📚 Year 12 CCEA Physics: Formula & Theorem Quick Reference | CCEA 物理：公式定理速查手册
Master the essential equations and principles for the CCEA AS Physics course. This guide covers kinematics, dynamics, materials, waves, electricity, and quantum phenomena – all in one place, with clear English and Chinese explanations side by side.
掌握 CCEA AS 物理课程的核心方程与原理。本手册覆盖运动学、动力学、材料、波、电学及量子现象，中英对照，一目了然。
1. Kinematics – Linear Motion | 运动学——直线运动
For an object moving with uniform acceleration a, the SUVAT equations relate initial velocity u, final velocity v, displacement s, and time t.
对于匀加速直线运动，SUVAT 方程组将初速度 u、末速度 v、位移 s、加速度 a 和时间 t 联系起来。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
Choose the equation that omits the unknown variable. For free fall, replace a with g = 9.81 m s⁻² (downward).
选择不含待求量的公式。自由落体运动中，将 a 替换为重力加速度 g = 9.81 m s⁻²（竖直向下）。
| Symbol | Meaning | 单位 |
| u | initial velocity | m s⁻¹ |
| v | final velocity | m s⁻¹ |
| a | acceleration | m s⁻² |
| s | displacement | m |
| t | time | s |
2. Dynamics – Newton's Laws & Forces | 动力学——牛顿定律与力
Newton's second law: F = ma, where resultant force F (N) equals mass m (kg) times acceleration a (m s⁻²).
牛顿第二定律：F = ma，合力 F（牛）等于质量 m（千克）乘加速度 a（m s⁻²）。
Weight is the force due to gravity: W = mg. On a slope, resolve weight into components parallel (mg sinθ) and perpendicular (mg cosθ) to the plane.
重力公式：W = mg。在斜面上，将重力分解为沿斜面分量（mg sinθ）和垂直斜面分量（mg cosθ）。
Friction: when limiting equilibrium, F_friction = µR, where µ is the coefficient of friction and R the normal reaction.
摩擦力：极限平衡时摩擦力 = µR，µ 为摩擦系数，R 为法向反作用力。
Moment (torque): moment = Fd, where d ents states that for equilibrium, sum of clockwise moments = sum of anticlockwise moments.
力矩：力矩 = Fd，d 为支点到力作用线的垂直距离。力矩原理：平衡时顺时针力矩之和等于逆时针力矩之和。
3. Momentum & Impulse | 动量与冲量
Momentum p = mv (kg m s⁻¹). Impulse equals change in momentum: FΔt = Δp = mv − mu.
动量：p = mv（千克·米/秒）。冲量等于动量变化量：FΔt = Δp = mv − mu。
ntum after collision. For a perfectly elastic collision, kinetic energy is also conserved.
动量守恒定律：在不受外力的封闭系统中，碰撞前总动量等于碰撞后总动量。完全弹性碰撞中，动能也守恒。
For a collision of two objects A and B along a straight line:
两物体 A、B 的一维碰撞：
mₐuₐ + mₑuₑ = mₐvₐ + mₑvₑ
Force-time graphs: the area under the graph gives impulse.
力–时间图像：图线下面积表示冲量。
4. Work, Energy & Power | 功、能与功率
Work done by a constant force: W = Fs cosθ, where θ is the angle between force and displacement.
恒力做功：W = Fs cosθ，θ 为力与位移的夹角。
Kinetic energy: Eₖ = ½mv². Gravitational potential energy: Eₚ = mgΔh (near Earth's surface).
动能：Eₖ = ½mv²。重力势能（地表附近）：Eₚ = mgΔh。
ated system remains constant. It may be transformed, e.g., kinetic → thermal via friction.
能量守恒定律：孤立系统的总能量保持不变。能量可以转化，例如摩擦使动能转变为热能。
Power is the rate of doing work: P = W/t or for a constant force moving at speed v, P = Fv.
功率是做功的快慢：P = W/t，或恒力下以速度 v 运动时 P = Fv。
Efficiency: efficiency = (useful output energy)/(total input energy) × 100%.
效率：效率 = （有用输出能量）/（总输入能量）× 100%。
5. Materials – Stress, Strain & Young Modulus | 材料学——应力、应变与杨氏模量
Tensile stress: σ = F/A (Pa). Tensile strain: ε = ΔL/L₀ (dimensionless).
拉伸应力：σ = F/A（帕斯卡）。拉伸应变：ε = ΔL/L₀（无单位）。
Young modulus: E = σ/ε = (F/A) / (ΔL/L₀). Its unit is Pa. It measures stiffness; a steeper stress-strain gradient indicates a higher Young modulus.
杨氏模量：E = σ/ε = (F/A) / (ΔL/L₀)，单位 Pa。它表示刚度；应力–应变曲线越陡峭，杨氏模量越大。
Hooke's law for a spring: F = kx, where k is the spring constant (N m⁻¹) and x the extension. Elastic potential energy stored: Eₑₗ = ½kx² (area under the force–extension graph).
弹簧的胡克定律：F = kx，k 为劲度系数（N m⁻¹），x 为伸长量。弹性势能：Eₑₗ = ½kx²（即力–伸长图线下面积）。
Types of deformation: elastic (returns to original shape) and plastic (permanent). Limit of proportionality and elastic limit are key points on a force-extension graph.
形变类型：弹性形变（恢复原状）和塑性形变（永久形变）。力–伸长图上的比例极限和弹性极限是关键点。
6. Waves – Basic Properties & the Wave Equation | 波的基本性质与波动方程
A progressive wave transfers energy without transferring matter. Key quantities: frequency f (Hz), wavelength λ (m), amplitude A (m), period T (s).
前进波传递能量而不传递物质。基本量：频率 f（赫兹）、波长 λ（米）、振幅 A（米）、周期 T（秒）。
The wave equation: v = fλ. Also T = 1/f.
波动方程：v = fλ。且 T = 1/f。
Transverse waves: oscillations perpendicular to energy transfer (light, water ripples). Longitudinal waves: oscillations parallel to energy transfer (sound). Polarisation can only occur for transverse waves.
横波：振动方向垂直于能量传递方向（光、水波）。纵波：振动方向平行于能量传递方向（声波）。只有横波才能发生偏振。
difference / λ). Two points in phase have a path difference of nλ; out of phase by (n+½)λ.
相位差（弧度或度）：Δφ = 2π（路程差 / λ）。同相两点路程差为 nλ；反相路程差为 (n+½)λ。
7. Refraction & Total Internal Reflection | 折射与全内反射
Snell's law: n₁ sin i = n₂ sin r, where n₁ and n₂ are the refractive indices of the two media. The refractive index of a medium is n = c/v, where c is the speed of light in vacuum.
斯涅尔定律：n₁ sin i = n₂ sin r，n₁、n₂ 为两种介质的折射率。介质的折射率 n = c/v，c 为真空中光速。
Critical angle for total internal reflection: sin C = n₂/n₁ (when light goes from denser to less dense medium). TIR occurs when angle of incidence > C.
全内反射的临界角：sin C = n₂/n₁（光从光密介质射向光疏介质）。当入射角 > C 时发生全内反射。
8. Superposition & Interference | 叠加与干涉
The principle of superposition: when two waves meet, the resultant displacement is the vector sum of individual displacements.
叠加原理：两列波相遇时，合位移是各分位移的矢量和。
Two-source interference (Young' right fringe) when path difference = nλ; destructive (dark) when path difference = (n+½)λ.
双缝干涉：光程差为 nλ 时加强（亮纹）；光程差为 (n+½)λ 时减弱（暗纹）。
Fringe spacing: Δy = λD/d, where D is the distance to the screen, d is the slit separation. This is used to measure wavelength.
条纹间距：Δy = λD/d，D 为双缝到屏幕的距离，d 为双缝间距。此式用于测量波长。
9. Electricity – Current, Voltage & Resistance | 电学——电流、电压与电阻
Charge: ΔQ = I Δt. Current is the rate of flow of charge: I = ΔQ/Δt.
电荷量：ΔQ = I Δt。电流是电荷流动的速率：I = ΔQ/Δt。
Ohm's law (for an ohmic conductor at constant temperature): V = IR. Resistance is defined as R = V/I.
欧姆定律（恒温下的欧姆导体）：V = IR。电阻定义为 R = V/I。
Resistance of a wire: R = ρL/A, where ρ is resistivity (Ω m), L length, A cross-sectional area.
导线的电阻：R = ρL/A，ρ 为电阻率（Ω m），L 长度，A 横截面积。
Power dissipated: P = VI = I²R = V²/R.
功率消耗：P = VI = I²R = V²/R。
10. DC Circuits – Series, Parallel & Potential Dividers | 直流电路——串联、并联与分压器
Series: current same, Rtotal = R₁ + R₂ + …, voltages split in ratio of resistances.
串联：电流相等，Rtotal = R₁ + R₂ + …，电压按电阻比例分配。
Parallel: voltage same, 1/Rtotal = 1/R₁ + 1/R₂ + …, currents split inversely with resistance.
并联：电压相等，1/Rtotal = 1/R₁ + 1/R₂ + …，电流按电阻反比分配。
Potential divider equation: Vout = Vin × (R₂/(R₁ + R₂)). Used in sensor circuits (LDR, thermistor).
分压公式：Vout = Vin × （R₂/（R₁ + R₂））。用于传感器电路（光敏电阻、热敏电阻）。
Internal resistance r of a cell: terminal pd V = ε − Ir, where ε is emf. Power delivered to load is maximised when load resistance equals internal resistance.
电池内阻 r：端电压 V = ε − Ir，ε 为电动势。当负载电阻等于内阻时，输出功率最大。
11. Photoelectric Effect & Photons | 光电效应与光子
Photon energy: E = hf = hc/λ, where h is Planck's constant (6.63 × 10⁻³⁴ J s).
光子能量：E = hf = hc/λ，h 为普朗克常数（6.63 × 10⁻³⁴ 焦·秒）。
Einstein's photoelectric equation: hf = φ + KE_max, where φ is the work function (minimum energy to eject an electron).
爱因斯坦光电效应方程：hf = φ + KE_max，φ 为逸出功（发射电子的最小能量）。
Threshold frequency: f₀ = φ/h. No electrons are emitted below this frequency, regardless of intensity. The number of photoelectrons increases with intensity, while their maximum kinetic energy depends only on frequency.
截止频率：f₀ = φ/h。低于此频率，无论光强多大都无电子逸出。光电子数量随光强增加，而最大动能仅取决于频率。
Stopping potential Vs: eVs = KE_max, allowing measurement of Planck's constant.
遏止电压 Vs：eVs = KE_max，可用于测量普朗克常数。
12. Atomic Structure & Spectra | 原子结构与光谱
Bohr model: electrons occupy discrete energy levels. Photon is emitted when an electron drops from a higher level E₂ to a lower level E₁: ΔE = E₂ − E₁ = hf.
玻尔模型：电子处于离散能级。电子从高能级 E₂ 跃迁至低能级 E₁ 时发射光子：ΔE = E₂ − E₁ = hf。
Ionisation energy: energy required to remove an electron from the ground state to infinity. In hydrogen, Eₙ = −13.6/n² eV.
电离能：将基态电子移至无限远所需能量。氢原子中 Eₙ = −13.6/n² eV。
Emission and absorption line spectra provide evidence for discrete energy levels. The Balmer series lies in the visible region.
发射光谱与吸收光谱证实了分立能级的存在。巴耳末系位于可见光区。
De Broglie wavelength of matter: λ = h/p = h/mv. This explains electron diffraction and standing waves in atomic orbits.
物质波的德布罗意波长：λ = h/p = h/mv。这解释了电子衍射和原子轨道中的驻波。
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