📚 Year 11 WJEC Physics: Formula & Theorem Quick Reference | Year 11 WJEC 物理：公式定理速查手册
Welcome to your ultimate quick-reference handbook for Year 11 WJEC Physics. This guide condenses the essential formulas, laws, and theorems you need to memorise and apply in your GCSE exams. Each formula is accompanied by a brief explanation of its variables and conditions of use. Study it regularly to boost your confidence in tackling numerical and conceptual questions.
欢迎使用这本面向 Year 11 WJEC 物理的终极速查手册。本指南汇集了 GCSE 考试中必须记忆和应用的核心公式、定律和定理。每个公式都附有简要说明，解释其变量和使用条件。定期学习它，提升你解决计算和概念问题的信心。
1. Kinematic Equations | 运动学方程
v = u + at
This equation calculates the final velocity (v) of an object moving with uniform acceleration. u is the initial velocity in m/s, a is the acceleration in m/s², and t is the time in seconds.
该方程用于计算匀加速运动物体的末速度 v。u 是初速度（单位 m/s），a 是加速度（单位 m/s²），t 是时间（单位 s）。
s = ut + ½ at²
Use this to find the displacement (s) when an object accelerates uniformly from an initial velocity u over time t. Displacement is measured in metres (m).
当物体从初速度 u 开始匀加速运动时间 t 时，用该方程求位移 s。位移单位为米（m）。
v² = u² + 2as
This links final velocity, initial velocity, acceleration, and displacement without involving time directly. It is useful when time is not given.
该方程联系末速度、初速度、加速度和位移，不直接包含时间。当题目未给出时间时，此式非常有用。
s = ½ (u + v) t
The average velocity formula gives displacement as the product of average velocity and time. Only valid for uniform acceleration.
该平均速度公式将位移表示为平均速度与时间的乘积。只适用于匀加速运动。
2. Forces and Newton's Laws | 力与牛顿定律
Newton’s First Law: An object remains at rest or in uniform motion unless acted upon by a resultant external force.
牛顿第一定律：任何物体在不受外力作用时，将保持静止或匀速直线运动状态。
Newton’s Second Law: The resultant force on an object is equal to the rate of change of its momentum. For constant mass, this simplifies to F = m a.
牛顿第二定律：物体所受合外力等于其动量的变化率。当质量恒定时，简化为 F = m a。
F = m a
Resultant force (F) in newtons (N) equals mass (m) in kilograms multiplied by acceleration (a) in m/s².
合外力 F（单位牛顿 N）等于质量 m（千克）乘以加速度 a（m/s²）。
W = m g
Weight (W) is the force of gravity on a mass. g is gravitational field strength, approximately 9.8 N/kg on Earth.
重力 W 是作用在物体上的引力。g 为引力场强度，在地球表面约为 9.8 N/kg。
p = m v
Momentum (p) in kg m/s is the product of mass and velocity. Momentum is a vector quantity and is conserved in collisions.
动量 p（单位 kg m/s）是质量与速度的乘积。动量是矢量，碰撞过程中动量守恒。
Newton’s Third Law: For every action force there is an equal and opposite reaction force; the two forces act on different objects.
牛顿第三定律：每一个作用力都有一个大小相等、方向相反的反作用力，且这两个力作用在不同的物体上。
3. Work, Energy and Power | 功、能和功率
W = F d
Work done (W) in joules (J) is the product of the force applied (F) and the distance moved in the direction of the force (d).
做功 W（单位焦耳 J）等于作用力 F 乘以物体在力的方向上移动的距离 d。
Eₖ = ½ m v²
Kinetic energy (Eₖ) is the energy an object possesses due to its motion. It depends on mass and the square of the speed.
动能 Eₖ 是物体由于运动而具有的能量，取决于质量和速度的平方。
Eₚ = m g h
Gravitational potential energy (Eₚ) gained by an object lifted through a height h in a uniform gravitational field.
物体在均匀引力场中被举高 h 时所增加的重力势能 Eₚ。h 为高度变化量。
P = W / t and P = E / t
Power (P) in watts (W) is the rate of doing work or transferring energy. 1 W = 1 J/s.
功率 P（单位瓦特 W）是做功或能量转移的速率。1 W = 1 J/s。
Conservation of Energy: Energy cannot be created or destroyed, only transferred, stored or dissipated. In a closed system total energy remains constant.
能量守恒定律：能量既不会凭空产生，也不会凭空消失，只能从一种形式转移、储存或耗散为另一种形式。在一个封闭系统中总能量保持不变。
4. Density and Pressure | 密度与压强
ρ = m / V
Density (ρ) is mass per unit volume. The SI unit is kg/m³, although g/cm³ is also commonly used in the lab.
密度 ρ 是单位体积的质量。国际单位为 kg/m³，实验室中 g/cm³ 也常被使用。
p = F / A
Pressure (p) in pascals (Pa) is the normal force acting per unit area. 1 Pa = 1 N/m².
压强 p（单位帕斯卡 Pa）是垂直作用在单位面积上的力。1 Pa = 1 N/m²。
p = h ρ g
For a liquid, pressure at a depth h depends on the liquid density and gravitational field strength. This pressure acts equally in all directions at a given depth.
液体内部深度为 h 处的压强取决于液体密度和引力场强度，在同一深度处液体向各个方向的压强相等。
5. Wave Properties | 波的性质
v = f λ
Wave speed (v, in m/s) equals the product of frequency (f, in hertz) and wavelength (λ, in metres). This applies to all wave types, including sound and electromagnetic waves.
波速 v（m/s）等于频率 f（赫兹 Hz）乘以波长 λ（米）。该公式适用于所有波，包括声波和电磁波。
T = 1 / f
The period (T) is the time taken for one complete wave cycle. It is the reciprocal of frequency.
周期 T 是完成一次完整振动所需的时间，为频率的倒数。
Reflection: Angle of incidence = angle of reflection, measured from the normal.
反射定律：入射角等于反射角，均从法线量起。
Refraction: When a wave crosses a boundary between two media, its speed and wavelength change, causing it to change direction unless it enters along the normal.
折射：当波穿过两种介质的边界时，波速和波长会改变，导致传播方向改变（除非沿法线入射）。
6. Electromagnetic Spectrum | 电磁波谱
t a common speed in a vacuum: c = 3.00 × 10⁸ m/s. The wave equation v = f λ still applies.
所有电磁波在真空中都以相同速度传播：c = 3.00 × 10⁸ m/s。波速公式 v = f λ 依然适用。
The main groups in order of decreasing wavelength (increasing frequency) are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.
按照波长递减（频率递增）的顺序，主要波段为：无线电波、微波、红外线、可见光、紫外线、X 射线、伽马射线。
Higher frequency electromagnetic waves carry more photon energy and can cause more ionisation. Gamma rays and X-rays are highly ionising; radio waves are non-ionising.
频率越高的电磁波光子能量越大，电离能力越强。伽马射线和 X 射线电离能力强；无线电波属于非电离辐射。
The uses and dangers are linked to a wave's ability to penetrate materials. For instance, microwaves are used for cooking and communications, while X-rays are used for medical imaging but can cause cell damage.
电磁波的用途与危害与其穿透能力相关。例如，微波用于烹饪和通信，X 射线用于医学成像但可能损伤细胞。
7. Electrical Circuits and Ohm's Law | 电路与欧姆定律
V = I R
Ohm's law states that the potential difference (V) across a resistor is directly proportional to the current (I) flowing through it, provided temperature remains constant. R is resistance in ohms (Ω).
欧姆定律指出，当温度恒定时，通过导体的电流 I 与导体两端的电压 V 成正比。R 为电阻，单位欧姆（Ω）。
Q = I t
Electric charge (Q) in coulombs (C) equals current (I) multiplied by time (t). This is used to calculate charge flowing in a circuit.
电荷量 Q（单位库仑 C）等于电流 I 乘以时间 t。用于计算电路中流过的电荷量。
E = Q V
ves through a potential difference V. This can be combined with Q = I t to give E = I t V.
当电荷 Q 通过电势差 V 时转移的能量 E。可与 Q = I t 结合得到 E = I t V。
Series circuits: Current is the same everywhere; total resistance Rtotal = R₁ + R₂ + … ; total p.d. is shared.
串联电路：电流处处相等；总电阻 Rtotal = R₁ + R₂ + … ；总电压在各元件上分配。
Parallel circuits: p.d. is the same across each branch; total current is the sum of branch currents; total resistance formula: 1/Rtotal = 1/R₁ + 1/R₂ + …
并联电路：各支路两端电压相等；总电流等于各支路电流之和；总电阻公式：1/Rtotal = 1/R₁ + 1/R₂ + …
8. Electrical Power and Energy Transfer | 电功率与能量传递
P = I V
Electrical power (P) in watts is the product of current and potential difference. This works for any component.
电功率 P（瓦特）等于通过元件的电流 I 与元件两端的电压 V 的乘积，适用于任何元件。
P = I² R and P = V² / R
rive these alternative forms. They describe the rate of thermal energy dissipation in a resistive component.
对于电阻元件，利用 V = I R 可导出另两个形式。它们表示电流通过电阻时单位时间产生的热量。
E = P t
Energy transferred (E, in joules or kilowatt-hours) equals power multiplied by time. For domestic electricity, the kilowatt-hour (kWh) is a common unit for energy billing.
转移的能量 E（焦耳或千瓦时）等于功率乘以时间。家庭用电量通常以千瓦
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