📚 Year 11 CIE Physics Formula & Theorem Quick Reference | 公式定理速查手册
This quick-reference handbook compiles the essential formulas, theorems and constants required for the Year 11 CIE IGCSE Physics syllabus. Each section presents the core equations in a clear, uncluttered format alongside concise explanations, helping you revise efficiently for exams. Use it as a portable memory aid, a checklist for problem-solving, and a confidence booster before your mocks and final papers.
这本速查手册整理了 Year 11 CIE IGCSE 物理大纲要求掌握的关键公式、定理与常数。每一部分用清晰的格式列出核心方程，并配以简要解释，帮助你高效复习备考。它既可作为便携式记忆卡片，也可作为解题时的核查清单，助你在模拟考和正式考试前增强信心。
1. Motion | 运动学
Average speed is defined as total distance travelled divided by total time taken. It is a scalar quantity and does not involve direction.
平均速率等于总路程除以总时间，是标量，不涉及方向。
average speed = total distance / total time vₐᵥ = s / t
Velocity is a vector; it describes speed in a given direction. When motion is in a straight line, average velocity equals displacement over time.
速度是矢量，描述某一方向上的快慢。直线运动中，平均速度等于位移除以时间。
average velocity = displacement / time vₐᵥ = Δx / t
Acceleration is the rate of change of velocity. It can be calculated using the change in velocity divided by the time interval.
加速度是速度的变化率，等于速度变化量除以时间间隔。
acceleration = change in velocity / time taken a = (v – u) / t
For uniform acceleration, three key equations of motion apply when initial velocity u, final velocity v, acceleration a, displacement s and time t are linked:
对于匀加速直线运动，三个核心运动学方程将初速度 u、末速度 v、加速度 a、位移 s 和时间 t 联系起来：
- v = u + a t
- s = u t + ½ a t²
- v² = u² + 2 a s
Distance–time graphs: the gradient gives speed. Velocity–time graphs: the gradient gives acceleration, and the area under the graph gives displacement.
距离–时间图：斜率表示速率。速度–时间图：斜率表示加速度，图线下面积表示位移。
2. Forces and Newton's Laws | 力与牛顿定律
Newton's First Law states that an object remains at rest or in uniform motion in a straight line unless acted upon by a resultant force.
牛顿第一定律：物体在不受合外力作用时，将保持静止或匀速直线运动状态。
Newton's Second Law relates resultant force, mass and acceleration. It is one of the most fundamental equations in mechanics.
牛顿第二定律将合外力、质量与加速度联系起来，是力学中最基本的公式之一。
force = mass × acceleration F = m a
Weight is the gravitational force on a mass. It depends on the gravitational field strength g (on Earth, approximately 9.8 N/kg).
重量是物体受到的重力，取决于引力场强度 g（地球表面约 9.8 N/kg）。
weight = mass × gravitational field strength W = m g
Newton's Third Law: when two objects interact, they exert equal and opposite forces on each other.
牛顿第三定律：两个物体相互作用时，彼此施加的力大小相等、方向相反。
Hooke's Law describes the extension of a spring within its elastic limit: the force applied is directly proportional to the extension.
胡克定律描述弹簧在弹性限度内的伸长：施加的力与伸长量成正比。
force = spring constant × extension F = k x
Friction is a force that opposes motion. It can be static or dynamic, and its magnitude often depends on the nature of the surfaces.
摩擦力阻碍相对运动，分为静摩擦和动摩擦，其大小常取决于接触面的性质。
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. The amount of work equals the force times the distance moved in that direction.
力在力的方向上使物体移动时做功，功的大小等于力乘以沿力方向的位移。
work done = force × distance moved in direction of force W = F d
Kinetic energy is the energy of a moving object. It depends on mass and the square of speed.
动能是运动物体所具有的能量，与质量和速度的平方有关。
kinetic energy = ½ × mass × speed² Eₖ = ½ m v²
Gravitational potential energy is the energy stored due to an object's height in a gravitational field.
重力势能是因物体在引力场中的高度而储存的能量。
gravitational potential energy = mass × g × height Eₚ = m g h
Power is the rate of doing work or transferring energy. It can be expressed as work done per unit time or as force times velocity for an object moving at constant speed.
功率是做功或能量转移的快慢，可表示为单位时间的功，或匀速运动物体所受的力乘以速度。
power = work done / time P = W / t or P = F v
Principle of conservation of energy: energy cannot be created or destroyed; it can only be transformed from one form to another.
能量守恒定律：能量既不会凭空产生也不会消失，只能从一种形式转化为另一种形式。
Efficiency is the ratio of useful output energy or power to total input energy or power, often expressed as a percentage.
效率是有用输出能量或功率与总输入能量或功率之比，常以百分数表示。
efficiency = (useful output energy / total input energy) × 100%
4. Momentum | 动量
Momentum is a vector quantity defined as the product of mass and velocity. Its unit is kg m/s.
动量是矢量，定义为质量与速度的乘积，单位是 kg m/s。
momentum = mass × velocity p = m v
The impulse of a force equals the change in momentum. For a constant force, impulse equals force multiplied by the time for which it acts.
冲量等于动量的变化。对于恒力，冲量等于力乘以作用时间。
impulse = force × time = change in momentum F Δt = m v – m u
Principle of conservation of momentum: in a closed system with no external forces, total momentum before an interaction equals total momentum after.
动量守恒定律：在没有外力的封闭系统中，相互作用前的总动量等于相互作用后的总动量。
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
Momentum is conserved in both collisions and explosions. In elastic collisions, kinetic energy is also conserved; in inelastic collisions it is not.
碰撞和爆炸中动量都守恒。弹性碰撞中动能也守恒，非弹性碰撞中动能不守恒。
5. Pressure and Density | 压强与密度
Density measures the mass per unit volume of a substance. It helps identify materials and predict floating or sinking.
密度衡量物质单位体积的质量，可用于鉴别材料和判断沉浮。
density = mass / volume ρ = m / V
efined as force acting per unit area. It is measured in pascals (Pa), where 1 Pa = 1 N/m².
压强是单位面积上所受的力，单位为帕斯卡 (Pa)，1 Pa = 1 N/m²。
pressure = force / area P = F / A
Pressure in a fluid (liquid or gas) at a certain depth depends on the density of the fluid, the depth and gravitational field strength.
液体或气体中某一深度的压强，取决于流体密度、深度和引力场强度。
pressure due to a fluid = density × g × depth P = ρ g h
Pascal's principle: a pressure change applied to an enclosed fluid is transmitted undiminished to all parts of the fluid. This is the basis for hydraulic systems.
帕斯卡原理：施加在密闭流体上的压强变化会大小不变地向流体各处传递，这是液压系统的基础。
6. Thermal Physics | 热学
The three common temperature scales are Celsius, Kelvin and Fahrenheit. In IGCSE, the Kelvin scale is essential for gas law calculations.
三种常见温标是摄氏、开尔文和华氏。IGCSE 中，气体定律计算必须使用开尔文温标。
temperature in K = temperature in °C + 273 T(K) = T(°C) + 273
Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 °C (or 1 K).
比热容是使 1 kg 物质温度升高 1 °C（或 1 K）所需的能量。
thermal energy = mass × specific heat capacity × temperature change Q = m c ΔT
Specific latent heat is the energy required to change the state of 1 kg of a substance without changing its temperature.
比潜热是使 1 kg 物质在温度不变的情况下发生相变所需的能量。
thermal energy = mass × specific latent heat Q = m L
The gas laws describe the behaviour of an ideal gas. For a fixed mass of gas at constant temperature (Boyle's law), pressure is inversely proportional to volume.
气体定律描述理想气体的行为。对于一定质量的气体，温度不变时（玻意耳定律）压强与体积成反比。
p V = constant p₁ V₁ = p₂ V₂
At constant pressure (Charles' law), volume is directly proportional to absolute temperature.
压强不变时（查理定律），体积与绝对温度成正比。
V / T = constant V₁ / T₁ = V₂ / T₂
At constant volume (Pressure law), pressure is directly proportional to absolute temperature.
体积不变时（压强定律），压强与绝对温度成正比。
p / T = constant p₁ / T₁ = p₂ / T₂
The combined gas equation links all three variables for a fixed mass of gas:
对于一定质量的气体，综合气体方程将三个变量联系起来：
p V / T = constant (p₁ V₁) / T₁ = (p₂ V₂) / T₂
7. Waves | 波
The wave equation links wave speed, frequency and wavelength. It applies to all types of waves, including sound, light and water waves.
波速方程将波速、频率和波长联系在一起，适用于所有波动，包括声波、光波和水波。
wave speed = frequency × wavelength v = f λ
Frequency is the number of complete oscillations per second, measured in hertz (Hz). The period is the time for one complete oscillation; they are inversely related.
频率是每秒完整振动的次数，单位是赫兹 (Hz)。周期是一次完整振动所需的时间，与频率互为倒数。
frequency = 1 / period f = 1 / T
Reflection: the angle of incidence equals the angle of reflection, measured relative to the normal.
反射定律：入射角等于反射角，均相对于法线测量。
θᵢ = θᵣ
Refraction: when a wave passes from one medium to another, its speed and wavelength change, causing a change in direction unless it enters along the normal.
折射：波从一种介质进入另一种介质时，速度和波长发生变化，导致方向改变，除非沿法线入射。
refractive index n = sin(angle of incidence) / sin(angle of refraction)
Snell' he speeds of light in the two media: n = c / v, where c is the speed of light in a vacuum.
斯涅尔定律也可用光在两种介质中的速度表示：折射率 n = c / v，其中 c 为真空中的光速。
The critical angle occurs when the angle of refraction becomes 90°. For total internal reflection, the angle of incidence must exceed the critical angle.
临界角是折射角达到 90° 时的入射角。发生全内反射时，入射角必须大于临界角。
sin(critical angle) = 1 / n
8. Light and Optics | 光与光学
The law of reflection is the same for light as for other waves: the angle of incidence equals the angle of reflection.
光的反射定律与其他波相同：入射角等于反射角。
For a plane mirror, the image is virtual, upright, laterally inverted and the same size as the object, located as far behind the mirror as the object is in front.
平面镜成像特点：虚像、正立、左右颠倒、与物等大，且像与物到镜面的距离相等。
Refractive index n is a measure of how much light slows down. It is also given by the ratio of the sine of the angle of incidence to the sine of the angle of refraction, when light travels from air (or vacuum) into the medium.
折射率 n 衡量光在介质中变慢的程度。光从空气（或真空）射入介质时，n 也等于入射角的正弦与折射角的正弦之比。
n = sin i / sin r and n = c / v
The thin lens formula relates the object distance u, image distance v and focal length f of a converging lens.
薄透镜公式将物距 u、像距 v 和焦距 f 联系起来，适用于会聚透镜。
1 / f = 1 / u + 1 / v
Magnification is the ratio of image height to object height, and for a thin lens it is also given by the ratio of image distance to object distance.
放大率是像高与物高之比，对薄透镜也可用像距与物距之比表示。
magnification = image height / object height = v / u
Dispersion occurs when white light passes through a prism and splits into its constituent colours because different wavelengths are refracted by different amounts.
色散是白光通过棱镜时分解为组成颜色，因为不同波长的光折射程度不同。
9. Electricity | 电学
Electric charge Q is measured in coulombs (C). The current I is the rate of flow of charge.
电荷 Q 的单位是库仑 (C)，电流 I 是电荷流动的速率。
charge = current × time Q = I t
Potential difference (voltage) is the energy transferred per unit charge. E.m.f. is the total energy supplied per unit charge by a source.
电势差（电压）是单位电荷转移的能量。电动势是电源提供的单位电荷总能量。
voltage = energy / charge V = E / Q and P = I V
Ohm's Law states that the current through a conductor is directly proportional to the potential difference across it, provided temperature remains constant.
欧姆定律：在温度保持不变的条件下，导体中的电流与其两端的电势差成正比。
resistance = voltage / current R = V / I
Resistance depends on the material's resistivity, the length and the cross-sectional area of the conductor. For a given material at constant temperature:
电阻取决于材料的电阻率、导体的长度和横截面积。对于给定材料且温度不变时：
R = ρ L / A
Electrical power is the rate of energy transfer. Three useful forms apply for resistive components.
电功率是能量转移的速率。对于纯电阻元件，三种形式均适用。
P = I V P = I² R P = V² / R
Energy transferred in a circuit can be calculated using power and time or directly from charge and voltage.
电路中转移的能量可通过功率与时间计算，或直接由电荷与电压得出。
energy = P t = I V t = V Q
Resistors in series: total resistance is the sum of individual resistances. Resistors in parallel: the reciprocal of total resistance equals the sum of reciprocals.
串联电阻：总电阻等于各电阻之和。并联电阻：总电阻的倒数等于各电阻倒数之和。
Series: Rₜ = R₁ + R₂ + … Parallel: 1/Rₜ = 1/R₁ + 1/R₂ + …
10. Magnetism and Electromagnetism | 磁学与电磁学
A magnetic field exists around a permanent magnet or a current-carrying wire. The right-hand grip rule gives the direction of the field around a straight wire.
永磁体或载流导线周围存在磁场。右手螺旋定则可判断直导线周围磁场的方向。
For a current-carrying conductor in a magnetic field, a force is exerted if the current is not parallel to the field. Fleming's left-hand rule relates force, field and current.
通电导体在磁场中将受到力的作用，只要电流不与磁场平行。弗莱明左手定则将力、磁场和电流方向联系起来。
force = magnetic flux density × current × length of conductor F = B I L
(This equation applies when the conductor is perpendicular to the magnetic field.)
（此公式适用于导体与磁场方向垂直的情况。）
Electromagnetic induction: a changing magnetic field (or movement of a conductor in a magnetic field) induces an e.m.f. The size of the induced e.m.f. can be increased by moving the wire faster, using a stronger magnet, or increasing the number of turns in a coil.
电磁感应：变化的磁场（或导体在磁场中运动）会产生感应电动势。增加导线运动速度、使用更强磁铁或增加线圈匝数均可增大感应电动势。
A simple a.c. generator (alternator) uses a rotating coil in a magnetic field to produce an alternating e.m.f. The slip rings ensure a.c. output.
简单交流发电机利用线圈在磁场中旋转产生交变电动势，滑环确保输出交流电。
Transformers change the voltage of an alternating supply. The turns ratio determines whether the voltage is stepped up or stepped down. An ideal transformer has no energy losses.
变压器改变交流电压，线圈匝数比决定升压或降压。理想变压器无能量损耗。
Vₚ / Vₛ = Nₚ / Nₛ and for 100% efficiency: Vₚ Iₚ = Vₛ Iₛ
11. Radioactivity | 放射性
Radioactive decay is a random process in which an unstable nucleus emits radiation. Three main types are alpha (α), beta (β) and gamma (γ) radiation.
放射性衰变是一种随机过程，不稳定的原子核会发出辐射。主要三种类型为 α 射线、β 射线和 γ 射线。
An alpha particle is a helium nucleus (⁴₂He), beta is a high-speed electron and gamma is electromagnetic radiation of very short wavelength.
α 粒子是氦核 (⁴₂He)，β 粒子是高速电子，γ 射线是波长极短的电磁辐射。
Half-life is the average time taken for half the radioactive nuclei in a sample to decay. It is constant for a given isotope.
半衰期是样品中一半放射性原子核发生衰变所需的平均时间，对特定同位素为常数。
s the number of decays per second, measured in becquerels (Bq). 1 Bq = 1 decay per second.
放射性源的活度是每秒钟衰变的次数，单位为贝克勒尔 (Bq)，1 Bq = 1 次衰变/秒。
Radiation can be detected using a Geiger-Müller tube connected to a counter or rate meter. The count rate decreases with distance and with intervening absorbers.
使用连接计数器或速率计的盖革-米勒管可探测辐射。计数率随距离增大和吸收体介入而下降。
Background radiation is always present; it comes from natural sources, such as cosmic rays, rocks, and radon gas, as well as artificial sources.
本底辐射始终存在，来源包括宇宙射线、岩石、氡气等天然源以及人工源。
12. Space Physics | 空间物理
The Earth rotates once every 24 hours on its axis, causing day and night. It orbits the Sun once every 365¼ days, giving rise to seasons due to the tilt of its axis.
地球每 24 小时自转一周，形成昼夜交替。它以约 365¼ 天绕太阳公转一周，地轴倾斜导致四季变化。
The average orbital speed of a planet can be approximated by the distance travelled in its orbit divided by the orbital period.
行星的平均轨道速度可由轨道长度除以公转周期近似求得。
orbital speed = 2πr / T
(where r is the average radius of the orbit and T is the orbital period.)
(r 为轨道平均半径，T 为公转周期。)
The Solar System consists of the Sun, eight planets, dwarf planets, moons, asteroids and comets. Gravity provides the centripetal force that keeps objects in orbit.
太阳系包含太阳、八颗行星、矮行星、卫星、小行星和彗星。万有引力提供使天体保持在轨道上的向心力。
The life cycle of a star depends on its mass. A star like the Sun will end as a white dwarf after passing through the red giant phase, while more massive stars may explode as supernovae and leave behind neutron stars or black holes.
恒星的生命周期由其质量决定。像太阳这样的恒星经历红巨星阶段后会成为白矮星，质量更大的恒星可能爆发为超新星，留下中子星或黑洞。
The Big Bang theory explains the origin of the Universe, suggesting it began from a hot, dense singularity about 13.8 billion years ago and has been expanding ever since.
大爆炸理论解释宇宙起源，认为约 138 亿年前宇宙由一个极热致密的奇点开始膨胀至今。
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