📚 Year 10 AQA Physics: Formula & Theorem Quick-Reference Handbook | AQA 十年级物理公式定理速查手册
This handbook brings together every key formula and theorem you will meet in AQA GCSE Physics for Year 10. Use it to revise relationships between physical quantities, practise rearranging equations, and secure the theory that underpins all practical work. Each section presents equations with standard symbols and units, followed by a clear statement of the underlying principle.
本手册汇集了 AQA 十年级物理中所有关键公式和定理。你可以用它梳理物理量之间的关系、练习公式变形，并巩固所有实验背后的原理。每个小节都给出带标准符号和单位的方程，随后用清晰的语言陈述对应的物理定理。
1. Energy and Energy Transfers | 能量与能量传递
Energy can be transferred usefully between stores or dissipated to the surroundings. The law of conservation of energy states that energy cannot be created or destroyed, only transferred.
能量可以在不同储存之间有用转移，也会耗散到环境中。能量守恒定律指出：能量不能被创造或毁灭，只能被转移。
The energy transferred by a device depends on its power rating and the time it operates: E = P t, where E is energy in joules (J), P is power in watts (W), and t is time in seconds (s).
用电器转移的能量取决于其额定功率和工作时间：E = P t，其中 E 为能量（焦耳 J），P 为功率（瓦特 W），t 为时间（秒 s）。
Efficiency is defined as the ratio of useful energy output to total energy input, often expressed as a percentage: efficiency = (useful output energy ÷ total input energy) × 100%. No machine can exceed 100 % efficiency.
效率定义为有用能量输出与总能量输入的比值，通常用百分数表示：效率 =（有用输出能量 ÷ 总输入能量）× 100%，任何机器的效率都不可能超过 100%。
2. Work, Power and Efficiency | 功、功率与效率
Work is done when a force moves an object through a distance. The work done equals the energy transferred: W = F s, with work W in joules (J), force F in newtons (N), and distance s in metres (m). One joule is the work done when a force of 1 N moves an object 1 m in the direction of the force.
当一个力使物体沿力的方向移动一段距离时，该力就做了功。功的大小等于转移的能量：W = F s，其中 W 为功（J），F 为力（N），s 为距离（m）。1 焦耳相当于 1 N 的力使物体在力的方向上移动 1 m 所做的功。
Power is the rate of doing work or transferring energy: P = W ÷ t and P = E ÷ t in watts (W), where 1 W = 1 J/s. A more powerful machine does the same work in less time.
功率是做功或转移能量的快慢：P = W ÷ t 以及 P = E ÷ t。功率的单位是瓦特（W），1 W = 1 J/s。功率越大的机器完成相同功所需的时间越短。
For any system, total energy input equals useful energy output plus wasted energy. The efficiency can also be calculated from power: efficiency = (useful power output ÷ total power input).
对任何系统，总能量输入等于有用能量输出加上浪费的能量。效率也可以从功率计算：效率 =（有用功率输出 ÷ 总功率输入）。
3. Kinetic and Potential Energy | 动能与势能
Moving objects store kinetic energy, which depends on mass and speed. The formula is Eₖ = ½ m v², where Eₖ is kinetic energy (J), m is mass (kg), and v is speed (m/s). Because speed is squared, doubling the speed quadruples the kinetic energy.
运动的物体具有动能，其大小取决于质量和速率。公式为 Eₖ = ½ m v²，其中 Eₖ 为动能（J），m 为质量（kg），v 为速率（m/s）。由于速率是平方项，速率加倍会使动能变为原来的四倍。
Objects raised above the ground store gravitational potential energy. The change in gravitational potential energy is ΔEₚ = m g Δh, with g being gravitational field strength (on Earth approximately 9.8 N/kg, typically 10 N/kg in GCSE problems), and Δh the change in height (m).
被举高的物体储存重力势能。重力势能的变化量为 ΔEₚ = m g Δh，其中 g 为重力场强度（在地球上约为 9.8 N/kg，GCSE 题目中常取 10 N/kg），Δh 为高度变化（m）。
In a closed system with no air resistance, the sum of kinetic and potential energy remains constant. This is an example of the conservation of energy.
在没有空气阻力的封闭系统中，动能和势能的总和保持不变，这是能量守恒定律的一个实例。
4. Electricity Basics: Charge, Current and Voltage | 电路基础：电荷、电流与电压
Electric current is the rate of flow of charge. The relationship is Q = I t, where Q is charge in coulombs (C), I is current in amperes (A), and t is time in seconds (s). One coulomb is the charge that passes a point in a circuit when 1 A flows for 1 s.
电流是电荷流动的速率。关系式为 Q = I t，其中 Q 为电荷（库仑 C），I 为电流（安培 A），t 为时间（秒 s）。当 1 A 电流流过 1 s 时，通过电路某一点的电荷量就是 1 库仑。
Voltage (potential difference) measures the energy transferred per unit charge. It is defined as V = W ÷ Q or V = E ÷ Q, where V is in volts (V). One volt means 1 joule of energy is transferred per coulomb of charge.
电压（电势差）计量了单位电荷转移的能量。定义式为 V = W ÷ Q 或 V = E ÷ Q，V 的单位是伏特（V）。1 伏特表示每库仑电荷转移 1 焦耳的能量。
5. Resistance and Ohm's Law | 电阻与欧姆定律
Resistance is a measure of how difficult it is for current to flow. The defining equation is R = V ÷ I, where resistance R is in ohms (Ω), V is potential difference (V), and I is current (A).
电阻衡量的是电流流动的难易程度。定义式为 R = V ÷ I，其中电阻 R 的单位是欧姆（Ω），V 为电势差（V），I 为电流（A）。
Ohm's law states that, for an ohmic conductor at constant temperature, the current is directly proportional to the potential difference across it. The resistance remains constant, and the I–V graph is a straight line through the origin.
欧姆定律指出：对温度不变的欧姆导体，电流与其两端的电势差成正比。此时电阻保持恒定，I–V 图像是一条过原点的直线。
In a series circuit, the total resistance is the sum of individual resistances: Rtotal = R₁ + R₂ + …. In a parallel circuit, the total resistance is less than the smallest individual resistance, and the reciprocal formula applies: 1/Rtotal = 1/R₁ + 1/R₂ + … (Higher Tier).
串联电路中，总电阻等于各分电阻之和：R总 = R₁ + R₂ + …。并联电路的总电阻小于最小的分电阻，其倒数关系为 1/R总 = 1/R₁ + 1/R₂ + …（高等级内容）。
6. Power and Energy in Circuits | 电路中的功率与能量
Electrical power can be calculated using three equivalent equations depending on the quantities known. The basic form is P = I V, where P is power (W), I is current (A), V is potential difference (V). It can be combined with Ohm's law to give P = I² R and P = V² ÷ R (Higher Tier).
电功率可根据已知量用三个等效方程计算。基本形式为 P = I V，其中 P 为功率（W），I 为电流（A），V 为电势差（V）。结合欧姆定律可推导出 P = I² R 和 P = V² ÷ R（高等级内容）。
The energy transferred by an electrical appliance is given by E = P t and, using the charge equation, E = Q V. This means the energy transferred equals the charge moved multiplied by the potential difference.
用电器转移的电能可用 E = P t 计算，也可利用电荷方程得到 E = Q V。这表明转移的电能等于流动的电荷量乘以电势差。
7. Particle Model and Density | 粒子模型与密度
The particle model describes the arrangement, movement and energy of particles in solids, liquids and gases. Density measures how much mass is contained in a given volume. The formula is ρ = m ÷ V, where ρ is density (kg/m³), m is mass (kg), and V is volume (m³).
粒子模型描述了固态、液态和气态中粒子的排列、运动和能量。密度衡量单位体积内所含的质量。公式为 ρ = m ÷ V，其中 ρ 为密度（kg/m³），m 为质量（kg），V 为体积（m³）。
When a substance changes state, mass is conserved but the arrangement of particles changes, so density usually changes. Gases typically have much lower densities than liquids and solids because particles are spread far apart.
物质物态变化时质量守恒，但粒子排列方式改变，因此密度通常会变化。由于粒子间隔很远，气体的密度通常远小于液体和固体。
8. Specific Heat Capacity and Latent Heat | 比热容与潜热
Specific heat capacity is the energy required to raise the temperature of 1 kg of a substance by 1 °C. The energy change is ΔE = m c Δθ, where ΔE is energy (J), m is mass (kg), c is specific heat capacity (J/kg°C), and Δθ is temperature change (°C).
比热容是使 1 kg 物质温度升高 1 °C 所需要的能量。能量变化为 ΔE = m c Δθ，其中 ΔE 为能量（J），m 为质量（kg），c 为比热容（J/kg°C），Δθ 为温度变化（°C）。
Specific latent heat is the energy required to change the state of 1 kg of a substance without a change in temperature. The formula is E = m L, where L is the specific latent heat (J/kg). Use Lf for fusion (melting/freezing) and Lv for vaporisation (boiling/condensing).
比潜热是使 1 kg 物质在不改变温度的情况下改变物态所需的能量。公式为 E = m L，L 为比潜热（J/kg）。熔解用 Lf，汽化用 Lv。
9. Atomic Structure and Radioactive Decay | 原子结构与放射性衰变
Atoms consist of a nucleus containing protons and neutrons, surrounded by electrons. An atom's atomic number is the number of protons, and its mass number is the total of protons and neutrons.
原子由包含质子和中子的原子核以及绕核运动的电子组成。原子序数等于质子数，质量数等于质子数与中子数之和。
Unstable nuclei emit radiation to become more stable. Alpha, beta and gamma radiation have different penetrating powers and ionising abilities. The half-life of a radioactive isotope is the time taken for half the unstable nuclei in a sample to decay, or for the count rate to halve.
不稳定的原子核通过放出辐射变得更稳定。α、β 和 γ 辐射有不同的穿透能力和电离能力。放射性同位素的半衰期是指样品中一半不稳定核发生衰变所需的时间，或计数率减半所需的时间。
An exponential decay curve describes the activity over time. The equation linking current activity A to initial activity A₀ after n half-lives is A = A₀ × (½)ⁿ (Higher Tier).
活度随时间的变化遵循指数衰减曲线。经过 n 个半衰期后，当前的活度 A 与初始活度 A₀ 的关系为 A = A₀ × (½)ⁿ（高等级内容）。
10. Waves: Speed, Frequency and Wavelength | 波：波速、频率与波长
Waves transfer energy without transferring matter. The wave speed equation applies to all waves: v = f λ, where v is wave speed (m/s), f is frequency (Hz), and λ is wavelength (m).
波传递能量而不传递物质。波速方程适用于所有波：v = f λ，其中 v 为波速（m/s），f 为频率（Hz），λ 为波长（m）。
The period of a wave is the time for one complete cycle to pass a point, and it is the reciprocal of frequency: T = 1 ÷ f, with period T in seconds (s).
波的周期是一个完整波形通过某一点所用的时间，它是频率的倒数：T = 1 ÷ f，周期 T 的单位为秒（s）。
× 10⁸ m/s. The same wave equation links the speed of light, its frequency and wavelength.
电磁波在真空中传播时，v = c = 3.0 × 10⁸ m/s。同样的波速方程联系着光速、频率和波长。
11. Forces and Motion: Speed and Acceleration | 力与运动：速率与加速度
Speed describes how fast an object moves. For uniform motion, average speed is v = s ÷ t, where v is speed (m/s), s is distance (m), and t is time (s). The gradient of a distance–time graph gives speed.
速率描述物体运动的快慢。对于匀速运动，平均速率 v = s ÷ t，v 为速率（m/s），s 为距离（m），t 为时间（s）。路程-时间图像的斜率表示速率。
Acceleration is the rate of change of velocity. It is calculated as a = Δv ÷ t, with acceleration a in m/s², Δv the change in velocity (m/s) and t time (s). A negative acceleration indicates deceleration.
加速度是速度的变化率。计算公式为 a = Δv ÷ t，加速度 a 的单位为 m/s²，Δv 为速度变化量（m/s），t 为时间（s）。负加速度表示减速。
The motion of an object under constant acceleration can be analysed using the equations of uniform acceleration. The equation linking final velocity, initial velocity, acceleration and distance is v² – u² = 2 a s (Higher Tier).
匀加速运动可以用匀加速运动方程分析。联系末速度、初速度、加速度和位移的方程为 v² – u² = 2 a s（高等级内容）。
12. Newton’s Laws and Momentum | 牛顿定律与动量
Newton's second law states that the acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass. This is summarised as F = m a, where F is resultant force (N), m is mass (kg), and a is acceleration (m/s²).
牛顿第二定律指出：物体的加速度与所受合力成正比，与其质量成反比。公式为 F = m a，其中 F 为合力（N），m 为质量（kg），a 为加速度（m/s²）。
object and is a direct application of F = m a, where a = g (gravitational field strength): W = m g.
重力是作用在物体上的万有引力，是 F = m a 的一个直接应用，其中 a = g（重力场强度）：W = m g。
Momentum is a property of moving objects, defined as p = m v, with p in kg m/s. In a closed system, the total momentum before an event equals the total momentum after the event: this is the conservation of momentum (Higher Tier).
动量是运动物体的一种属性，定义为 p = m v，p 的单位为 kg m/s。在封闭系统中，事件前后的总动量相等，这就是动量守恒（高等级内容）。
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