📚 Year 9 WJEC Physics: Formula and Theorem Quick Reference Handbook | 九年级 WJEC 物理：公式定理速查手册
This handbook provides a concise summary of the essential formulas and principles you will encounter in Year 9 WJEC Physics. Mastering these equations and understanding the related concepts is the foundation for solving problems and performing well in assessments. Use this guide for quick revision and as a daily reference when tackling practice questions.
本手册简要总结了九年级 WJEC 物理课程中的核心公式与定理。掌握这些方程并理解相关概念是解决问题、在评估中取得好成绩的基础。请将本指南用于快速复习，并在做练习题时作为日常参考。
1. Speed and Velocity | 速度与速率
Speed is a measure of how fast an object is moving, calculated as the distance travelled per unit time. It is a scalar quantity, meaning it has no direction. Velocity, on the other hand, is the speed in a given direction and is a vector quantity.
速度是衡量物体运动快慢的量，定义为单位时间内移动的距离。它是标量，即没有方向。而速率则是带有方向的速度，属于矢量。
The average speed of an object can be found using the following equation:
物体的平均速度可用以下公式求得：
v = d ÷ t
In this equation, v represents speed (measured in metres per second, m/s), d is the distance travelled (in metres, m), and t is the time taken (in seconds, s).
式中，v 表示速度（单位为米/秒，m/s），d 为移动距离（单位为米，m），t 为所用时间（单位为秒，s）。
2. Acceleration | 加速度
Acceleration describes how quickly the velocity of an object changes. It is a vector quantity, so it has both magnitude and direction. An object accelerates if it speeds up, slows down (decelerates) or changes direction.
加速度描述物体速度变化的快慢。它是一个矢量，既有大小也有方向。如果物体加速、减速或改变方向，都是在做加速度运动。
The acceleration of an object can be calculated using the formula:
物体的加速度可用以下公式计算：
a = Δv ÷ t
Here, a is acceleration (m/s²), Δv (delta v) is the change in velocity (m/s), and t is the time taken for that change (s). The symbol Δ means 'change in'.
其中，a 为加速度（m/s²），Δv（德尔塔 v）为速度变化量（m/s），t 为该变化所用时间（s）。符号 Δ 表示“变化量”。
3. Forces and Newton's Laws of Motion | 力与牛顿运动定律
Newton's First Law states that an object will remain at rest or continue to move at a constant velocity unless acted upon by a resultant (net) force. Newton's Second Law links force, mass and acceleration.
牛顿第一定律指出，除非受到合外力作用，否则物体将保持静止或匀速直线运动状态。牛顿第二定律将力、质量和加速度联系起来。
The resultant force on an object is equal to its mass multiplied by its acceleration:
物体所受的合外力等于其质量乘以加速度：
F = m × a
In this formula, F is force in newtons (N), m is mass in kilograms (kg), and a is acceleration in metres per second squared (m/s²). Newton's Third Law reminds us that forces come in pairs: if object A exerts a force on object B, then B exerts an equal and opposite force on A.
式中，F 为力，单位牛顿 (N)；m 为质量，单位千克 (kg)；a 为加速度，单位米/秒² (m/s²)。牛顿第三定律提醒我们，力是成对出现的：若物体 A 对物体 B 施加一个力，则 B 同时会对 A 施加一个大小相等、方向相反的力。
4. Density | 密度
Density is a measure of how much mass is packed into a given volume. It is a characteristic property of a material and does not depend on the size of the sample.
密度是衡量单位体积内所含质量的量。它是材料的一种特性，与样品的大小无关。
The density of a substance is calculated as:
物质的密度计算公式为：
ρ = m ÷ V
Where ρ (the Greek letter rho) is density (kg/m³), m is mass (kg), and V is volume (m³). Sometimes density is expressed in g/cm³.
其中，ρ（希腊字母 rho）表示密度（kg/m³），m 为质量（kg），V 为体积（m³）。有时密度也用 g/cm³ 表示。
5. Pressure | 压强
Pressure tells us how concentrated a force is over an area. A large force acting on a small area creates high pressure, while the same force spread over a larger area produces lower pressure.
压强表示力在面积上的集中程度。作用在较小面积上的大力会产生较大的压强，而同样的力分布在较大面积上则压强较小。
Pressure is defined by the equation:
压强的定义式为：
p = F ÷ A
Here, p is pressure in pascals (Pa), F is the force acting perpendicular to the surface in newtons (N), and A is the area in square metres (m²). 1 Pa equals 1 N/m².
式中，p 为压强，单位帕斯卡 (Pa)；F 为垂直作用在表面上的力，单位牛顿 (N)；A 为面积，单位平方米 (m²)。1 Pa 等于 1 N/m²。
6. Hooke's Law | 胡克定律
Hooke's Law describes the behaviour of springs and other elastic objects. It states that the extension of an elastic object is directly proportional to the force applied, provided the limit of proportionality is not exceeded.
胡克定律描述了弹簧和其他弹性物体的行为。它指出，在不超过比例极限的情况下，弹性物体的伸长量与所施加的力成正比。
The law is expressed mathematically as:
该定律的数学表达式为：
F = k × e
F is the force applied (N), k is the spring constant (N/m) – a measure of the stiffness of the spring, and e is the extension (m) – the increase in length from the original position.
F 为施加的力 (N)，k 为弹簧常数 (N/m)，即弹簧刚度的一种量度，e 为伸长量 (m)，即相对于原长的增加量。
7. Work Done | 功
In physics, work is done whenever a force moves an object through a distance. Energy is transferred when work is done, and both are measured in joules (J).
在物理学中，只要力使物体移动一段距离，就做了功。做功时会发生能量转移，功和能量均以焦耳 (J) 为单位。
The amount of work done is given by:
做功的多少由下式给出：
W = F × d
W represents work done (J), F is the force applied in the direction of motion (N), and d is the distance moved (m). If the force is applied at an angle, only the component of force in the direction of motion does work.
W 表示功 (J)，F 为沿运动方向施加的力 (N)，d 为移动的距离 (m)。如果力以某个角度施加，则只有沿运动方向的分力做功。
8. Gravitational Potential Energy and Kinetic Energy | 重力势能与动能
Energy exists in different forms. Two important mechanical energy stores are gravitational potential energy (GPE) and kinetic energy (KE). Energy is always conserved: it cannot be created or destroyed, only transferred between stores.
能量以不同形式存在。两种重要的机械能储存是重力势能 (GPE) 和动能 (KE)。能量总是守恒的：它不能被创造或消灭，只能在不同的能量储存之间转移。
The gravitational potential energy of an object raised above the ground is:
物体被抬高到地面以上时所具有的重力势能为：
GPE = m × g × h
Where m is mass (kg), g is the gravitational field strength (approximately 9.8 N/kg on Earth, often taken as 10 N/kg), and h is height (m).
式中，m 为质量 (kg)，g 为重力场强度（地球表面约为 9.8 N/kg，常取 10 N/kg），h 为高度 (m)。
The kinetic energy of a moving object is:
运动物体的动能为：
KE = ½ × m × v²
m is mass (kg) and v is speed (m/s). Note the squared relationship: doubling the speed quadruples the kinetic energy.
m 为质量 (kg)，v 为速度 (m/s)。注意这里的平方关系：速度加倍，动能变为原来的四倍。
9. Electrical Circuits: Ohm's Law and Power | 电路：欧姆定律与电功率
Ohm's Law is a fundamental rule for many electrical circuits at constant temperature. It relates the potential difference (voltage), current and resistance.
欧姆定律是许多恒温下电路的基本规律。它将电势差（电压）、电流和电阻联系起来。
According to Ohm's Law:
根据欧姆定律：
V = I × R
V is potential difference in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω).
V 为电势差，单位伏特 (V)；I 为电流，单位安培 (A)；R 为电阻，单位欧姆 (Ω)。
Electrical power is the rate at which electrical energy is transferred. Two useful power equations are:
电功率是电能转移的速率。两个有用的功率公式为：
P = I × V and P = I² × R
Here, P is power in watts (W). Using these, you can calculate how much energy a component dissipates or converts per second.
其中，P 为功率，单位瓦特 (W)。利用这些公式，可以计算元件每秒消耗或转换的能量。
10. Wave Speed | 波速
Waves transfer energy without transferring matter. The speed of a wave depends on the medium and is linked to its frequency and wavelength.
波传递能量而不传递物质。波速取决于介质，并与频率和波长有关。
The wave speed equation is:
波速公式为：
v = f × λ
v is wave speed (m/s), f is frequency in hertz (Hz) – the number of complete waves per second, and λ (lambda) is wavelength (m) – the distance between two consecutive equivalent points on a wave.
v 为波速 (m/s)，f 为频率 (Hz)，即每秒完整波的个数，λ (lambda) 为波长 (m)，即波上两个相邻等效点之间的距离。
11. Efficiency | 效率
Efficiency measures how well a device or process converts input energy into useful output energy. No process is 100% efficient because some energy is always transferred to less useful stores, often as heat.
效率衡量设备或过程将输入能量转化为有用输出能量的程度。没有任何过程能达到 100% 的效率，因为总有一部分能量会转移到用处较小的能量储存中，通常以热的形式散失。
Efficiency can be calculated as a percentage using:
效率可用以下公式以百分比形式计算：
