📚 Year 10 WJEC Physics: Quick Reference Formula & Theorem Handbook | Year 10 WJEC 物理：公式定理速查手册
This handbook provides a concise, topic-by-topic summary of all the essential formulae and laws you need to memorise for Year 10 WJEC Physics. It is designed for quick revision before tests and exams. Each key equation is presented with a clear explanation in both English and Chinese, alongside standard scientific units.
本手册按主题简明总结了 Year 10 WJEC 物理需要记忆的全部核心公式和定律，专为考前快速复习而设计。每个关键方程都配有中英文清晰解释，并标注了标准科学单位。
1. Motion and SUVAT Equations | 运动与匀加速方程
In uniform acceleration problems, there are five quantities: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). The following four equations allow you to calculate an unknown quantity when the other three are known.
在匀加速问题中，共有五个物理量：位移（s）、初速度（u）、末速度（v）、加速度（a）和时间（t）。以下四个方程可让你在已知三个量的情况下求出未知量。
v = u + at
This version is used when displacement is not involved. It shows that final velocity is the initial velocity plus the change in velocity from constant acceleration over time t.
此式不涉及位移，表明末速度等于初速度加上匀加速在时间 t 内产生的速度变化量。
s = ut + ½ at²
Used when the final velocity is unknown. Displacement is the sum of the distance travelled at the initial velocity and the extra distance due to acceleration.
当末速度未知时使用。位移等于以初速度移动的距离与由加速度引起的额外距离之和。
v² = u² + 2as
This equation links velocity and displacement without requiring time. It is very useful for problems where time is not given or asked.
该方程直接将速度与位移联系起来而不需要时间，在未给出或未要求时间的问题中非常有用。
s = (u + v)/2 × t
Since acceleration is constant, the average velocity is (u+v)/2. Multiplying by time gives displacement.
由于加速度恒定，平均速度为 (u+v)/2，再乘以时间即得位移。
Remember that acceleration is defined as the rate of change of velocity: a = (v – u) / t. It is a vector quantity, so direction matters.
记住，加速度定义为速度的变化率：a = (v – u) / t。它是矢量，因此方向很重要。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s three laws of motion are the foundation of all force and motion calculations in WJEC Physics. The second law gives the most important mathematical link: net force equals mass times acceleration.
牛顿运动三定律是 WJEC 物理中所有力和运动计算的基础。第二定律给出了最重要的数学联系：合外力等于质量乘加速度。
F = m a
The resultant force (F, in newtons) acting on an object is equal to the product of its mass (m, in kg) and acceleration (a, in m/s²). This is always used with the net force, not just a single applied force.
作用在物体上的合力（F，单位牛顿）等于物体质量（m，单位千克）与加速度（a，单位 m/s²）的乘积。务必使用合力，而非某个单独的力。
W = m g
Weight is the force of gravity on a mass. On Earth, the gravitational field strength g is approximately 9.8 N/kg (often taken as 10 N/kg for estimation).
重量是作用在物体上的重力。地球上重力场强度 g 约为 9.8 N/kg（估算时常取 10 N/kg）。
Newton’s first law states that an object will remain at rest or in uniform motion unless acted upon by a resultant force. This is the concept of inertia.
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。这就是惯性的概念。
The third law reminds us that forces always occur in pairs: if object A exerts a force on object B, then B exerts an equal and opposite force on A.
第三定律提醒我们，力总是成对出现：若物体 A 对 B 施加一个力，则 B 同时对 A 施加一个大小相等、方向相反的力。
3. Momentum | 动量
Momentum is a property of moving objects and is conserved in all collisions and explosions, provided no external forces act. The law of conservation of momentum is a powerful problem-solving tool.
动量是运动物体的一种属性，在没有外力作用的碰撞和爆炸中总是守恒。动量守恒定律是一个强有力的解题工具。
p = m v
Momentum (p, in kg m/s) equals mass times velocity. Since velocity is a vector, momentum also has direction.
动量（p，单位 kg m/s）等于质量乘速度。由于速度是矢量，动量也有方向。
Total momentum before = Total momentum after
For two objects colliding: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂, where u represents velocities before collision and v after. This applies to both elastic and inelastic collisions.
对于两个物体的碰撞：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂，其中 u 表示碰撞前速度，v 表示碰撞后速度。此式对弹性碰撞和非弹性碰撞均成立。
F = Δp / Δt
Newton’s second law in its more general form: force equals the rate of change of momentum. In many GCSE problems, this is simplified to F = (mv – mu) / t, which links force to the change in motion.
牛顿第二定律的更普遍形式：力等于动量的变化率。在许多 GCSE 问题中，此式简化为 F = (mv – mu) / t，将力与运动的变化联系起来。
4. Energy, Work and Power | 能量、功和功率
Energy can be stored or transferred. Work done and power are measures of energy transfer. The principle of conservation of energy states that energy cannot be created or destroyed, only transferred into different forms.
能量可以被储存或转移。功和功率是能量转移的量度。能量守恒定律指出，能量不能被创造或消灭，只能转化为不同形式。
W = F d
Work done (in joules) is the product of the force applied in the direction of motion and the distance moved. If the force is perpendicular to motion, no work is done.
做功（单位焦耳）等于沿运动方向施加的力与移动距离的乘积。若力垂直于运动方向，则不做功。
Eₚ = m g h
Gravitational potential energy gained by an object lifted through a height h. Only changes in height matter; the zero reference level can be chosen arbitrarily.
物体被抬高高度 h 所获得的引力势能。只与高度变化有关，零势能参考面可任意选取。
Eₖ = ½ m v²
Kinetic energy of a moving object. This is a scalar quantity; it depends only on speed, not direction.
运动物体的动能。动能是标量，仅取决于速率而非方向。
P = W / t and P = E / t
Power (in watts) is the rate of doing work or transferring energy. 1 W = 1 J/s. Students often need to convert between power, energy and time.
功率（单位瓦特）是做功或转移能量的速率。1 W = 1 J/s。学生常需在功率、能量和时间之间进行换算。
Efficiency = (useful output energy / total input energy) × 100%. No device is 100% efficient; some energy is always dissipated as thermal energy.
效率 = （有用输出能量 / 总输入能量）× 100%。没有设备能达到 100% 效率，总有一部分能量耗散为热能。
5. Density and Pressure | 密度与压强
Understanding density and pressure is vital for explaining why objects float or sink, and for designing hydraulic systems.
理解密度和压强对于解释物体的浮沉以及设计液压系统至关重要。
ρ = m / V
Density (ρ, in kg/m³) is mass per unit volume. It is a material property; the density of water is 1000 kg/m³.
密度（ρ，单位 kg/m³）是单位体积的质量，属于材料属性；水的密度为 1000 kg/m³。
p = F / A
Pressure (in pascals, Pa) is defined as the force acting normally per unit area. 1 Pa = 1 N/m². The smaller the area for a given force, the larger the pressure.
压强（单位帕斯卡，Pa）定义为垂直作用在单位面积上的力。1 Pa = 1 N/m²。力一定时，面积越小压强越大。
p = h ρ g
Pressure due to a column of liquid. It depends only on the height of the liquid column, the liquid’s density and gravitational field strength, not on the shape of the container.
液体内部压强公式。它只与液柱高度、液体密度和重力场强度有关，与容器形状无关。
6. Thermal Physics | 热物理
When materials are heated, their temperature may rise or they may change state. The specific heat capacity and specific latent heat quantify these processes.
材料受热时，温度可能升高，也可能发生物态变化。比热容和比潜热就是对这两个过程的定量描述。
Q = m c Δθ
The thermal energy needed to raise the temperature of a mass m by Δθ. c is the specific heat capacity (J/kg °C). No change of state occurs.
将质量 m 的物质温度升高 Δθ 所需的热能。c 为比热容（J/kg °C）。此过程中不发生物态变化。
Q = m L
The thermal energy needed to change the state of a mass m at constant temperature. L is the specific latent heat (J/kg) – use Lf for fusion (melting) and Lv for vaporisation (boiling).
使质量 m 的物质在恒温下发生物态变化所需的热能。L 为比潜热（J/kg）——熔化时用 Lf，汽化时用 Lv。
7. Waves | 波
Waves transfer energy without transferring matter. The wave equation links wave speed, frequency and wavelength. Refraction is described by Snell’s law.
波传播能量而不传递物质。波速方程联系了波速、频率和波长。折射由斯涅尔定律描述。
v = f λ
Wave speed (v, in m/s) equals frequency (f, in Hz) multiplied by wavelength (λ, in m). This applies to both transverse and longitudinal waves.
波速（v，单位 m/s）等于频率（f，单位 Hz）乘以波长（λ，单位 m）。此式适用于横波和纵波。
T = 1 / f
The period (T) is the time for one complete wave cycle. It is the reciprocal of frequency.
周期（T）是完成一个完整波循环所需的时间，它是频率的倒数。
n = sin i / sin r
Refractive index n of a medium. When light travels from a vacuum (or air) into the medium, i is the angle of incidence and r is the angle of refraction.
介质的折射率 n。当光从真空（或空气）射入该介质时，i 为入射角，r 为折射角。
sin c = 1 / n
For total internal reflection, the critical angle c is the angle of incidence in the denser medium for which the angle of refraction is 90°. This only happens when light travels from a denser to a less dense medium.
对于全内反射，临界角 c 是光密介质中使折射角为 90° 的入射角。这仅发生在光从光密介质射向光疏介质时。
8. Electromagnetic Spectrum | 电磁波谱
All electromagnetic waves travel at the speed of light in a vacuum, c = 3.00 × 10⁸ m/s. They differ in wavelength and frequency, which are linked by the wave equation.
所有电磁波在真空中均以光速 c = 3.00 × 10⁸ m/s 传播。它们的波长和频率不同，二者通过波速方程相联系。
c = f λ
The speed of light is constant in vacuum, so a lower frequency implies a longer wavelength, and vice versa.
真空中光速恒定，因此频率越低波长越长，反之亦然。
The spectrum in order of increasing frequency (decreasing wavelength): radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. You must recall the order, typical uses and dangers.
波谱按频率递增（波长递减）的顺序为：无线电波、微波、红外线、可见光、紫外线、X
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