📚 Year 7 WJEC Physics: Formula & Theorem Quick Reference Handbook | WJEC 七年级物理：公式定理速查手册
This compact reference handbook collects the essential formulas, equations, and scientific principles that every Year 7 WJEC Physics student needs to know. Whether you are reviewing for a test, completing homework, or building a solid foundation for Years 8 and 9, these carefully organised notes will help you calculate, reason, and explain physical phenomena with confidence. Each section presents the key relationship in a clear, uncluttered form, explains the meaning of every symbol, and provides a worked example where helpful. Keep this guide close — it is your shortcut to mastering the fundamentals of physics.
这本精简的速查手册汇集了每一位七年级 WJEC 物理学生必须掌握的核心公式、方程和科学原理。无论你是在备考小测、完成家庭作业，还是在为八、九年级打基础，这些精心组织的内容都能帮助你自信地完成计算、进行推理并解释物理现象。每个小节都以清晰简洁的方式呈现关键关系，解释每个符号的含义，并在合适的地方提供例题。请将这本指南放在手边——它是你掌握物理基础知识的快捷通道。
1. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance travelled, and time taken is one of the most fundamental ideas in motion. When an object moves at a constant speed, the formula is simply the distance divided by the time.
速度、运动距离和所用时间之间的关系是运动学中最基本的物理概念之一。当物体做匀速运动时，公式就是简单的距离除以时间。
speed = distance ÷ time
v = s / t
where v stands for average speed (m/s), s is the distance travelled (m), and t v × t) or time (t = s / v). In WJEC Year 7 exams, you are often expected to convert units — for example, from minutes to seconds or from kilometres to metres — before using the formula.
其中 v 代表平均速度（米/秒），s 是运动的距离（米），t 是时间间隔（秒）。同一个公式可以变形求出距离（s = v × t）或时间（t = s / v）。在 WJEC 七年级的考试中，通常需要先进行单位转换——例如将分钟换算为秒，或将千米换算为米——然后再代入公式。
If she maintained that speed for 2 minutes (120 s), she would cover s = 15 × 120 = 1800 m.
一名自行车手以稳定速度在 40 秒内骑行了 600 米。她的速度为 v = 600 m / 40 s = 15 m/s。如果她以该速度骑 2 分钟（120 秒），她将骑行的距离为 s = 15 × 120 = 1800 米。
2. Acceleration | 加速度
Acceleration tells us how quickly the velocity of an object changes. In Year 7, we treat acceleration as the change in speed per second, so the formula is a straightforward one: acceleration equals the change in speed divided by the time taken for that change.
加速度描述物体速度变化的快慢。在七年级阶段，我们将加速度视为每秒速度的变化量，因此公式非常简单：加速度等于速度的变化量除以产生该变化所用的时间。
acceleration = change in speed / time
a = (v − u) / t
Here a is acceleration (m/s²), v is final speed (m/s), u is initial speed (m/s), and t is the time (s). A positive value means the object is speeding up; a negative value (deceleration) means it is slowing down.
这里 a 是加速度（米/秒²），v 是末速度（米/秒），u 是初速度（米/秒），t 是时间（秒）。若结果为正值，表示物体在加速；若为负值（减速度），则表示物体在减速。
d from 5 m/s to 17 m/s in 6 seconds. The acceleration is a = (17 − 5) / 6 = 12/6 = 2 m/s².
一辆汽车在 6 秒内将速度从 5 m/s 提高到 17 m/s。加速度为 a = (17 − 5) / 6 = 12/6 = 2 m/s²。
3. Density | 密度
Density links the mass of a material to the volume it occupies. It is a characteristic property that can help identify substances. For a regular solid, liquid, or gas sample, density is calculated as mass per unit volume.
密度将物质的质量与其占据的体积联系起来。它是一种可以帮助鉴别物质的特征性质。对于规则固体、液体或气体样品，密度被计算为单位体积的质量。
density = mass / volume
ρ = m / V
The symbol ρ (Greek letter rho) stands for density (kg/m³ or g/cm³), m is mass (kg or g), and V n an object is placed in water, an object with density less than 1 g/cm³ will float; an object with density greater than 1 g/cm³ will sink.
符号 ρ（希腊字母 rho）表示密度（千克/米³ 或 克/厘米³），m 是质量（千克或克），V 是体积（米³ 或 厘米³）。请记住 1 cm³ = 1 mL，且 1 g/cm³ = 1000 kg/m³。当物体放入水中时，密度小于 1 g/cm³ 的物体会浮起，密度大于 1 g/cm³ 的物体会下沉。
of 100 cm³. Its density is ρ = 800 / 100 = 8 g/cm³ (or 8000 kg/m³). It will sink in water.
一块金属的质量为 800 克，体积为 100 cm³。其密度为 ρ = 800 / 100 = 8 g/cm³（或 8000 kg/m³）。它会沉入水中。
4. Weight and Mass | 重量与质量
Weight is the force of gravity acting on an object’s mass. It is measured in newtons (N), whereas mass is measured in kilograms (kg). The two are related by the gravitational field strength, g, which on Earth is approximately 9.8 N/kg (often rounded to 10 N/kg for classroom calculations).
重量是作用在物体质量上的重力，单位为牛顿（N）；质量则以千克（kg）为单位。两者通过重力场强度 g 相关联，地球上的 g 约为 9.8 N/kg（课堂计算中常取 10 N/kg）。
weight = mass × gravitational field strength
W = m g
Where W is weight (N), m is mass (kg), and g is gravitational field strength (N/kg). An object’s mass stays the same everywhere, but its weight can change if it moves to a different planet where g is different.
其中 W 是重量（N），m 是质量（kg），g 是重力场强度（N/kg）。物体的质量在任何地方都保持不变，但如果它移动到另一个星球，由于 g 不同，它的重量会发生改变。
10 = 450 N. On the Moon, g is only about 1.6 N/kg, so her weight would be 45 × 1.6 = 72 N.
一名七年级学生的质量为 45 kg。在地球上（g = 10 N/kg），她的重量为 W = 45 × 10 = 450 N。在月球上，g 只有约 1.6 N/kg，因此她的重量将是 45 × 1.6 = 72 N。
5. Pressure | 压强
Pressure describes how concentrated a force is over a surface. A sharp knife cuts easily because the same force is spread over a very small area, creating high pressure. The formula expresses this idea clearly.
压强描述力在一个表面上的集中程度。锋利的刀刃之所以容易切割，是因为同样的力分布在极小的面积上，产生了高压强。下面的公式清晰地表达了这一概念。
pressure = force / area
p = F / A
p is pressure (Pa or N/m²), F is the force applied at right angles to the surface (N), and A is the area of contact (m²). A larger area reduces pressure; a smaller area increases it. This principle explains why camels have wide feet and why drawing pins are easy to push into a noticeboard.
p 是压强（Pa 或 N/m²），F 是垂直于表面的力（N），A 是接触面积（m²）。面积越大，压强越小；面积越小，压强越大。这一原理解释了为什么骆驼的脚掌宽大，以及为什么图钉容易钉入公告板。
k is turned onto a smaller face of area 0.05 m², the pressure becomes 50 / 0.05 = 1000 Pa.
一个重 50 N 的物块放置在桌上，接触面积为 0.2 m²。压强为 p = 50 / 0.2 = 250 Pa。如果将同一物块转到面积为 0.05 m² 的更小的面上，压强就会变成 50 / 0.05 = 1000 Pa。
6. Moments and Turning Effect | 力矩与转动效应
A moment is the turning effect of a force. It depends on two things: the size of the force and how far it is applied from the pivot (the distance on the lever arm). This is a vital concept for understanding levers, seesaws, and spanners.
力矩是力的转动效应，它取决于两个因素：力的大小，以及力离支点的垂直距离（杠杆臂上的距离）。这是理解杠杆、跷跷板和扳手工作原理的关键概念。
moment = force × perpendicular distance from pivot
M = F × d
M is the 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). When an object is balanced, the total clockwise moment equals the total anticlockwise moment — this is the principle of moments.
M 是力矩（牛·米），F 是力（牛），d 是从支点到力作用线的垂直距离（米）。当物体平衡时，总顺时针力矩等于总逆时针力矩——这就是力矩原理。
on the opposite side acts at 0.2 m, its moment is 3 × 0.2 = 0.6 Nm, balancing the system.
一个 2 N 的力施加在离核桃夹支点 0.3 m 处，力矩为 M = 2 × 0.3 = 0.6 Nm。如果在另一侧有一个 3 N 的力作用在 0.2 m 处，它的力矩为 3 × 0.2 = 0.6 Nm，系统保持平衡。
7. Hooke’s Law | 胡克定律
When you stretch a spring, the extension (increase in length) is directly proportional to the force applied, as long as the spring’s elastic limit is not exceeded. This linear relationship is known as Hooke’s Law and is often investigated in Year 7 practical work.
当拉伸弹簧时，只要没有超过弹簧的弹性极限，伸长量（长度的增加）就与施加的力成正比。这种线性关系被称为胡克定律，是七年级实验中经常探究的内容。
force = spring constant × extension
F = k x
F is the stretching force (N), k is the spring constant (N/m), a measure of how stiff the spring is, and x is the extension (m), not the total length. A stiffer spring has a larger k value.
F 是拉伸力（N），k 是弹簧常数（N/m），用于衡量弹簧的刚度，x 是伸长量（m），而不是弹簧的总长度。弹簧越硬，k 值越大。
m, the force needed would be 50 × 0.3 = 15 N, provided the elastic limit is not exceeded.
一根 k = 50 N/m 的弹簧在受力后伸长了 0.1 m。所需的力为 F = 50 × 0.1 = 5 N。如果同一根弹簧伸长 0.3 m，需要的力将是 50 × 0.3 = 15 N，前提是没有超过弹性极限。
8. Energy, Work and Power | 能量、功与功率
Energy is the ability to do work. In mechanics, work is done when a force moves an object in the direction of the force. Power measures how quickly work is done or energy is transferred. These three quantities are neatly linked by a few simple equations.
能量是做功的本领。在力学中，当一个力使物体沿力的方向移动时，这个力就做了功。功率衡量做功或能量传递的快慢。这三个物理量通过几个简单的方程巧妙地联系在一起。
work done = force × distance moved in direction of force
W = F × d
power = work done / time taken
P = W / t
ational potential energy is also often needed: ΔEₚ = m g h, where h is the change in height.
功（W）的单位是焦耳（J），力（F）的单位是牛顿，距离（d）的单位是米。功率（P）的单位是瓦特（W，1 W = 1 J/s）。重力势能的公式也经常需要用到：ΔEₚ = m g h，其中 h 是高度的变化量。
kJ). If the lift takes 20 seconds, the power output is P = 30 000 / 20 = 1500 W (1.5 kW).
一台起重机将 2000 N 的重物提升 15 m。克服重力所做的功为 W = 2000 × 15 = 30 000 J（30 kJ）。如果提升过程花了 20 秒，那么功率为 P = 30 000 / 20 = 1500 W（1.5 kW）。
9. Electric Current and Charge | 电流与电荷
Electric current is a flow of charge. The size of the current tells us how much charge passes a point in a circuit per second. In a series circuit, the current is the same at all positions. In a parallel circuit, the total current is the sum of the currents in the branches.
电流是电荷的流动。电流的大小告诉我们每秒钟有多少电荷通过电路中的某一点。在串联电路中，各处电流相等；在并联电路中，总电流等于各支路电流之和。
charge = current × time
Q = I t
Q is the electric charge in coulombs (C), I is the current in amperes (A), and t is the time in seconds (s). A current of 1 A means 1 C of charge flows past a point each second. This equation is often used to calculate how long a battery can last or how much charge is transferred in a component.
Q 是电荷量，单位是库仑（C）；I 是电流，单位是安培（A）；t 是时间，单位是秒（s）。1 A 的电流意味着每秒钟有 1 C 的电荷流经某点。这个方程常用于计算电池可以持续多长时间的供电，或者某个元件中转移了多少电荷。
of 0.4 A for 5 minutes (300 s). The charge that flows through it is Q = 0.4 × 300 = 120 C.
一个小电动机工作 5 分钟（300 秒），电流为 0.4 A。流过它的电荷量为 Q = 0.4 × 300 = 120 C。
10. Ohm’s Law and Resistance | 欧姆定律与电阻
For a metal conductor at constant temperature, the current flowing through it is directly proportional to the voltage across it. This relationship is called Ohm’s Law. The ratio of voltage to current gives the resistance, which measures how difficult it is for charges to move.
对于温度不变的金属导体，通过它的电流与它两端的电压成正比。这一关系被称为欧姆定律。电压与电流的比值就是电阻，它衡量电荷移动的难易程度。
voltage = current × resistance
V = I R
V is the potential difference (voltage) in volts (V), I is current in amperes (A), and R Ω). The formula can be rearranged to R = V / I or I = V / R. Resistors in series add up: Rtotal = R₁ + R₂ + …
V 是电势差（电压），单位为伏特（V）；I 是电流，单位为安培（A）；R 是电阻，单位为欧姆（Ω）。该公式可以变形为 R = V / I 或 I = V / R。串联电阻的总电阻等于各电阻之和：Rtotal = R₁ + R₂ + …
ted in series, the total resistance becomes 40 Ω and the current drops to 6 / 40 = 0.15 A.
一盏灯连接在 6 V 的电池上，通过的电流为 0.3 A。它的电阻为 R = 6 / 0.3 = 20 Ω。如果串联上另一盏相同的灯，总电阻变为 40 Ω，电流降至 6 / 40 = 0.15 A。
11. Wave Speed Equation | 波速方程
Waves transfer energy from one place to another without transferring matter. The wave speed depends on the frequency and wavelength. Sound waves, water waves, and light all obey the same basic equation. In Year 7 you may measure the speed of a ripple on water or a pulse on a spring.
波将能量从一处传递到另一处，而不传递物质。波速取决于频率和波长。声波、水波和光都遵循同一个基本方程。在七年级，你可能会测量水面上涟漪的速度或弹簧上脉冲的速度。
wave speed = frequency × wavelength
v = f λ
v is wave speed (m/s), f is frequency (Hz, or 1/s), and λ (lambda) is wavelength (m). Frequency tells you how many complete waves pass a point per second; wavelength is the distance between two consecutive crests. In air at room temperature, sound travels at about 340 m/s.
v 是波速（m/s），f 是频率（Hz，或 1/s），λ（lambda）是波长（m）。频率表示每秒钟有多少个完整的波通过某一点；波长是两个相邻波峰之间的距离。在室温下的空气中，声速约为 340 m/s。
cy doubles to 4 Hz while the wavelength stays the same, the speed also doubles to 0.6 m/s.
一个水波的频率为 2 Hz，波长为 0.15 m。其波速为 v = 2 × 0.15 = 0.3 m/s。如果频率加倍到 4 Hz，而波长不变，波速也会加倍到 0.6 m/s。
12. Energy Stores, Transfers and Conservation | 能量储存、转移与守恒
The universe obeys one of the most powerful principles in all of science: energy cannot be created or destroyed, only transferred from one store to another or dissipated. In Year 7 WJEC Physics, you learn to identify the main energy stores (kinetic, gravitational potential, thermal, chemical, elastic, electrostatic, magnetic, nuclear) and the four pathways of energy transfer (by heating, mechanically, electrically, and by radiation).
宇宙遵循着整个科学世界最强大的原理之一：能量既不能被创造，也不能被消灭，只能从一种储存形式转移到另一种，或者被耗散。在 WJEC 七年级物理中，你会学习识别主要的能量储存形式（动能、重力势能、内能/热能、化学能、弹性势能、静电势能、磁能、核能）以及能量转移的四种途径（通过加热、力学做功、电流做功和辐射）。
The conservation principle is often written as:
这条守恒原理通常表述为：
Total energy before = Total energy after
Ebefore = Eafter
ferred to kinetic energy (Eₖ = ½mv²) and a small amount warms the air. When drawing Sankey diagrams, the width of the arrow represents the quantity of energy, and the total input width always equals the total output width.
在任何过程中，能量的总量保持不变。例如，当一个球被释放下落时，重力势能（Eₚ = mgh）转化为动能（Eₖ = ½mv²），还有一小部分使空气变热。在绘制桑基图时，箭头的宽度代表能量的多少，且总输入宽度始终等于总输出宽度。
otal energy output is 45 kJ useful energy + 5 kJ wasted = 50 kJ, which matches the input. Efficiency can be calculated as useful output / total input.
一个电热水壶将 50 kJ 的电能转移到水的热能储存中，但同时也有 5 kJ 以热量形式耗散到周围环境中。总能量输出为 45 kJ 有用功 + 5 kJ 浪费 = 50 kJ，与输入一致。效率可以计算为 有用输出 / 总输入。
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