Year 10 CIE Physics: Formula and Theorem Quick Reference Handbook | Year 10 CIE 物理：公式定理速查手册

📚 Year 10 CIE Physics: Formula and Theorem Quick Reference Handbook | Year 10 CIE 物理：公式定理速查手册

This handbook serves as a concise reference for the essential formulas and theorems required for Year 10 CIE Physics. It covers kinematics, dynamics, momentum, energy, pressure, thermal physics, waves, electricity, magnetism, and atomic physics. Each formula is presented with its meaning, typical units, and a brief note on its application. Use this guide for quick revision before exams.

本手册是 Year 10 CIE 物理考试必备公式和定理的速查参考，涵盖运动学、动力学、动量、能量、压强、热学、波、电学、磁学和原子物理。每个公式都附有含义、常用单位和应用说明，供考前快速复习使用。

1. Kinematics | 运动学

Acceleration is the rate of change of velocity. The standard equation is:

加速度是速度的变化率，标准公式为：

a = (v − u) / t

where u = initial velocity (m/s), v = final velocity (m/s), t = time (s). Acceleration is measured in m/s².

其中 u = 初速度 (m/s)，v = 末速度 (m/s)，t = 时间 (s)。加速度单位为 m/s²。

The three equations of uniformly accelerated motion (with constant acceleration) are:

匀加速运动的三个方程为：

v = u + a t

s = u t + ½ a t²

v² = u² + 2 a s

where s is displacement (m). The average velocity for uniform acceleration can also be found from:

其中 s 为位移 (m)。匀加速运动的平均速度也可由下式求得：

average speed = (u + v) / 2

Speed is distance travelled per unit time (scalar): v = d / t, while velocity is speed in a given direction (vector). For objects falling freely near Earth's surface, the acceleration of free fall g ≈ 9.8 m/s² (usually taken as 10 m/s² in some problems).

速率是单位时间通过的距离（标量）：v = d / t；而速度是带有方向的速率（矢量）。对地表附近的自由落体，自由落体加速度 g ≈ 9.8 m/s²（部分题目中常取 10 m/s²）。

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2. Forces and Motion | 力与运动

Newton's second law relates resultant force, mass and acceleration:

牛顿第二定律表明合力、质量与加速度的关系：

F = m a

F is force in newtons (N), m is mass in kilograms (kg), a is acceleration in m/s².

F 是力 (N)，m 是质量 (kg)，a 是加速度 (m/s²)。

Weight is the force of gravity on a mass:

重力是质量所受的重力：

W = m g

where g is gravitational field strength (N/kg) or acceleration of free fall (m/s²). On Earth, g ≈ 9.8 N/kg.

其中 g 是重力场强度 (N/kg) 或自由落体加速度 (m/s²)。在地球表面，g ≈ 9.8 N/kg。

Hooke's Law for a spring states that extension is proportional to the applied force within the elastic limit:

胡克定律指出，在弹性限度内弹簧的伸长量与外力成正比：

F = k x

k is the spring constant (N/m), x is extension (m). This relationship is linear until the limit of proportionality.

k 是弹簧常数 (N/m)，x 是伸长量 (m)。该关系在比例极限内呈线性。

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3. Momentum | 动量

Momentum is the product of mass and velocity:

动量是质量和速度的乘积：

p = m v

Unit: kg m/s. The principle of conservation of momentum states that in a closed system, total momentum before a collision equals total momentum after:

单位：kg m/s。动量守恒定律指出，在一个封闭系统中，碰撞前的总动量等于碰撞后的总动量：

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

where u₁, u₂ are initial velocities and v₁, v₂ are final velocities for two objects.

其中 u₁, u₂ 为两物体的初速度，v₁, v₂ 为末速度。

Impulse is the change in momentum caused by a force acting over time:

冲量是力在一段时间内作用引起的动量变化：

F t = Δp = m v − m u

This is the impulse–momentum theorem. In many safety applications (airbags, crumple zones), increasing the impact time reduces the average force.

这就是冲量–动量定理。在许多安全应用（安全气囊、溃缩区）中，延长撞击时间可降低平均力。

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4. 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:

当一个力使物体沿力的方向运动时，就做了功：

W = F d

W is work (J), F is force (N), d is distance moved in the direction of the force (m).

W 是功 (J)，F 是力 (N)，d 是沿力方向移动的距离 (m)。

Kinetic energy:

动能：

Eₖ = ½ m v²

Gravitational potential energy change near Earth's surface:

地表附近重力势能的变化：

ΔEₚ = m g Δh

where Δh is change in height (m).

其中 Δh 是高度的变化 (m)。

Power is the rate of doing work or transferring energy:

功率是做功或能量转移的速率：

P = W / t

or P = E / t. Unit: watt (W).

或 P = E / t。单位：瓦特 (W)。

Efficiency is the ratio of useful output energy to total input energy, often expressed as a percentage:

效率是有用输出能量与总输入能量的比值，常以百分比表示：

Efficiency = (useful output energy / total input energy) × 100%

or using power: Efficiency = (useful output power / input power) × 100%.

或用功率表示：效率 = (有用输出功率 / 输入功率) × 100%。

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5. Pressure | 压强

Pressure is force per unit area:

压强是单位面积上的力：

p = F / A

p in pascals (Pa), F in newtons (N), A in m². 1 Pa = 1 N/m².

p 的单位为帕斯卡 (Pa)，F 为牛顿 (N)，A 为 m²。1 Pa = 1 N/m²。

Pressure in a liquid depends on depth, density and gravitational field strength:

液体的压强取决于深度、密度和重力场强度：

p = ρ g h

where ρ is density of the liquid (kg/m³), g is gravitational field strength, h is depth (m). The pressure is the same at all points at the same depth in a static liquid.

其中 ρ 是液体密度 (kg/m³)，g 是重力场强度，h 是深度 (m)。在静止液体中，同一深度的各点压强相同。

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6. Thermal Physics | 热学

Heat energy transferred to a substance causing a temperature change is given by:

热传递给物质引起温度变化的热量由下式给出：

Q = m c Δθ

Q is heat energy (J), m is mass (kg), c is specific heat capacity (J/(kg °C)), Δθ is temperature change (°C or K).

Q 是热量 (J)，m 是质量 (kg)，c 是比热容 (J/(kg °C))，Δθ 是温度变化 (°C 或 K)。

During a change of state, temperature remains constant and the energy transferred is:

在物态变化过程中，温度保持不变，传递的能量由以下公式给出：

Q = m L

L is specific latent heat (J/kg). For melting (fusion) use L_f, for boiling (vaporisation) use L_v.

L 是比潜热 (J/kg)。对于熔化（熔化潜热）使用 L_f，对于沸腾（汽化潜热）使用 L_v。

For a fixed mass of an ideal gas at constant temperature, Boyle's law applies:

对于恒定温度下的一定质量理想气体，适用玻意耳定律：

p₁ V₁ = p₂ V₂

For a gas at constant pressure, Charles's law gives V₁ / T₁ = V₂ / T₂ (with T in kelvin). The pressure law for constant volume is p₁ / T₁ = p₂ / T₂.

对于恒定压强下的气体，查理定律给出 V₁ / T₁ = V₂ / T₂（T 用开尔文）。等容下的压强定律为 p₁ / T₁ = p₂ / T₂。

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7. Waves | 波

The wave speed equation links speed, frequency and wavelength:

波速方程连接了波速、频率和波长：

v = f λ

v is wave speed (m/s), f is frequency (Hz), λ is wavelength (m). Frequency is the reciprocal of period: f = 1 / T.

v 是波速 (m/s)，f 是频率 (Hz)，λ 是波长 (m)。频率是周期的倒数：f = 1 / T。

For light, refraction is described by Snell's law:

对于光，折射由斯涅尔定律描述：

n = sin i / sin r

where n is the refractive index, i is the angle of incidence, r is the angle of refraction. The critical angle c for total internal reflection is given by:

其中 n 是折射率，i 是入射角，r 是折射角。全内反射的临界角 c 由下式给出：

sin c = 1 / n

Refractive index can also be expressed as n = speed of light in vacuum / speed of light in medium.

折射率也可表示为 n = 真空中光速 / 介质中光速。

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8. Electricity | 电学

Electric current is the rate of flow of charge:

电流是电荷流动的速率：

I = Q / t

I in amperes (A), Q in coulombs (C), t in seconds (s).

I 单位安培 (A)，Q 单位库仑 (C)，t 单位秒 (s)。

Voltage (potential difference) is energy per unit charge:

电压（电势差）是单位电荷的能量：

V = W / Q

Resistance is defined by Ohm's law (for ohmic conductors):

电阻由欧姆定律（对于欧姆导体）定义：

R = V / I

R in ohms (Ω).

R 单位欧姆 (Ω)。

For resistors in series:

串联电阻：

R_total = R₁ + R₂ + …

For resistors in parallel:

并联电阻：

1 / R_total = 1 / R₁ + 1 / R₂ + …

Electrical power can be calculated in several forms:

电功率可用多种形式计算：

P = I V = I² R = V² / R

Energy dissipated in a component over time:

元件随时间消耗的电能：

E = I V t

All these formulas assume a constant current and voltage.

以上所有公式均假定电流和电压恒定。

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9. Magnetism and Electromagnetism | 磁学与电磁学

For an ideal transformer (100% efficient), the ratio of voltages equals the ratio of turns:

对于理想变压器（效率 100%），电压之比等于匝数之比：

Vₚ / Vₛ = Nₚ / Nₛ

where Vₚ and Vₛ are primary and secondary voltages, Nₚ and Nₛ are the number of turns. Because power input ≈ power output (for ideal transformer):

其中 Vₚ、Vₛ 为初级和次级电压，Nₚ、Nₛ 为匝数。由于输入功率 ≈ 输出功率（理想变压器）：

Iₚ Vₚ = Iₛ Vₛ

Hence, Iₚ / Iₛ = Nₛ / Nₚ. If the efficiency is less than 100%, then output power = efficiency × input power.

因此，Iₚ / Iₛ = Nₛ / Nₚ。若效率低于 100%，则输出功率 = 效率 × 输入功率。

The force on a current-carrying conductor in a magnetic field (motor effect) is given by Fleming's left-hand rule. The magnitude of the force depends on magnetic flux density B, current I and length of conductor l when the field is perpendicular to the current:

载流导体在磁场中的受力（电动机效应）由弗莱明左手定则判断。当磁场与电流垂直时，力的大小取决于磁通量密度 B、电流 I 和导体长度 l：

F = B I l

This formula is often used in the context of motors and loudspeakers.

此公式常用于电动机和扬声器的背景中。

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10. Atomic Physics | 原子物理

Radioactivity is the spontaneous and random emission of radiation from unstable nuclei. The three types of nuclear radiation are alpha (α), beta (β) and gamma (γ).

放射性是不稳定原子核自发、随机地发射辐射。三种核辐射类型是 α 辐射、β 辐射和 γ 辐射。

Alpha particles are helium nuclei (⁴₂He), beta particles are high-energy electrons (⁰₋₁e), and gamma rays are electromagnetic waves. A decay equation must balance both mass number and atomic number. Example of alpha decay:

α 粒子是氦核（⁴₂He），β 粒子是高能电子（⁰₋₁e），γ 射线是电磁波。衰变方程必须平衡质量数和原子序数。α 衰变示例：

²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

Beta decay example:

β 衰变示例：

¹⁴₆C → ¹⁴₇N + ⁰₋₁e

The half-life of a radioactive isotope is the time taken for half the nuclei in a sample to decay, or for the count rate to fall to half its initial value. It is a constant for a given isotope. The process is random, but the average decay rate follows an exponential decay pattern, which can be represented graphically.

放射性同位素的半衰期是指样品中一半原子核发生衰变所需的时间，或计数率降至其初始值一半所需的时间。对于给定的同位素，半衰期是一个常数。过程是随机的，但平均衰变速率遵循指数衰减规律，这可用图形表示。

Background radiation comes from natural sources (rocks, cosmic rays) and man-made sources. It must be subtracted from measured count rates in experiments.

背景辐射来自天然源（岩石、宇宙射线）和人造源。在实验中，必须从测得的计数率中扣除背景辐射。

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