📚 Year 13 CCEA Physics: Formula & Theorem Quick Reference Handbook | Year 13 CCEA 物理：公式定理速查手册
This handbook compiles essential equations and theorems for CCEA Year 13 Physics, serving as a rapid revision tool. Each section pairs a clear English statement with a parallel Chinese explanation, helping you memorise and apply key concepts effectively for your examinations.
本手册汇编了 CCEA Year 13 物理的核心公式与定理，是快速复习的利器。每个部分均包含清晰的英文陈述与对应的中文解释，帮助你高效记忆并灵活运用关键概念，备战考试。
1. Circular Motion | 圆周运动
the circle. The centripetal acceleration a = v²/r = rω² always points towards the centre.
在匀速圆周运动中，线速度 v 与角速度 ω 的关系为 v = rω，其中 r 为圆周半径。向心加速度 a = v²/r = rω²，始终指向圆心。
ce is the resultant of all real forces acting toward the centre; it is not an extra force.
维持物体做圆周运动的向心力为 F = mv²/r = mrω²。该力是所有指向圆心的实际作用力的合力，并非额外施加的力。
ω is also given by ω = 2π/T = 2πf, where T is the period and f the frequency of rotation.
角速度 ω 亦可表示为 ω = 2π/T = 2πf，其中 T 为周期，f 为转动频率。
2. Simple Harmonic Motion (SHM) | 简谐运动 (SHM)
onal to its displacement x from equilibrium and directed opposite to the displacement: a = –ω²x. The defining constant ω is the angular frequency.
当物体的加速度 a 与其离开平衡位置的位移 x 成正比且方向相反时，即 a = –ω²x，物体做简谐运动。定义中的常数 ω 为角频率。
= A sin(ωt + φ), where A is amplitude and φ is the phase constant. The velocity is v = ±ω√A² – x² and the maximum speed is vₘₐₓ = ωA.
简谐运动的位移可表示为 x = A cos(ωt + φ) 或 x = A sin(ωt + φ)，其中 A 为振幅，φ 为初相位。速度 v = ±ω√A² – x²，最大速率 vₘₐₓ = ωA。
For a mass–spring system, the period T = 2π√m/k, where m is the mass and k is the spring constant. For a simple pendulum, T = 2π√l/g, where l is the length and g the gravitational field strength.
弹簧振子的周期 T = 2π√m/k，其中 m 为质量，k 为劲度系数。单摆的周期 T = 2π√l/g，l 为摆长，g 为重力场强度。
gy K = ½ m v² and potential energy U = ½ k x² interchange without loss in an ideal system.
简谐运动中的总能量守恒：Eₜₒₜ = ½ k A² = ½ m ω² A²。动能 K = ½ m v² 与势能 U = ½ k x² 在理想系统中无损耗地相互转化。
3. Gravitational Fields | 引力场
Newton' universal gravitational constant (6.67 × 10⁻¹¹ N m² kg⁻²). The force is always attractive.
牛顿万有引力定律：两个质点 M 和 m，相距 r，其间引力 F = GMm/r²，其中 G 为万有引力常量（6.67 × 10⁻¹¹ N m² kg⁻²）。引力始终为吸引力。
g at a point is the force per unit mass: g = F/m = GM/r² for a point mass M. Near a planet's surface, g = GM/R² where R is the planet's radius, and it can be treated as uniform.
引力场强度 g 定义为单位质量所受的力：g = F/m。对于质点为 M 的场，g = GM/r²。靠近行星表面时，g = GM/R²（R 为行星半径），可视为匀强场。
point is the work done per unit mass to bring a test mass from infinity to that point: V = –GM/r. The potential energy of a mass m is then U = mV = –GMm/r.
引力势 V 是把单位质量的检验质点从无穷远处移至该点外力所做的功：V = –GM/r。质量为 m 的物体在该点的势能 U = mV = –GMm/r。
4. Electric Fields | 电场
Coulomb' ≈ 8.99 × 10⁹ N m² C⁻². The force is repulsive for like charges, attractive for opposites.
库仑定律：两电荷 Q 与 q 之间的作用力 F = kQq/r²，其中 k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻²。同种电荷相斥，异种电荷相吸。
parallel plates, E = V/d, where V is the potential difference and d the plate separation.
电场强度 E 定义为单位正电荷所受的力：E = F/q。点电荷 Q 产生的电场 E = kQ/r²。在平行板间的匀强电场中，E = V/d，V 为电势差，d 为板间距。
onvolt (eV) is the energy gained by an electron moving through 1 V: 1 eV = 1.60 × 10⁻¹⁹ J.
点电荷 Q 在距离 r 处产生的电势 V = kQ/r。电荷 q 在该点的电势能 U = qV。电子伏特 (eV) 是电子经过 1 V 电势差获得的能量：1 eV = 1.60 × 10⁻¹⁹ J。
5. Capacitors | 电容器
(F). For a parallel-plate capacitor, C = ε₀A/d, where A is plate area and d is separation.
电容 C 定义为单位电势差储存的电荷量：C = Q/V，单位为法拉 (F)。平行板电容器的电容 C = ε₀A/d，A 为板面积，d 为间距。
U = ½ QV = ½ CV² = ½ Q²/C. This energy is stored in the electric field between the plates.
电容器储存的能量 U = ½ QV = ½ CV² = ½ Q²/C。该能量储存在两极板间的电场中。
hrough a resistor, the charge Q, current I, and voltage V decay exponentially: Q = Q₀ e⁻ᵗ/ᴿᶜ, I = I₀ e⁻ᵗ/ᴿᶜ, V = V₀ e⁻ᵗ/ᴿᶜ. The time constant τ = RC is the time for the quantity to fall to 1/e ≈ 37% of its initial value.
电容器通过电阻放电时，电荷 Q、电流 I 和电压 V 均按指数衰减：Q = Q₀ e⁻ᵗ/ᴿᶜ，I = I₀ e⁻ᵗ/ᴿᶜ，V = V₀ e⁻ᵗ/ᴿᶜ。时间常数 τ = RC，表示物理量衰减到初始值的 1/e ≈ 37% 所需的时间。
Charging a capacitor follows V = V₀(1 – e⁻ᵗ/ᴿᶜ) and I = I₀ e⁻ᵗ/ᴿᶜ, with the same time constant.
电容器充电过程满足 V = V₀(1 – e⁻ᵗ/ᴿᶜ) 和 I = I₀ e⁻ᵗ/ᴿᶜ，时间常数相同。
6. Magnetic Fields | 磁场
e B is the magnetic flux density, v is the speed, and θ is the angle between velocity and field. The direction is given by Fleming's left-hand rule for positive charges.
磁场对运动电荷的作用力为 F = BQv sinθ，B 为磁感应强度，v 为速率，θ 为速度与磁场方向的夹角。方向由左手定则判定（针对正电荷）。
ic field, the force is F = BIL sinθ. When the field is perpendicular to the wire, F = BIL.
长度为 L、通有电流 I 的导线在磁场中所受的力 F = BIL sinθ。当磁场与导线垂直时，F = BIL。
is Φ = BA cosθ, where θ is the angle between the normal to the area and the field. Faraday's law of electromagnetic induction states that the induced emf ε = –N ΔΦ/Δt (Lenz's law included).
通过面积 A 的磁通量 Φ = BA cosθ，θ 为面积法线与磁场的夹角。法拉第电磁感应定律：感应电动势 ε = –N ΔΦ/Δt（包含楞次定律）。
7. Thermal Physics | 热物理
8.31 J mol⁻¹ K⁻¹ and k = 1.38 × 10⁻²³ J K⁻¹. Temperature in Kelvin T(K) = θ(°C) + 273.15.
理想气体状态方程：pV = nRT = NkT，其中 R = 8.31 J mol⁻¹ K⁻¹，k = 1.38 × 10⁻²³ J K⁻¹。开氏温度 T(K) = θ(°C) + 273.15。
The kinetic theory model gives the pressure exerted by an ideal gas: p = ⅓ (Nm/V) ⟨c²⟩ = ⅓ ρ⟨c²⟩, where ⟨c²⟩ is the mean square speed. The average translational kinetic energy of a molecule is ⟨K⟩ = (3/2)kT.
气体动理论给出理想气体的压强：p = ⅓ (Nm/V) ⟨c²⟩ = ⅓ ρ⟨c²⟩，⟨c²⟩ 为方均速率。分子的平均平动动能 ⟨K⟩ = (3/2)kT。
heat L is the energy required to change the phase of 1 kg at constant temperature: Q = mL.
比热容 c 是使 1 kg 物质温度升高 1 K 所需的能量：Q = mcΔT。比潜热 L 是使 1 kg 物质在恒温下发生相变所需的能量：Q = mL。
The first law of thermodynamics for a closed system: ΔU = Q + W (or ΔU = Q – sign convention; CCEA usually uses ΔU = Q + W where work done on the system is positive).
热力学第一定律（封闭系统）：ΔU = Q + W（习惯上外界对系统做功为正）。
8. Nuclear Physics | 核物理
Mass-energy equivalence is given by Einstein' e unified atomic mass unit u is 1 u = 1.661 × 10⁻²⁷ kg, equivalent to 931.5 MeV of energy.
质能方程 E = mc²，更常用 ΔE = Δm c²。统一原子质量单位 1 u = 1.661 × 10⁻²⁷ kg，相当于 931.5 MeV 的能量。
and A is the mass number. This implies nuclear density is approximately constant for all nuclei.
原子核半径近似为 R = R₀ A¹/³，R₀ ≈ 1.2 × 10⁻¹⁵ m，A 为质量数。这意味着所有原子核的密度近乎相同。
Radioactive decay follows the exponential law N = N₀ e⁻ˡᵗᵗ, where λ is the decay constant. Activity A = λN = A₀ e⁻ˡᵗᵗ. The half-life t₁/₂ = ln 2/λ.
放射性衰变遵循指数规律 N = N₀ e⁻ˡᵗᵗ，λ 为衰变常量。活度 A = λN = A₀ e⁻ˡᵗᵗ。半衰期 t₁/₂ = ln 2/λ。
The binding energy of a nucleus is the energy required to separate it into its constituent nucleons. Binding energy per nucleon is a measure of stability; iron-56 has one of the highest values.
原子核的结合能是将其分解为单个核子所需的能量。每个核子的平均结合能是衡量稳定性的指标；铁-56 具有最高值之一。
9. Waves and Optics | 波动与光学
, and wavelength λ: v = fλ. For electromagnetic waves in vacuum, v = c = 3.00 × 10⁸ m s⁻¹.
波动方程联系波速 v、频率 f 和波长 λ：v = fλ。真空中电磁波的波速 c = 3.00 × 10⁸ m s⁻¹。
Refractive index n of a medium is n = c/v. Snell' ction is n₁ sinθ₁ = n₂ sinθ₂. For total internal reflection to occur, the critical angle θ𝒸 satisfies sinθ𝒸 = n₂/n₁ (n₁ > n₂).
介质的折射率 n = c/v。斯涅耳折射定律：n₁ sinθ₁ = n₂ sinθ₂。发生全反射时，临界角 θ𝒸 满足 sinθ𝒸 = n₂/n₁（n₁ > n₂）。
Young' lit separation. For a diffraction grating, maxima occur at d sinθ = nλ (n = 0, 1, 2, ...).
杨氏双缝干涉条纹间距 Δy = λD/d，D 为缝到屏的距离，d 为双缝间距。衍射光栅的极大条件满足 d sinθ = nλ（n = 0, 1, 2, ...）。
10. Particle Physics | 粒子物理
In the Standard Model, hadrons are particles made of quarks, while leptons are fundamental. Baryons (e.g., proton, neutron) consist of three quarks; mesons (e.g., pion) consist of a quark–antiquark pair.
在标准模型中，强子由夸克组成，轻子为基本粒子。重子（如质子、中子）由三个夸克组成；介子（如 π 介子）由一个夸克和一个反夸克组成。
Conservation laws always apply to particle interactions: charge, baryon number, lepton number (separately for each family), and energy–momentum must be conserved. Strangeness is conserved in strong interactions but not in weak interactions.
粒子相互作用必须遵守守恒定律：电荷、重子数、轻子数（各家族分别守恒）以及能量–动量守恒。奇异数在强相互作用中守恒，但在弱相互作用中不守恒。
The de Broglie wavelength of a particle is λ = h/p = h/(mv), showing wave– cribed by hf = φ + Kₘₐₓ, where φ is the work function and Kₘₐₓ = eVₛ (stopping potential).
德布罗意波长 λ = h/p = h/(mv)，体现了波粒二象性。光电效应方程为 hf = φ + Kₘₐₓ，其中 φ 为逸出功，Kₘₐₓ = eVₛ（遏止电势）。
11. Electromagnetic Induction | 电磁感应
pendicular to a magnetic field B is ε = BLv. For a coil of N turns with changing flux, ε = –N dΦ/dt.
长度为 L 的直导线以速度 v 垂直于磁场 B 运动时，感应电动势的大小 ε = BLv。对于匝数为 N、磁通量变化的线圈，ε = –N dΦ/dt。
ₚ = Nₛ/Nₚ = Iₚ/Iₛ. Power in primary equals power in secondary: Vₚ Iₚ = Vₛ Iₛ, assuming 100% efficiency.
理想变压器的变压器方程：Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ。假设效率为 100%，输入功率等于输出功率：Vₚ Iₚ = Vₛ Iₛ。
Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it. This is responsible for the negative sign in Faraday's law.
楞次定律指出，感应电流的方向总是阻碍引起它的磁通量变化。法拉第定律中的负号就是楞次定律的体现。
12. Data and Constants Quick List | 常用数据与常数速查
lectron mass mₑ = 9.11 × 10⁻³¹ kg; proton mass mₚ = 1.67 × 10⁻²⁷ kg; Planck constant h = 6.63 × 10⁻³⁴ J s; speed of light in vacuum c = 3.00 × 10⁸ m s⁻¹; permittivity of free space ε₀ = 8.85 × 10⁻¹² F m⁻¹; Avogadro constant Nₐ = 6.02 × 10²³ mol⁻¹; molar gas constant R = 8.31 J mol⁻¹ K⁻¹; Boltzmann constant k = 1.38 × 10⁻²³ J K⁻¹.
万有引力常量 G = 6.67 × 10⁻¹¹ N m² kg⁻²；地表重力加速度 g = 9.81 N kg⁻¹ (m s⁻²)；元电荷 e = 1.60 × 10⁻¹⁹ C；电子质量 mₑ = 9.11 × 10⁻³¹ kg；质子质量 mₚ = 1.67 × 10⁻²⁷ kg；普朗克常量 h = 6.63 × 10⁻³⁴ J s；真空光速 c = 3.00 × 10⁸ m s⁻¹；真空介电常量 ε₀ = 8.85 × 10⁻¹² F m⁻¹；阿伏伽德罗常量 Nₐ = 6.02 × 10²³ mol⁻¹；摩尔气体常量 R = 8.31 J mol⁻¹ K⁻¹；玻尔兹曼常量 k = 1.38 × 10⁻²³ J K⁻¹。
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