📚 Year 9 CIE Physics: Quick Reference Handbook of Formulas and Theorems | Year 9 CIE 物理：公式定理速查手册
This quick reference handbook brings together the essential formulas, equations and key principles that every Year 9 CIE Physics student needs. Each entry is presented with its meaning, standard units and a brief note on how it is used. Use these pages to check your memory, practise rearranging equations, and build confidence for your assessments.
本速查手册汇集了每一位 Year 9 CIE 物理学生都需要掌握的核心公式、方程和重要原理。每条公式都配有其物理含义、标准单位以及简要的使用说明。你可以通过本手册检验记忆、练习方程变形，并为评估考试建立信心。
1. Speed, Distance and Time | 速度、距离和时间
The speed of an object describes how fast it is moving. The relationship between speed, distance and time is fundamental to describing motion.
物体的速度描述它运动的快慢。速度、距离和时间之间的关系是描述运动的基础。
v = s / t
where v is speed (metres per second, m/s), s is distance travelled (metres, m) and t is time taken (seconds, s). When speed is not constant, the average speed is still given by total distance divided by total time.
其中 v 为速度（米/秒，m/s），s 为通过的距离（米，m），t 为所用时间（秒，s）。当速度不恒定时，平均速度仍等于总距离除以总时间。
2. Acceleration | 加速度
Acceleration tells us how quickly the velocity of an object is changing. It can be a positive change (speeding up) or a negative change (slowing down, sometimes called deceleration).
加速度表示物体速度变化的快慢。加速度可以为正值（加速），也可以为负值（减速，有时也叫负加速度）。
a = Δv / Δt = (v − u) / t
Here a is acceleration (m/s²), Δv is change in velocity, v is final velocity (m/s), u is initial velocity (m/s) and t is the time taken for the change (s). The unit m/s² means the velocity changes by so many metres per second each second.
这里 a 为加速度（m/s²），Δv 为速度变化量，v 为末速度（m/s），u 为初速度（m/s），t 为速度变化所用的时间（s）。单位 m/s² 表示每秒钟速度改变多少米每秒。
3. Newton's Second Law | 牛顿第二定律
An unbalanced resultant force acting on a mass causes it to accelerate. The acceleration is directly proportional to the resultant force and inversely proportional to the mass of the object.
作用在物体上的不平衡合力会使物体产生加速度。加速度的大小与合力成正比，与物体的质量成反比。
F = m a
In this equation, F is the resultant force (newtons, N), m is the mass (kilograms, kg), and a is the acceleration (m/s²). 1 N is equal to 1 kg m/s².
在此方程中，F 为合力（牛顿，N），m 为质量（千克，kg），a 为加速度（m/s²）。1 N 等于 1 kg·m/s²。
4. Weight and Mass | 重量和质量
Mass is the amount of matter in an object and is measured in kilograms. Weight is the gravitational force acting on that mass and varies with the strength of gravity.
质量是物体所含物质的多少，单位为千克。重量是作用在该质量上的引力，随引力场强度变化而改变。
W = m g
where W is weight (N), m is mass (kg) and g is gravitational field strength (N/kg). On Earth, g r quick estimates). Weight and mass are often confused; weight changes with location, mass does not.
其中 W 为重量（N），m 为质量（kg），g 为引力场强度（N/kg）。在地球表面，g 约等于 9.8 N/kg（快速估算时常取 10 N/kg）。重量和质量常被混淆；重量随位置变化而质量不变。
5. Density | 密度
Density is a property that tells us how much mass is packed into a given volume. Materials with tightly packed particles tend to be denser.
密度是表示单位体积内含有多少质量的物理量。粒子排列越紧密的材料通常密度越大。
ρ = m / V
ρ (Greek letter rho) is density (kg/m³ or g/cm³), m is mass (kg or g) and V is volume (m³ or cm³). To measure density directly, find the mass using a balance and the volume from a ruler or displacement can, then divide.
ρ（希腊字母 rho）为密度（kg/m³ 或 g/cm³），m 为质量（kg 或 g），V 为体积（m³ 或 cm³）。直接测量密度时，用天平测质量，用直尺或排水法测体积，然后相除即可。
6. Pressure | 压强
Pressure is the force acting perpendicularly on a surface per unit area. It explains why sharp objects cut more easily and why broad tyres do not sink into mud.
压强是垂直作用在单位面积上的力。这解释了为什么尖锐的物体更容易切入，以及为什么宽轮胎不容易陷入泥中。
P = F / A
P is pressure (pascals, Pa), F is force (N) acting at right angles to the surface, and A the area (m²). 1 Pa = 1 N/m². For the same force, a smaller area gives a larger pressure.
P 为压强（帕斯卡，Pa），F 为垂直于表面的力（N），A 为受力面积（m²）。1 Pa = 1 N/m²。当力相同时，面积越小，压强越大。
7. Work, Energy and Power | 功、能和功率
Energy can be stored or transferred. Work is done when a force moves an object, transferring energy from one store to another. Power is the rate at which energy is transferred.
能量可以被储存或转移。当力使物体移动时，力做了功，能量从一个储存库转移到另一个储存库。功率是能量转移的速率。
Work done: W = F d
Kinetic energy: K.E. = ½ m v²
Gravitational potential energy: ΔG.P.E. = m g Δh
Power: P = W / t = ΔE / t
In these, W is work (J), F is force (N), d is distance moved in the direction of the force (m), m is mass (kg), v is speed (m/s), g is gravitational field strength (N/kg), Δh is change in height (m), P is power (W, watts), t is time (s) and ΔE uared. Efficiency can be calculated from (useful energy output / total energy input) × 100%.
在上述公式中，W 是功（J），F 是力（N），d 是在力的方向上移动的距离（m），m 是质量（kg），v 是速度（m/s），g 是引力场强度（N/kg），Δh 是高度变化（m），P 是功率（瓦，W），t 是时间（s），ΔE 是转移的能量（J）。动能公式表明，速度因被平方而对动能的影响远大于质量。效率可以用（有效输出的能量 / 总输入的能量）× 100% 计算。
8. Specific Heat Capacity | 比热容
When an object is heated or cooled, the energy transferred depends on its mass, the material it is made of, and the temperature change. Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 °C.
物体受热或冷却时，转移的能量取决于它的质量、材料种类和温度变化。比热容是使 1 kg 某种物质的温度升高 1 °C 所需的能量。
ΔQ = m c Δθ
ΔQ is thermal energy transferred (J), m is mass (kg), c is specific heat capacity (J/(kg °C)) and Δθ is the temperature change (°C or K). Water has a high specific heat capacity (about 4200 J/(kg °C)), meaning it stores a lot of energy for a small temperature rise.
ΔQ 是传递的热能（J），m 为质量（kg），c 为比热容（J/(kg·°C)），Δθ 为温度变化（°C 或 K）。水的比热容很高（约为 4200 J/(kg·°C)），这意味着温度小幅升高就能储存大量能量。
9. Waves: Speed, Frequency and Wavelength | 波：波速、频率和波长
All waves obey the same relationship between wave speed, frequency and wavelength. Knowing two of these quantities allows the third to be calculated readily.
所有波都遵循波速、频率和波长之间的相同关系。已知其中任意两个量，便可轻易算出第三个量。
v = f λ
and the period of a wave is the reciprocal of the frequency:
T = 1 / f
Here v is wave speed (m/s), f is frequency (hertz, Hz), λ (lambda) is wavelength (m) and T is period (s). Frequency is the number of complete waves passing a point per second; the period is the time for one complete wave to pass.
这里 v 是波速（m/s），f 是频率（赫兹，Hz），λ（lambda）是波长（m），T 是周期（s）。频率是每秒钟通过某一点的完整波的个数；周期是一个完整波通过所需的时间。
10. Electricity: Ohm's Law, Power and Energy | 电学：欧姆定律、电功率和电能
Ohm's law describes the relationship between voltage, current and resistance for many conductors at constant temperature. Electrical power and energy use these quantities to show how fast energy is supplied and how much is used.
欧姆定律描述了在恒定温度下，许多导体的电压、电流和电阻之间的关系。电功率和电能利用这些量来表示能量供给的快慢以及消耗了多少能量。
V = I R
P = I V
E = P t = I V t
In these, V is potential difference or voltage (volts, V), I is current (amperes, A), R is resistance (ohms, Ω), P is power (watts, W), E is electrical energy transferred (joules, J) and t P = I² R and P = V² / R, which are useful when certain quantities are not directly known.
在这些公式中，V 为电势差或电压（伏特，V），I 为电流（安培，A），R 为电阻（欧姆，Ω），P 为功率（瓦特，W），E 为转移的电能（焦耳，J），t 为时间（s）。将 P = I V 与 V = I R 结合可以得到 P = I² R 和 P = V² / R，这在某些量未知时非常有用。
11. Moments and the Principle of Moments | 力矩与力矩原理
A moment is the turning effect of a force. The size of a moment depends on both the magnitude of the force and its perpendicular distance from the pivot.
力矩是力的转动效应。力矩的大小取决于力的大小和力到支点的垂直距离。
M = F × d
where M is the moment (newton metres, N m), F is the force (N) and d is the perpendicular distance from the pivot to the line of action of the force (m). The principle of moments states that for a system to be in equilibrium, the sum of clockwise moments about any pivot must equal the sum of anti-clockwise moments.
其中 M 为力矩（牛顿米，N·m），F 为力（N），d 为支点到力作用线的垂直距离（m）。力矩原理指出，对于一个处于平衡的系统，对任意支点，顺时针力矩之和必须等于逆时针力矩之和。
12. Boyle's Law (Gas Pressure and Volume) | 玻意耳定律（气体压强与体积）
For a fixed mass of gas held at a constant temperature, the pressure of the gas is inversely proportional to its volume. This relationship helps explain compressing syringes or syringes filled with gas.
对于一定质量的气体，在温度保持不变时，其压强与体积成反比。这一关系有助于解释用注射器压缩气体等现象。
p V = constant
p₁ V₁ = p₂ V₂
Here p is pressure (Pa or any consistent unit), V is volume (m³ or any consistent unit). As the volume decreases, the particles hit the walls more frequently, so the pressure increases; doubling the volume halves the pressure, provided the temperature does not change.
这里 p 是压强（Pa 或任意一致单位），V 是体积（m³ 或任意一致单位）。当体积减小时，粒子
Published by TutorHao | Year 9 Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图