📚 Year 9 CIE Physics: Quick Reference Handbook for Formulas and Theorems | 九年级 CIE 物理：公式定理速查手册
This handbook provides a concise collection of the most important formulas and theorems you will encounter in Year 9 CIE Physics. Each entry includes the equation, a clear explanation of its meaning, and its standard units — all presented in a side‑by‑side bilingual format for effective revision. Use this as your go‑to reference to build confidence and accuracy when solving physics problems.
本手册精要汇编了九年级 CIE 物理课程中最核心的公式与定理。每个条目都给出了公式本身、对其含义的清晰解释以及标准单位，并以中英对照的形式呈现，便于高效复习。把这份资料当作你的随身速查工具，在解题时帮你建立信心、提升准确性。
1. Speed and Velocity | 速率与速度
Speed is the distance travelled per unit time, while velocity is speed in a given direction. The basic formula is used for constant speed motion.
速率是单位时间内通过的距离，而速度是带有方向的速率。该基本公式用于匀速运动。
v = s / t
where v is speed or velocity (m/s), s is distance (m), and t is time (s).
其中 v 为速率或速度（米/秒），s 为距离（米），t 为时间（秒）。
Remember that average speed is total distance divided by total time, even if the speed varies during the journey.
需注意，平均速率等于总路程除以总时间，即便运动过程中速率有所变化也是如此。
2. Acceleration | 加速度
Acceleration measures how quickly velocity changes. An object can accelerate by speeding up, slowing down, or changing direction.
加速度衡量速度变化的快慢。物体可以通过加快、减慢或改变方向来实现加速。
a = Δv / Δt
or a = (v − u) / t, where a is acceleration (m/s²), v is final velocity (m/s), u is initial velocity (m/s), and t is time (s).
或 a = (v − u) / t，其中 a 为加速度（米/秒²），v 为末速度（米/秒），u 为初速度（米/秒），t 为时间（秒）。
A negative acceleration (often called deceleration) indicates the object is slowing down. In uniform acceleration problems, you may also encounter the equation v² = u² + 2as.
负的加速度（常称为减速度）表示物体正在减速。在匀加速问题中，你还会遇到公式 v² = u² + 2as。
3. Density | 密度
Density relates the mass of a substance to the volume it occupies. It tells you how tightly matter is packed.
密度将物质的质量与其占据的体积联系起来，它表示物质排列的紧密程度。
ρ = m / V
ρ (rho) is density (kg/m³ or g/cm³), m is mass (kg or g), and V is volume (m³ or cm³).
ρ（rho）为密度（千克/米³ 或 克/厘米³），m 为质量（千克 或 克），V 为体积（米³ 或 厘米³）。
Objects with a density less than that of a fluid will float, while those with a greater density will sink, assuming no other forces are at play.
在没有其他力作用的前提下，密度小于流体的物体会漂浮，密度大于流体的物体会下沉。
4. Hooke's Law | 胡克定律
Hooke's Law describes the elastic behaviour of many materials, especially springs, up to their elastic limit.
胡克定律描述了众多材料（尤其是弹簧）在弹性限度内的弹性行为。
F = kx
F is the applied force (N), k is the spring constant (N/m), and x is the extension from the natural length (m).
F 为施加的力（牛顿），k 为劲度系数（牛顿/米），x 为相对原长的伸长量（米）。
The spring constant k measures the stiffness of the spring: a stiffer spring has a larger k and requires more force for the same extension.
劲度系数 k 衡量弹簧的软硬程度：越硬的弹簧 k 值越大，产生相同伸长量需要更大的力。
5. Pressure | 压强
Pressure quantifies the force acting per unit area. It explains why sharp objects cut easily and why broad tyres reduce sinking.
压强用于描述单位面积上所受力的大小，它解释了为什么尖锐物体容易切割，以及宽轮胎为何能减少下陷。
P = F / A
P is pressure (Pa or N/m²), F is force acting perpendicular to the surface (N), and A is the area over which the force acts (m²).
P 为压强（帕斯卡 或 牛顿/米²），F 为垂直于表面的力（牛顿），A 为力施加的面积（米²）。
For fluids, pressure increases with depth according to P = hρg, where h is depth, ρ is fluid density, and g is gravitational field strength.
对于流体，压强随深度增加，遵循 P = hρg，其中 h 为深度，ρ 为流体密度，g 为重力场强度。
6. Moments | 力矩
A moment is the turning effect of a force about a pivot. It depends on both the size of the force and its distance from the pivot.
力矩是力绕支点产生的转动效果，它同时取决于力的大小和力到支点的距离。
M = Fd
M is moment (Nm), F is the force (N), and d is the perpendicular distance from the pivot to the line of action of the force (m).
M 为力矩（牛顿·米），F 为力（牛顿），d 为支点到力作用线的垂直距离（米）。
The principle of moments states that for an object in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about any pivot.
力矩原理指出，当物体处于平衡状态时，对任意支点，顺时针力矩之和等于逆时针力矩之和。
7. Work, Energy and Power | 功、能量与功率
Work is done whenever a force moves an object in the direction of the force. Energy is the capacity to do work, and power is the rate of doing work.
每当力使物体沿力的方向移动时，就做了功。能量是做功的本领，功率则是做功的快慢。
W = Fd PE = mgh KE = ½mv² P = W / t
W is work (J), F force (N), d distance moved in direction of force (m); PE gravitational potential energy (J), m mass (kg), g gravitational field strength (≈ 9.8 N/kg on Earth), h height (m); KE kinetic energy (J), v velocity (m/s); P power (W or J/s), t time (s).
W 为功（焦耳），F 为力（牛顿），d 为沿力方向移动的距离（米）；PE 为重力势能（焦耳），m 为质量（千克），g 为重力场强度（地球约 9.8 牛/千克），h 为高度（米）；KE 为动能（焦耳），v 为速度（米/秒）；P 为功率（瓦特 或 焦耳/秒），t 为时间（秒）。
Energy is conserved; it may be transferred between stores, but the total always remains constant in a closed system.
能量是守恒的；它可以在不同的储存库之间传递，但在封闭系统中，总量始终保持不变。
8. Thermal Energy Transfer | 热传递
When a substance is heated, its internal energy increases. The temperature change depends on mass, specific heat capacity, and the energy supplied.
物质受热时内能增加。温度的变化取决于质量、比热容和提供的能量。
Q = mcΔθ
Q is thermal energy transferred (J), m is mass (kg), c is specific heat capacity (J/(kg°C)), and Δθ is temperature change (°C or K).
Q 为传递的热量（焦耳），m 为质量（千克），c 为比热容（焦/(千克·摄氏度)），Δθ 为温度变化（摄氏度 或 开尔文）。
Specific heat capacity is a property of the material; water has a high value, meaning it takes a lot of energy to raise its temperature.
比热容是材料的属性；水的比热容很大，意味着升高其温度需要吸收很多能量。
9. Wave Equation | 波动方程
All waves — sound, light, water — share a fundamental relationship between their speed, frequency, and wavelength.
一切波——声波、光波、水波——其速度、频率和波长之间都满足一个基本关系。
v = f λ
v is wave speed (m/s), f is frequency (Hz), and λ (lambda) is wavelength (m).
v 为波速（米/秒），f 为频率（赫兹），λ（lambda）为波长（米）。
Frequency is the number of complete waves passing a point per second, while wavelength is the distance between two consecutive identical points on a wave, such as crest to crest.
频率是每秒钟通过某点的完整波个数，波长是波上两个相邻相同点（例如波峰到波峰）之间的距离。
10. Electrical Quantities and Ohm's Law | 电学量与欧姆定律
Electric circuits bring together current, voltage, resistance, and power. Ohm's Law applies to many conductors at constant temperature.
电路将电流、电压、电阻和功率联系在一起。欧姆定律适用于许多恒温条件下的导体。
V = IR P = IV E = QV
V is potential difference / voltage (V), I is current (A), R is resistance (Ω); P is power (W); E is energy transferred (J), Q is charge (C).
V 为电位差/电压（伏特），I 为电流（安培），R 为电阻（欧姆）；P 为功率（瓦特）；E 为转移的能量（焦耳），Q 为电荷量（库仑）。
For resistors in series: Rtotal = R₁ + R₂. For resistors in parallel: 1/Rtotal = 1/R₁ + 1/R₂. These rules are essential for circuit analysis.
串联电阻：R总 = R₁ + R₂。并联电阻：1/R总 = 1/R₁ + 1/R₂。这些规则对于电路分析至关重要。
11. Magnetic Force on a Current‑carrying Conductor | 通电导体在磁场中的受力
When a current flows through a wire in a magnetic field, the wire experiences a force. This is the principle behind electric motors.
当电流流过处于磁场中的导线时，导线会受到力的作用，这便是电动机的基本原理。
F = BIL
F is force (N), B is magnetic flux density (T), I is current (A), and L is length of conductor in the magnetic field (m), provided the field is perpendicular to the current.
F 为力（牛顿），B 为磁通量密度（特斯拉），I 为电流（安培），L 为在磁场中的导体长度（米），且磁场方向与电流方向垂直。
The direction of the force is given by Fleming's left‑hand rule: thumb — force, first finger — magnetic field, second finger — current.
力的方向由弗莱明左手定则确定：拇指指向力，食指指向磁场方向，中指指向电流方向。
12. Transformer Equation | 变压器公式
Transformers change the size of an alternating voltage. They work on the principle of electromagnetic induction and are highly efficient.
变压器可以改变交流电压的大小。它们依据电磁感应原理工作，效率很高。
Vp / Vs = Np / Ns
Vp is primary voltage, Vs is secondary voltage, Np is number of turns on the primary coil, and Ns is number of turns on the secondary coil. The unit is volts (V) for both voltages.
Vp 为原线圈电压，Vs 为副线圈电压，Np 为原线圈匝数，Ns 为副线圈匝数。电压单位均为伏特（V）。
If efficiency is 100%, input power equals output power: IpVp = IsVs. Step‑up transformers increase voltage and decrease current, useful for long‑distance power transmission.
若效率为 100%，输入功率等于输出功率：IpVp = IsVs。升压变压器提高电压、降低电流，适用于远距离电力输送。
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