📚 CIE Year 10 Physics Formula & Theorem Quick Reference | CIE 十年级物理公式定理速查手册
This article provides a concise, bilingual summary of the core formulas and theorems in the CIE Year 10 Physics syllabus. It is designed as a rapid revision tool for students who need to memorise and apply key relationships for their examinations. Each section pairs the English explanation with Chinese translation to ensure clarity and deep understanding.
本文为 CIE 十年级物理大纲中的核心公式和定理提供简明扼要的中英双语总结，旨在帮助学生快速复习，熟记并运用关键关系。每个章节的英文解释与中文解释一一对应，确保清晰理解和深刻掌握。
1. Kinematics | 运动学
Kinematics describes motion without considering its causes. The following equations relate displacement, velocity, acceleration, and time for uniform acceleration in a straight line.
运动学描述物体的运动而不考虑引起运动的原因。以下方程适用于匀加速直线运动，将位移、速度、加速度和时间联系起来。
v = u + at
v is final velocity, u is initial velocity, a is constant acceleration, and t is time. This formula gives the velocity after a period of acceleration.
v 是末速度，u 是初速度，a 是恒定加速度，t 是时间。该公式给出匀加速一段时间后的速度。
s = ut + ½at²
s is displacement. This equation calculates the distance travelled under uniform acceleration from an initial velocity u.
s 是位移。该公式计算从初速度 u 开始匀加速运动所经过的距离。
v² = u² + 2as
This form is useful when time is not known. It relates velocity to displacement directly.
当时间未知时此式很有用。它直接建立了速度与位移的关系。
average speed = total distance / total time
For non-uniform motion, average speed is defined simply as the ratio of total distance to total time taken.
对于非匀速运动，平均速度简单地定义为总距离与总时间之比。
2. Forces and Newton's Laws | 力与牛顿定律
Newton's laws govern the motion of objects under the action of forces. They are fundamental to understanding how and why objects move.
牛顿定律描述了物体在力作用下的运动规律，是理解物体如何运动及为何运动的基础。
F = ma
Newton's second law: the resultant force F on an object equals its mass m multiplied by its acceleration a. The unit of force is the newton (N).
牛顿第二定律：作用在物体上的合力 F 等于物体的质量 m 乘以其加速度 a。力的单位是牛顿 (N)。
W = mg
Weight W is the gravitational force on a mass m. g is the gravitational field strength, approximately 9.8 N/kg on Earth's surface.
重量 W 是作用在质量 m 上的重力。g 是引力场强度，在地球表面约为 9.8 N/kg。
F₁ = −F₂
Newton's third law: if body A exerts a force on body B, then body B exerts an equal and opposite force on body A.
牛顿第三定律：如果物体 A 对物体 B 施加一个力，那么物体 B 同时对物体 A 施加一个大小相等、方向相反的力。
moment = F × d
The moment of a force about a pivot is the product of the force F and the perpendicular distance d from the pivot to the line of action of the force.
力对支点的力矩等于力 F 与支点到力的作用线的垂直距离 d 的乘积。
- Spring extension: F = kx (Hooke's Law within the elastic limit) — F is force, k is spring constant, x is extension.
- 弹簧伸长：F = kx (弹性限度内的胡克定律) — F 为力，k 为弹簧常数，x 为伸长量。
3. Energy and Power | 能量和功率
Energy can be stored in different forms and transferred between systems. Power is the rate of doing work or transferring energy.
能量可以以不同形式储存，并在系统间转移。功率是做功或能量转移的速率。
work done = F × d × cos θ
, work done W = F × d. If the force is at an angle θ to the displacement, work = Fd cos θ.
当力 F 使物体沿力的方向移动距离 d 时，做功 W = F × d。若力与位移夹角为 θ，则做功为 Fd cos θ。
kinetic energy Eₖ = ½mv²
Kinetic energy is the energy an object possesses due to its motion, where m is mass and v is speed.
动能是物体由于运动而具有的能量，m 为质量，v 为速率。
gravitational potential energy Eₚ = mgh
Near Earth's surface, the change in gravitational potential energy is mass × g × change in height h.
在地球表面附近，重力势能的变化量等于质量 × g × 高度变化 h。
power P = work done / time = energy transferred / time
Power is measured in watts (W). 1 W = 1 J/s. It indicates how fast energy is converted.
功率的单位是瓦特 (W)，1 W = 1 J/s。它表示能量转换的快慢。
efficiency = (useful energy output / total energy input) × 100%
y can also be expressed in terms of power: (useful power output / total power input) × 100%.
效率也可用功率表示：(有用输出功率 / 总输入功率) × 100%。
4. Pressure | 压强
Pressure quantifies how concentrated a force is over a surface. It is relevant for solids, liquids, and gases.
压强衡量力在表面上的集中程度，对固体、液体和气体均适用。
p = F / A
ting perpendicularly per unit area A. The SI unit is the pascal (Pa), where 1 Pa = 1 N/m².
压强 p 等于垂直作用在单位面积 A 上的力 F。国际单位是帕斯卡 (Pa)，1 Pa = 1 N/m²。
p = ρgh
In a liquid of density ρ, the pressure at depth h below the surface is given by ρgh, where g is the gravitational field strength. This is the hydrostatic pressure caused by the weight of the liquid column.
在密度为 ρ 的液体中，液面下深度 h 处的压强为 ρgh，g 为引力场强度。这是由液柱重量引起的静液压强。
The total pressure at a point in a liquid is (atmospheric pressure + ρgh).
液体中某点的总压强为 (大气压强 + ρgh)。
5. Thermal Physics | 热学
Thermal physics deals with heat, temperature, and the behaviour of particles in matter. Key concepts include internal energy, temperature scales, and heat transfer.
热学研究热量、温度以及物质中粒子的行为。关键概念包括内能、温标和热量传递。
ΔQ = mcΔθ
The thermal energy Q required to change the temperature of a substance of mass m by Δθ (in K or °C) depends on its specific heat capacity c. No phase change occurs during this process.
使质量为 m 的物质温度升高 Δθ (K 或 °C) 所需的热量 Q 取决于其比热容 c。此过程中不发生相变。
Q = mL
ed or released is Q = mL, where L is the specific latent heat (of fusion or vaporisation).
当物质在恒定温度下发生物态变化时，吸收或释放的能量 Q = mL，L 为比潜热 (熔化潜热或汽化潜热)。
Temperature in kelvin (K) = temperature in °C + 273.
开尔文温度 (K) = 摄氏温度 (°C) + 273。
ume: p/T = constant (pressure law). For a fixed mass and pressure, V/T = constant (Charles' law).
在质量与体积固定时，气体的压强与温度的关系：p/T = 常数 (压强定律)。在质量与压强固定时，V/T = 常数 (查理定律)。
6. Waves | 波
Waves transfer energy without transferring matter. The wave equation links speed, frequency, and wavelength.
波传播能量而不传播物质。波动方程将波速、频率和波长联系起来。
v = f λ
Wave speed v equals frequency f multiplied by wavelength λ. The unit of frequency is hertz (Hz), equal to s⁻¹.
波速 v 等于频率 f 乘波长 λ。频率的单位是赫兹 (Hz)，即 s⁻¹。
For transverse waves (e.g. light, water waves), particles oscillate perpendicular to the direction of energy transfer. For longitudinal waves (e.g. sound), particles oscillate parallel to the direction of energy transfer.
对于横波 (如光波、水波)，质点振动方向垂直于能量传播方向。对于纵波 (如声波)，质点振动方向平行于能量传播方向。
T = 1 / f
Period T is the time for one complete wave cycle. It is the reciprocal of frequency.
周期 T 是完成一个完整波循环所需的时间，为频率的倒数。
Refraction is described by Snell's Law:
折射由斯涅尔定律描述：
n = sin i / sin r
medium. The relationship between speeds is n = c / v, where c is speed of light in vacuum.
n 为折射率，i 为真空 (或空气) 中的入射角，r 为介质中的折射角。折射率与波速的关系为 n = c / v，c 为真空中的光速。
7. Electricity | 电学
Electric circuits involve the flow of charge. Ohm's law and power equations are fundamental for analysing circuits.
电路涉及电荷的流动。欧姆定律和功率公式是分析电路的基础。
V = IR
Ohm's law: the potential difference V across a conductor is proportional to the current I flowing through it, provided temperature is constant. Resistance R is measured in ohms (Ω).
欧姆定律：当温度恒定时，导体两端的电势差 V 与通过它的电流 I 成正比。电阻 R 的单位是欧姆 (Ω)。
P = IV
Electrical power P is the product of current I and voltage V. Using Ohm's law, it can also be written as P = I²R or P = V² / R.
电功率 P 是电流 I 与电压 V 的乘积。利用欧姆定律，也可写为 P = I²R 或 P = V² / R。
E = IVt
Energy transferred E in a circuit is power multiplied by time t. It is often measured in joules (J) or kilowatt-hours (kWh).
电路中转移的能量 E 等于功率乘时间 t。常用焦耳 (J) 或千瓦时 (kWh) 来量度。
For series circuits: current is the same everywhere; total resistance Rtotal m of individual p.d.s. For parallel circuits: total current is the sum of branch currents; voltage across each branch is the same; total resistance is given by 1/Rtotal = 1/R₁ + 1/R₂ + ...
串联电路：电流处处相等；总电阻 Rtotal = R₁ + R₂ + ...；总电压等于各分电压之和。并联电路：总电流等于各支路电流之和；各支路两端电压相等；总电阻由 1/Rtotal = 1/R₁ + 1/R₂ + ... 给出。
8. Magnetism and Electromagnetism | 磁与电磁
Magnetic fields are produced by magnets and by current-carrying conductors. Electromagnetic induction links electricity and magnetism.
磁场由磁体和载流导体产生。电磁感应将电与磁联系在一起。
The direction of the magnetic field around a straight wire is given by the right-hand grip rule: thumb points along conventional current direction, fingers curl in the field direction.
直导线周围的磁场方向由右手螺旋定则判断：拇指指向常规电流方向，四指弯曲方向为磁场方向。
For a solenoid, the magnetic field is similar to that of a bar magnet. The strength of the electromagnet can be increased by increasing current, number of turns, or inserting a soft iron core.
螺线管的磁场与条形磁铁相似。增大电流、增加线圈匝数或插入软铁芯均可增强电磁铁。
F = BIL
o a uniform magnetic field of flux density B is F = BIL. The direction is given by Fleming's left-hand rule.
处于匀强磁场 B 中、与磁场方向垂直的长度为 L 的载流导体所受的力 F = BIL。方向由弗莱明左手定则判定。
Vₚ / Vₛ = Nₚ / Nₛ (ideal transformer)
ondary voltage Vₛ equals the ratio of primary turns Nₚ to secondary turns Nₛ. Assuming 100% efficiency, IₚVₚ = IₛVₛ, so Iₚ / Iₛ = Nₛ / Nₚ.
对于理想变压器，原边电压 Vₚ 与副边电压 Vₛ 之比等于原边匝数 Nₚ 与副边匝数 Nₛ 之比。假设 100% 效率，有 IₚVₚ = IₛVₛ，因此 Iₚ / Iₛ = Nₛ / Nₚ。
9. Atomic Physics and Radioactivity | 原子物理与放射性
Atomic structure and radioactivity explain the nature of nuclear radiation and its uses. Decay is a random process.
原子结构和放射性解释了核辐射的性质及其应用。衰变是一个随机过程。
An atom consists of a nucleus containing protons and neutrons, surrounded by electrons. Nuclide notation: ᴬ₂X, where A is mass number (protons + neutrons) and Z is atomic number (protons).
原子由包含质子和中子的原子核及绕核运动的电子组成。核素符号：ᴬ₂X，A 为质量数 (质子数 + 中子数)，Z 为原子序数 (质子数)。
Three types of nuclear radiation: alpha (α, helium nucleus ⁴₂He), beta (β, electron or positron), gamma (γ, electromagnetic wave). Their penetrating power and ionising ability differ.
三种核辐射：α 射线 (氦核 ⁴₂He)、β 射线 (电子或正电子)、γ 射线 (电磁波)。它们的穿透能力和电离能力各不相同。
(Bq), where 1 Bq = 1 decay per second. The decay law is A = λN, with λ the decay constant.
放射源的活度 A 以贝克勒尔 (Bq) 为单位，1 Bq = 每秒一次衰变。衰变规律为 A = λN，λ 为衰变常量。
Half-life is the time taken for half the nuclei in a sample to decay, or for the activity to halve. No simple equation is required, but graphical interpretation is important.
半衰期是样本中一半的原子核发生衰变所需的时间，或活度减半所需的时间。虽不要求记忆简单方程，但图形分析很重要。
10. Space Physics (Optional Topic) | 空间物理 (选修专题)
This section covers basic astronomical measurements and concepts. Some schools include it in Year 10.
本节涵盖基础的天文测量和概念，部分学校在十年级教学中涉及。
speed of light c ≈ 3.0 × 10⁸ m/s
The speed of light in a vacuum is a fundamental constant. Distance in space is often expressed in light-years (the distance light travels in one year).
真空中的光速是一个基本常数。太空中的距离常用光年 (光在一年中传播的距离) 表示。
v = H₀d
Hubble's law states that the recessional speed v of a galaxy is proportional to its distance d from Earth. H₀ is the Hubble constant.
哈勃定律指出，星系的退行速度 v 与其离地球的距离 d 成正比，H₀ 为哈勃常数。
Evidence for the Big Bang includes cosmic microwave background radiation and the redshift of distant galaxies.
大爆炸的证据包括宇宙微波背景辐射和遥远星系的红移现象。
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