📚 Year 7 CCEA Physics: Formula & Theorem Quick Reference Handbook | Year 7 CCEA 物理：公式定理速查手册
This quick reference handbook has been carefully compiled for Year 7 students following the CCEA Key Stage 3 physics curriculum. It brings together the essential formulas, laws, and key relationships you will encounter during your study of forces, motion, energy, electricity, and waves. Each entry presents the equation in words and symbols, explains the units, and highlights important points to help you solve problems and prepare for tests with confidence.
本速查手册为学习 CCEA Key Stage 3 物理课程的 Year 7 学生精心编写，汇集了你在学习力、运动、能量、电学和波等内容时将会遇到的基本公式、定律和重要关系。每个条目都以文字和符号形式给出方程，解释单位，并强调重点，帮助你自信地解题和备考。
1. Speed, Distance and Time | 速度、距离与时间
The average speed of an object can be calculated using the formula: speed = distance ÷ time. In symbols, v = d / t, where v is speed, d is distance, and t is time. The SI unit of speed is metres per second (m/s), but kilometres per hour (km/h) or miles per hour (mph) are also commonly used. To convert from km/h to m/s, divide by 3.6.
物体的平均速度可用公式：速度 = 距离 ÷ 时间 计算。符号表示为 v = d / t，其中 v 是速度，d 是距离，t 是时间。速度的国际单位是米/秒（m/s），也常用千米/小时（km/h）或英里/小时（mph）。将 km/h 转换为 m/s 需除以 3.6。
To find the distance travelled, rearrange the equation to d = v × t. To find the time taken, use t = d / v. Always ensure the units for time and distance are consistent before calculating.
若要求路程，可将公式变形为 d = v × t；若要求时间，则用 t = d / v。计算前务必确保时间与距离的单位一致。
2. Weight and Mass (Gravity) | 重量与质量（重力）
Weight is the force of gravity acting on an object. It is directly proportional to the object’s mass: weight = mass × gravitational field strength, written as W = m g. On Earth, the gravitational field strength g is approximately 10 N/kg (or 9.8 N/kg). Weight is measured in newtons (N), while mass is measured in kilograms (kg).
重量是作用在物体上的重力，与物体的质量成正比：重量 = 质量 × 重力场强度，写作 W = m g。在地球表面，重力场强度 g 约为 10 N/kg（或 9.8 N/kg）。重量的单位是牛顿（N），质量的单位是千克（kg）。
Mass is a measure of the amount of matter in an object and remains constant everywhere. Weight, however, changes if the gravitational field strength changes – for example, on the Moon g ≈ 1.6 N/kg, so an object would weigh only about one-sixth of its Earth weight.
质量是物体所含物质的量，无论何处都保持不变；但重量会随重力场强度变化——例如，月球上的 g ≈ 1.6 N/kg，同一物体在月球上所受重力仅为地球上的约六分之一。
3. Density | 密度
Density tells us how tightly matter is packed in a substance. The formula is: density = mass ÷ volume, symbolically ρ = m / V. The SI unit is kilograms per cubic metre (kg/m³), but grams per cubic centimetre (g/cm³) are also widely used. Note that 1 g/cm³ = 1000 kg/m³.
密度表示物质内部质量的紧密程度。公式为：密度 = 质量 ÷ 体积，符号为 ρ = m / V。国际单位是千克/立方米（kg/m³），也常用克/立方厘米（g/cm³）。注意 1 g/cm³ = 1000 kg/m³。
If you know density and volume, mass can be found by m = ρ × V. If you know mass and density, volume can be found by V = m / ρ. Liquids and solids typically have much higher densities than gases.
已知密度和体积，可用 m = ρ × V 求质量；已知质量和密度，则用 V = m / ρ 求体积。液体和固体的密度通常远大于气体。
4. Hooke’s Law (Springs) | 胡克定律（弹簧）
Hooke’s Law describes the behaviour of many elastic materials, such as springs: the extension x is directly proportional to the applied force F, provided the elastic limit is not exceeded. The equation is F = k x, where F is the force (N), k is the spring constant (N/m), and x is the extension (m).
胡克定律描述了许多弹性材料（如弹簧）的形变规律：在不超过弹性限度时，伸长量 x 与施加的力 F 成正比。公式为 F = k x，其中 F 是力（N），k 是劲度系数（N/m），x 是伸长量（m）。
The spring constant k indicates the stiffness of the spring – a larger k means a stiffer spring. If the force becomes too large, the spring will be permanently stretched and will no longer obey Hooke’s Law.
劲度系数 k 反映弹簧的软硬程度——k 越大，弹簧越硬。若施力过大，弹簧会发生永久形变，不再遵从胡克定律。
5. Moments (Turning Effect) | 力矩（转动效应）
A moment measures the turning effect of a force about a pivot. It is calculated by: moment = force × perpendicular distance from the pivot, or M = F × d. The unit is the newton-metre (N m).
力矩衡量力绕支点转动的效应。计算公式为：力矩 = 力 × 支点到力作用线的垂直距离，即 M = F × d。单位是牛顿·米（N m）。
For an object in rotational equilibrium, the principle of moments states that the total clockwise moment equals the total anticlockwise moment: ΣMclockwise = ΣManticlockwise. This principle is used to solve problems with levers and seesaws.
当物体处于转动平衡时，力矩原理指出，顺时针力矩之和等于逆时针力矩之和：ΣM顺时针 = ΣM逆时针。该原理可用于解决杠杆和跷跷板相关问题。
6. Pressure | 压强
Pressure is the force acting per unit area. The formula is: pressure = force ÷ area, or P = F / A. The SI unit is the pascal (Pa), where 1 Pa = 1 N/m². A large force concentrated on a small area produces a high pressure, which is why nails and pins have sharp points.
压强是单位面积上所受的力。公式为：压强 = 力 ÷ 面积，即 P = F / A。国际单位是帕斯卡（Pa），1 Pa = 1 N/m²。在较小面积上施加较大的力会产生较大压强，这正是钉子和针具有尖端的原因。
The same pressure formula can be rearranged to find force (F = P × A) or area (A = F / P). When talking about fluids, pressure increases with depth and acts in all directions.
该公式也可变形为 F = P × A 求力，或 A = F / P 求面积。对于流体，压强随深度增加，且向各个方向作用。
7. Work Done and Energy Transfer | 做功与能量转移
In physics, work is done when a force moves an object. The amount of work done (or energy transferred) is given by: work = force × distance moved in the direction of the force, written as W = F s. The unit of work and energy is the joule (J): 1 J = 1 N m.
在物理中，当力使物体移动时，就做了功。做功（或转移的能量）大小为：功 = 力 × 沿力方向移动的距离，写作 W = F s。功和能量的单位是焦耳（J），1 J = 1 N m。
This formula applies not only to mechanical work but also to gravitational potential energy gain: when you lift an object through a height h, the work done against gravity is W = m g h. Work can also be transformed into kinetic energy or thermal energy.
该公式不仅适用于机械功，也适用于重力势能增加：将物体提升高度 h 时，克服重力做的功为 W = m g h。功还可转换为动能或内能。
8. Power | 功率
Power is the rate of doing work or transferring energy. The equation is: power = energy transferred ÷ time, or P = E / t (also P = W / t). The unit of power is the watt (W), where 1 W = 1 J/s. A higher power rating means more energy is transferred each second.
功率是做功或转移能量的速率。公式为：功率 = 转移的能量 ÷ 时间，即 P = E / t（也可写作 P = W / t）。功率的单位是瓦特（W），1 W = 1 J/s。功率越大，表示每秒转移的能量越多。
For example, a 60 W light bulb converts 60 J of electrical energy into light and heat every second. When comparing appliances, those with higher wattage use energy more quickly.
例如，一盏 60 W 的灯泡每秒将 60 J 的电能转化为光和热。比较电器时，瓦数越高的电器消耗能量的速度越快。
9. Ohm’s Law and Resistance | 欧姆定律与电阻
Ohm’s Law is a fundamental rule for many electrical circuits: the voltage V across a component is equal to the current I flowing through it multiplied by its resistance R. In symbols: V = I × R. Resistance is measured in ohms (Ω).
欧姆定律是许多电路的基本规律：元件两端的电压 V 等于流过它的电流 I 乘以其电阻 R。符号表示为 V = I × R。电阻的单位是欧姆（Ω）。
For a fixed resistor at constant temperature, resistance remains constant; doubling the voltage will double the current. You can rearrange the formula to find resistance (R = V / I) or current (I = V / R). Remember that a higher resistance reduces the current for a given voltage.
对于一定温度下的固定电阻，其阻值不变；电压加倍则电流加倍。你可将公式变形为 R = V / I 求电阻，或 I = V / R 求电流。记住，在电压一定时，电阻越大，电流越小。
10. Series and Parallel Circuit Rules | 串联与并联电路规则
In a series circuit, the current through each component is the same: Itotal = I₁ = I₂ = I₃ = … The total voltage supplied by the battery is shared across the components: Vtotal = V₁ + V₂ + V₃ + … The total resistance is the sum of individual resistances: Rtotal = R₁ + R₂ + … .
在串联电路中，通过每个元件的电流相等：Itotal = I₁ = I₂ = I₃ = …。电池提供的总电压由各元件分担：Vtotal = V₁ + V₂ + V₃ + …。总电阻等于各电阻之和：Rtotal = R₁ + R₂ + … 。
In a parallel circuit, the voltage across each branch is the same as the supply voltage: V₁ = V₂ = Vtotal. The total current from the source is the sum of the currents in the branches: Itotal = I₁ + I₂ + I₃ + … The effective total resistance is always less than the smallest individual branch resistance and is given by 1/Rtotal = 1/R₁ + 1/R₂ + … .
在并联电路中，各支路两端的电压等于电源电压：V₁ = V₂ = Vtotal。从电源流出的总电流等于各支路电流之和：Itotal = I₁ + I₂ + I₃ + …。并联后的总电阻总是小于各支路中最小的电阻，计算公式为 1/Rtotal = 1/R₁ + 1/R₂ + … 。
11. Wave Speed Equation | 波速公式
The speed of a wave is linked to its frequency and wavelength by the wave equation: wave speed = frequency × wavelength, or v = f λ. The unit for wave speed is metres per second (m/s), for frequency is hertz (Hz, meaning number of waves per second), and for wavelength is metres (m).
波速与频率、波长的关系由波动方程给出：波速 = 频率 × 波长，即 v = f λ。波速的单位是米/秒（m/s），频率的单位是赫兹（Hz，每秒完整波的个数），波长的单位是米（m）。
This equation applies to all forms of waves, including sound, light, and water waves. To find frequency, rearrange to f = v / λ; to find wavelength, use λ = v
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