v 运动的情况，P = F v。
5. Circular Motion | 圆周运动
For an object moving in a circle of radius r at constant speed v, the centripetal acceleration is directed towards the centre.
物体以恒定速率 v 在半径为 r 的圆周上运动时，向心加速度指向圆心。
a = v² / r = ω² r
Here ω is the angular speed in rad s⁻¹, related to linear speed by v = ω r.
其中 ω 为角速度（单位：rad s⁻¹）, 与线速度的关系为 v = ω r。
Centripetal force: F = m v² / r = m ω² r. This force is always perpendicular to the velocity, doing no work.
向心力：F = m v² / r = m ω² r。该力始终与速度垂直，因此不做功。
6. Waves: General Properties | 波：一般性质
The wave equation links speed (v), frequency (f) and wavelength (λ):
波的基本方程将波速 (v)、频率 (f) 和波长 (λ) 联系起来：
v = f λ
Frequency is the number of complete oscillations per second; period T = 1/f.
频率是每秒完整振动的次数；周期 T = 1/f。
Intensity I is proportional to the square of the amplitude: I ∝ A².
强度 I 与振幅的平方成正比：I ∝ A²。
For all waves, reflection, refraction, diffraction and interference occur. Electromagnetic waves travel at speed of light c = 3.00 × 10⁸ m s⁻¹ in a vacuum.
所有波都会发生反射、折射、衍射和干涉。电磁波在真空中的速度为光速 c = 3.00 × 10⁸ m s⁻¹。
7. Wave Phenomena: Superposition and Standing Waves | 波的叠加与驻波
The principle of superposition: when two or more waves meet, the resultant displacement is the vector sum of the individual displacements.
叠加原理：当两个或更多波相遇时，合位移是各分位移的矢量和。
Constructive interference occurs when waves are in phase (path difference = nλ); destructive interference when out of phase (path difference = (n + ½)λ).
当波同相时（波程差 = nλ）产生相长干涉；当波反相时（波程差 = (n + ½)λ）产生相消干涉。
A standing wave is formed by the superposition of two progressive waves of the same frequency travelling in opposite directions. Nodes are points of zero amplitude; antinodes are points of maximum amplitude. Separation between adjacent nodes or antinodes is λ/2.
驻波由两列相同频率、反向传播的行波叠加而成。波节是振幅为零的点；波腹是振幅最大的点。相邻波节或波腹之间的距离为 λ/2。
8. Optics: Refraction and Lenses | 光学：折射与透镜
Snell’s law describes refraction: n₁ sinθ₁ = n₂ sinθ₂, where n is the refractive index.
斯涅尔定律描述折射：n₁ sinθ₁ = n₂ sinθ₂，其中 n 是折射率。
Refractive index n = c / v, where c is the speed of light in vacuum and v is the speed in the medium.
折射率 n = c / v，c 为真空光速，v 为介质中的光速。
The critical angle θ_c for total internal reflection satisfies: sinθ_c = n₂ / n₁ (when n₁ > n₂).
全内反射的临界角 θ_c 满足：sinθ_c = n₂ / n₁（当 n₁ > n₂ 时）。
Thin lens formula (real-is-positive convention): 1/f = 1/u + 1/v, where f is focal length, u is object distance and v is image distance.
薄透镜公式（实正虚负约定）：1/f = 1/u + 1/v，其中 f 为焦距，u 为物距，v 为像距。
Linear magnification m = image height / object height = -v / u.
线性放大率 m = 像高 / 物高 = -v / u。
9. Electricity: Current, Voltage and Resistance | 电流、电压与电阻
Electric current I is the rate of flow of charge: I = ΔQ / Δt.
电流 I 是电荷流动的速率：I = ΔQ / Δt。
Potential difference (V) is the energy transferred per unit charge: V = W / Q.
电势差 (V) 是单位电荷转移的能量：V = W / Q。
Ohm’s law for an ohmic conductor at constant temperature: V = I R.
欧姆定律适用于恒温下的欧姆导体：V = I R。
Resistance R depends on resistivity ρ, length L and cross-sectional area A: R = ρ L / A.
电阻 R 取决于电阻率 ρ、长度 L 和横截面积 A：R = ρ L / A。
Electrical power: P = I V = I² R = V² / R.
电功率：P = I V = I² R = V² / R。
10. DC Circuits and Kirchhoff’s Laws | 直流电路与基尔霍夫定律
Kirchhoff’s Current Law (KCL): the sum of currents entering a junction equals the sum leaving.
基尔霍夫电流定律 (KCL)：流入一个节点的电流之和等于流出电流之和。
Kirchhoff’s Voltage Law (KVL): the sum of the emfs around any closed loop equals the sum of the potential drops.
基尔霍夫电压定律 (KVL)：沿任一闭合回路的电动势之和等于电势降之和。
For resistors in series: R_total = R₁ + R₂ + …
电阻串联：R_total = R₁ + R₂ + …
For resistors in parallel: 1/R_total = 1/R₁ + 1/R₂ + …
电阻并联：1/R_total = 1/R₁ + 1/R₂ + …
Potential divider formula: V_out = V_in × (R₂ / (R₁ + R₂)).
分压公式：V_out = V_in × (R₂ / (R₁ + R₂))。
A source of emf ε has internal resistance r; terminal potential difference V = ε – I r.
电动势为 ε 的电源具有内阻 r；路端电压 V = ε – I r。
11. Materials: Stress, Strain and Young Modulus | 材料：应力、应变与杨氏模量
Tensile stress (σ) = force / cross-sectional area: σ = F / A. Unit: Pa.
拉伸应力 (σ) = 力 / 横截面积：σ = F / A，单位：Pa。
Tensile strain (ε) = extension / original length: ε = ΔL / L₀, dimensionless.
拉伸应变 (ε) = 伸长量 / 原始长度：ε = ΔL / L₀，无量纲。
Young modulus E: E = tensile stress / tensile strain = (F L₀) / (A ΔL).
杨氏模量 E：E = 拉伸应力 / 拉伸应变 = (F L₀) / (A ΔL)。
Hooke’s law: extension is proportional to applied force up to the limit of proportionality. For a spring, F = k Δx, where k is the spring constant.
胡克定律：在比例极限内，伸长量与施加的力成正比。对于弹簧，F = k Δx，k 为劲度系数。
Elastic strain energy stored in a stretched spring: E_el = ½ F Δx = ½ k (Δx)².
拉伸弹簧中储存的弹性势能：E_el = ½ F Δx = ½ k (Δx)²。
12. Particles and Quantum Phenomena | 粒子物理与量子现象
Photon energy: E = h f = h c / λ, where h is Planck’s constant (6.63 × 10⁻³⁴ J s).
光子能量：E = h f = h c / λ，h 为普朗克常数 (6.63 × 10⁻³⁴ J s)。
Einstein’s photoelectric equation: E_k_max = h f – φ, where φ is the work function.
爱因斯坦光电效应方程：E_k_max = h f – φ，φ 为逸出功。
Threshold frequency f₀ = φ / h; the stopping potential V_s is related by e V_s = E_k_max.
截止频率 f₀ = φ / h；遏止电势 V_s 满足 e V_s = E_k_max。
Wave-particle duality: the de Broglie wavelength of a particle with momentum p is λ = h / p.
波粒二象性：动量为 p 的粒子的德布罗意波长 λ = h / p。
In electron diffraction, the observed pattern confirms the wave nature of electrons.
在电子衍射中，观察到的图样证实了电子的波动性。
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