📚 Year 11 CIE Physics: Formula & Theorem Quick Reference Handbook | 11年级CIE物理：公式定理速查手册
Mastering physics at Year 11 level means having instant recall of the essential equations and principles. This handbook brings together the core formulas from the CIE IGCSE / O-Level syllabus, covering mechanics, thermal physics, waves, electricity, and more. Each section pairs a clear English statement with its Chinese equivalent, so you can switch between languages with ease. Use it for last‑minute revision, daily practice, or to build a solid foundation for Year 12.
在11年级阶段掌握物理，意味着必须熟练记忆并理解核心公式与原理。本手册整合了CIE IGCSE/O-Level课程中的关键公式，涵盖力学、热学、波动、电学等内容。每个部分均提供清晰的英文表述及对应的中文翻译，帮助你轻松实现双语切换。可用于考前速查、日常练习或为12年级打下坚实基础。
1. Kinematics – Motion in a Straight Line | 运动学 – 直线运动
The four equations of motion for uniform acceleration link initial velocity (u), final velocity (v), acceleration (a), time (t) and displacement (s). They assume motion along a straight line with constant acceleration.
描述匀加速直线运动的四个基本方程，将初速度(u)、末速度(v)、加速度(a)、时间(t)和位移(s)联系在一起。使用前提是加速度恒定且沿直线运动。
v = u + a t
s = u t + ½ a t²
s = (u + v) t / 2
v² = u² + 2 a s
These equations are vector‑based: remember to assign positive and negative directions consistently when plugging in values.
这些方程均为矢量方程：代入数值时注意始终统一正方向，反向取负。
2. Forces and Newton’s Laws | 力与牛顿定律
A resultant force produces an acceleration proportional to the mass of the object. Newton’s second law is the backbone of dynamics, while the first and third laws describe inertia and interaction pairs.
合力使物体产生加速度，加速度与物体的质量成反比。牛顿第二定律是动力学的核心，而第一、第三定律分别描述了惯性和相互作用力。
F = m a
Weight is the gravitational force on a mass: W = m g, with g ≈ 9.8 m s⁻² on Earth. The extension of a spring obeys Hooke’s law, provided the elastic limit is not exceeded.
重量是引力作用在质量上的结果：W = m g，地表g≈9.8 m s⁻²。弹簧的伸长量在弹性限度内遵循胡克定律。
F = k x
In equilibrium problems, always draw a free‑body diagram to identify all forces acting on a single object.
在平衡问题中，必须画出单个物体的受力分析图，完整标出所有作用力。
3. Energy, Work and Power | 能量、功与功率
Work is done when a force moves an object in the direction of the force. Energy is the capacity to do work, and power describes how quickly energy is transferred.
当力使物体沿力的方向移动时，力对物体做功。能量是做功的本领，功率描述能量转化的快慢。
W = F d cos θ
Gravitational potential energy gained: Eₚ = m g h. Kinetic energy of a moving object: Eₖ = ½ m v². In a closed system, total mechanical energy is conserved if only conservative forces do work.
重力势能的增加：Eₚ = m g h。物体的动能：Eₖ = ½ m v²。在只有保守力做功的封闭系统中，总机械能守恒。
P = W / t = E / t
Efficiency compares useful output to total input, expressed as a percentage: η = (useful energy output / total energy input) × 100%.
效率比较有用输出与总输入，用百分数表示：η = (有用能量输出 / 总能量输入) × 100%。
4. Momentum and Impulse | 动量与冲量
Momentum is the product of mass and velocity and is conserved in any closed system where no external resultant force acts. The principle of conservation of momentum is essential for solving collision and explosion problems.
动量是质量与速度的乘积。在无外力作用的封闭系统中总动量守恒。动量守恒原理是解决碰撞、爆炸问题的核心。
p = m v
Impulse equals the change in momentum and also the average resultant force multiplied by the time interval: F Δt = Δp = m v – m u.
冲量等于动量的变化量，也等于平均合力与作用时间的乘积：F Δt = Δp = m v – m u。
For two‑body collisions: m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂ (in the absence of external net force).
两体碰撞（无外力）：m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂。
5. Density, Pressure and Fluid Statics | 密度、压强与流体静力学
Density measures how much mass is packed into a given volume. Pressure relates the perpendicular force to the area over which it acts. For liquids, pressure increases with depth independent of the shape of the container.
密度衡量单位体积内所含质量的多少。压强是垂直作用在单位面积上的力。液体的压强随深度增加，与容器形状无关。
ρ = m / V
P = F / A
Pressure at depth h in a liquid of density ρ: P = ρ g h. This acts equally in all directions at a given depth.
液体中深度h处压强：P = ρ g h。同一深度各个方向的压强大小相等。
For a U‑tube or hydraulic system, pressure transmitted through a fluid follows Pascal’s principle, so F₁ / A₁ = F₂ / A₂.
U形管或液压系统中，液体传递的压强遵循帕斯卡原理：F₁ / A₁ = F₂ / A₂。
6. Thermal Physics – Heat and Temperature | 热学 – 热量与温度
When a substance changes temperature, its internal energy alters. The specific heat capacity links temperature rise to energy supplied, while latent heat governs phase changes at constant temperature.
物体温度变化时，内能随之改变。比热容将温度升高与吸收的热量联系起来，而潜热描述温度不变时发生的相变。
Q = m c Δθ
Here Δθ is the temperature change in °C or K. For phase changes: Q = m L, where L is the specific latent heat of fusion or vaporisation.
Δθ为温度变化量（℃或K）。相变时：Q = m L，L为熔化潜热或汽化潜热。
The relationship between the Celsius scale and the absolute thermodynamic scale is: T (K) = θ (°C) + 273.
摄氏温标与热力学温标的关系：T (K) = θ (°C) + 273。
7. Waves – General Properties | 波 – 基本性质
All waves transfer energy without transferring matter. The wave equation links speed, frequency and wavelength. Both transverse and longitudinal waves follow this relation.
所有波都传递能量而不传递物质。波速方程把波速、频率和波长联系在一起。横波和纵波都遵循这一关系。
v = f λ
Reflection, refraction and diffraction are characteristic behaviours. Refraction occurs because the speed of the wave changes when it enters a new medium, causing a change in wavelength while frequency stays constant.
反射、折射和衍射是波的典型行为。折射的产生是由于波进入新介质时速度改变，导致波长变化，但频率保持不变。
The angle of incidence and reflection are equal (i = r), measured from the normal.
入射角等于反射角（i = r），均从法线量起。
8. Light – Optics and Lenses | 光 – 光学与透镜
The refractive index of a medium quantifies how much light slows down and bends. Snell’s law provides the rule for refraction at a boundary.
介质的折射率定量描述光减速和偏折的程度。斯涅耳定律给出界面折射的规律。
n = sin i / sin r
Critical angle c for total internal reflection: sin c = 1 / n (when light goes from denser to rarer medium).
全反射的临界角c：sin c = 1 / n（光从光密介质射向光疏介质）。
For a thin converging lens, the lens equation relates object distance (u), image distance (v) and focal length (f). Use the real‑is‑positive sign convention.
对于薄凸透镜，透镜方程将物距(u)、像距(v)和焦距(f)联系起来。采用实正虚负符号规则。
1 / f = 1 / u + 1 / v
Magnification: M = image height / object height = v / u.
放大率：M = 像高 / 物高 = v / u。
9. Current Electricity – Ohm’s Law and Resistance | 电流 – 欧姆定律与电阻
Electric current is a flow of charge. Ohm’s law holds for metallic conductors at constant temperature, relating potential difference, current and resistance.
电流是电荷的定向流动。欧姆定律适用于恒温下的金属导体，描述了电势差、电流和电阻之间的关系。
V = I R
Charge, current and time: Q = I t. Resistance in a uniform wire depends on length ℓ, cross‑sectional area A and resistivity ρ: R = ρ ℓ / A.
电荷、电流与时间：Q = I t。均匀导线的电阻取决于长度ℓ、横截面积A及电阻率ρ：R = ρ ℓ / A。
Series resistors: Rₜₒₜ = R₁ + R₂ + …. Parallel resistors: 1 / Rₜₒₜ = 1 / R₁ + 1 / R₂ + ….
串联电阻：Rₜₒₜ = R₁ + R₂ + …。并联电阻：1 / Rₜₒₜ = 1 / R₁ + 1 / R₂ + …。
10. Electrical Power and Energy | 电功率与电能
Power in an electrical component is the rate at which it converts electrical energy to other forms. Several equivalent expressions allow calculation from voltage, current or resistance.
用电器的电功率是电能转化为其他形式能量的速率。由电压、电流或电阻可推导出多个等价表达式。
P = I V
P = I² R
P = V² / R
Electrical energy transferred: E = P t = I V t. In household electricity, the kilowatt‑hour (kWh) is a unit of energy: 1 kWh = 3.6 × 10⁶ J.
电能转化量：E = P t = I V t。家庭用电常用千瓦时(kWh)作为能量单位：1 kWh = 3.6 × 10⁶ J。
11. Electromagnetism – Motors and Generators | 电磁学 – 电动机与发电机
A current‑carrying conductor in a magnetic field experiences a force (the motor effect). The force is greatest when the conductor is perpendicular to the field.
磁场中的载流导体会受到力的作用（电动机效应）。当导线与磁场方向垂直时，作用力最大。
F = B I ℓ
(For a straight conductor of length ℓ in a uniform field B, with current I perpendicular to B.)
（长度为ℓ的直导线置于均匀磁场B中，电流I垂直于B时成立。）
A potential difference is induced across a conductor when it cuts magnetic flux lines (generator effect). The induced e.m.f. depends on the rate of cutting flux.
当导体切割磁感线时，会产生感应电动势（发电机效应）。感应电动势的大小取决于磁通量的切割速率。
The right‑hand grip rule gives the field direction around a straight wire, while Fleming’s left‑hand rule determines the direction of force, field and current.
右手螺旋定则确定通电直导线周围的磁场方向，弗莱明左手定则判定力、磁场与电流的方向关系。
12. Radioactivity and Nuclear Physics | 放射性与核物理
The nucleus is held together by the strong nuclear force. Unstable nuclei emit alpha, beta or gamma radiation. The activity of a source measures the number of decays per second.
原子核由强核力维系。不稳定的原子核会放射α、β或γ射线。源的活度指每秒衰变的次数。
Key definitions: atomic number Z, mass number A. Alpha decay reduces A by 4 and Z by 2; beta decay increases Z by 1 while A stays constant.
关键定义：原子序数Z，质量数A。α衰变使A减少4、Z减少2；β衰变使Z增加1而A不变。
Half‑life t₁/₂ is the time for half the undecayed nuclei to decay: N = N₀ (½)^(t / t₁/₂). Background radiation must be subtracted from all measurements.
半衰期t₁/₂是未衰变原子核数目减半所需时间：N = N₀ (½)^(t / t₁/₂)。所有测量须扣除本底辐射。
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