📚 Year 9 WJEC Physics: Formula & Theorem Quick Reference Handbook | Year 9 WJEC 物理：公式定理速查手册
This quick reference handbook compiles the essential formulas, laws, and principles you need to master Year 9 WJEC Physics. Each section presents key equations with clear explanations in English and Chinese, helping you to revise efficiently and apply your knowledge with confidence.
这本速查手册汇编了 Year 9 WJEC 物理必须掌握的核心公式、定律和原理。每个章节以中英对照的形式呈现关键方程和清晰解释，帮助你高效复习、自信地应用所学知识。
1. Motion: Speed, Velocity, and Acceleration | 运动：速度、速率和加速度
. The formula is v = d / t. Speed is a scalar quantity; it has magnitude but no direction.
物体的平均速率定义为总路程除以总时间。公式为 v = d / t。速率是标量，只有大小，没有方向。
v = d / t
= (v - u) / t, where u is initial velocity, v is final velocity, and t is the time taken.
速度是给定方向上的速率，属于矢量。加速度是速度的变化率，计算公式为 a = (v - u) / t，其中 u 为初速度，v 为末速度，t 为所用时间。
a = (v − u) / t
+ 2as, where s is displacement. These equations only apply when acceleration is constant.
对于匀加速运动，还可以使用方程 v² = u² + 2as，其中 s 表示位移。这些方程仅在加速度恒定时适用。
2. Forces and Newton's Laws | 力与牛顿定律
Newton' newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²).
牛顿第二定律指出，物体所受的合力等于其质量与加速度的乘积，公式为 F = ma。力的单位是牛顿 (N)，质量单位为千克 (kg)，加速度单位为米每二次方秒 (m/s²)。
F = ma
e gravitational field strength. On Earth, g is approximately 9.8 N/kg, but 10 N/kg is often used for simplicity.
重量是由于重力作用在物体上的力，公式为 W = mg，其中 g 为重力场强度。在地球表面，g 约为 9.8 N/kg，为简化常取 10 N/kg。
W = mg
Hooke' n x is directly proportional to the force applied: F = kx, where k is the spring constant.
胡克定律描述弹簧的伸长量。在不超过弹性极限时，伸长量 x 与所施加的力 F 成正比：F = kx，其中 k 为弹簧常数。
3. Energy, Work, and Power | 能量、功和功率
e in newtons and d is the distance moved in the direction of the force. Work and energy are measured in joules (J).
力使物体移动时就做了功。功的计算公式为 W = Fd，其中 F 为力（牛顿），d 为沿力方向移动的距离。功和能量的单位都是焦耳 (J)。
W = Fd
Gravitational potential energy (GPE) is the energy stored due to an object' E) is the energy of motion: KE = ½ mv². In a closed system, the total energy is conserved.
重力势能 (GPE) 是由物体离地高度所储存的能量：GPE = mgh。动能 (KE) 是物体因运动而具有的能量：KE = ½ mv²。在封闭系统中，总能量守恒。
GPE = mgh
KE = ½ mv²
re t is the time taken. The unit of power is the watt (W). Efficiency is the ratio of useful energy output to total energy input, often expressed as a percentage.
功率是做功或传递能量的速率：P = W / t，其中 t 为时间。功率的单位是瓦特 (W)。效率是指有用能量输出与总能量输入之比，通常以百分比表示。
Efficiency = (Useful output energy) / (Total input energy)
4. Density, Pressure, and the Particle Model | 密度、压强与粒子模型
/ V, where ρ is density, m is mass, and V is volume. The unit is typically kg/m³ or g/cm³.
密度衡量单位体积内所含物质的质量，公式为 ρ = m / V，其中 ρ 为密度，m 为质量，V 为体积。单位通常为 kg/m³ 或 g/cm³。
ρ = m / V
ssure is p = hρg, where ρ is the liquid density and g is the gravitational field strength.
压强是单位面积上所受的力：p = F / A，单位为帕斯卡 (Pa) 或 N/m²。对于高度为 h 的液柱，其压强为 p = hρg，其中 ρ 为液体密度，g 为重力场强度。
p = F / A
p = hρg
The particle model explains that solids have fixed, closely packed particles; liquids have particles that slide past each other; gases have widely spaced particles moving rapidly. Changes of state involve energy transfer without a change in temperature.
粒子模型可以解释：固体的粒子位置固定且紧密排列；液体的粒子可以相互滑动；气体的粒子间距大且快速运动。状态变化涉及能量转移，但温度保持不变。
5. Waves: The Wave Equation | 波：波动方程
Waves transfer energy without transferring matter. In transverse waves, the oscillations are perpendicular to the direction of energy transfer. In longitudinal waves, oscillations are parallel.
波传递能量而不传递物质。在横波中，振动方向与能量传递方向垂直；在纵波中，振动方向与能量传递方向平行。
e number of waves per second, measured in hertz (Hz). The period T of a wave is T = 1 / f.
波速方程将波速 v、频率 f 和波长 λ 联系起来：v = fλ。频率是每秒通过的波的个数，单位是赫兹 (Hz)。波的周期 T 为 T = 1 / f。
v = fλ
T = 1 / f
m/s. Sound waves travel much slower and require a medium. When a wave moves from one medium to another, its speed and wavelength change, but its frequency stays constant.
所有电磁波在真空中的传播速度相同，c = 3.0 × 10⁸ m/s。声波传播速度慢得多，且需要介质。波从一种介质进入另一种介质时，波速和波长改变，但频率保持不变。
6. Electricity: Current, Voltage, and Resistance | 电学：电流、电压与电阻
harge Q (coulombs), current I (amperes), and time t (seconds). In a metal, current is a flow of electrons.
电流是电荷流动的速率。公式 Q = It 将电荷量 Q（库仑）、电流 I（安培）和时间 t（秒）联系起来。在金属中，电流是电子的流动。
Q = It
al difference (voltage) is the work done per unit charge. It is measured in volts (V). Ohm' directly proportional to the voltage: V = IR, where R is resistance measured in ohms (Ω).
电势差（电压）是单位电荷所做的功，单位为伏特 (V)。欧姆定律指出，对于欧姆导体，在温度恒定时，电流与电压成正比：V = IR，其中 R 为电阻，单位是欧姆 (Ω)。
V = IR
Resistance depends on the material, length, and cross-sectional area of a wire. A longer wire has higher resistance; a thicker wire has lower resistance.
电阻取决于导线的材料、长度和横截面积。导线越长，电阻越大；导线越粗，电阻越小。
7. Series and Parallel Circuits | 串联与并联电路
In a series circuit, the current is the same at all points. The total potential difference is the sum of the voltages across each component. The total resistance is Rtotal = R₁ + R₂ + ...
在串联电路中，各处电流相等。总电压等于各元件两端电压之和。总电阻为 Rtotal = R₁ + R₂ + ...
Rtotal = R₁ + R₂ + ...
In a parallel circuit, the potential difference across each branch is the same as the source voltage. The total current is the sum of the currents in each branch. The total resistance is found using 1/Rtotal = 1/R₁ + 1/R₂ + ...
在并联电路中，各支路两端的电压相同，都等于电源电压。总电流等于各支路电流之和。总电阻由公式 1/Rtotal = 1/R₁ + 1/R₂ + ... 计算。
1 / Rtotal = 1 / R₁ + 1 / R₂ + ...
Components in series share the voltage; if one goes out, the circuit is broken. In parallel, each component receives the full voltage and operates independently.
串联元件会分压；如果一个元件断开，整个电路中断。在并联电路中，每个元件获得全电压，并且独立工作。
8. Domestic Electricity and Power Calculations | 家庭用电与功率计算
an appliance is given by P = IV and also by P = I²R. Power is the rate of energy transfer.
英国家用电源提供 230 V、50 Hz 的交流电。用电器的功率由 P = IV 给出，也可由 P = I²R 计算。功率是能量传递的速率。
P = IV
ed to calculate the cost of electricity, where energy is measured in kilowatt-hours (kWh).
用电器消耗的能量为 E = Pt。代入 Q = It 可得 E = QV。这些公式用于计算电费，其中能量以千瓦时 (kWh) 为单位。
E = Pt E = QV
A fuse is a safety device that melts when the current exceeds its rating, breaking the circuit. The fuse rating should be just above the normal operating current of the appliance. The earth wire provides a low-resistance path to the ground in case of a fault.
保险丝是一种安全装置，当电流超过额定值时熔断，从而切断电路。保险丝的额定值应略高于用电器的正常工作电流。地线在发生故障时提供一条低电阻接地通路。
9. Thermal Energy: Specific Heat Capacity | 热学：比热容
sing Q = mcΔθ, where Q is energy, m is mass, c is specific heat capacity, and Δθ is the temperature change.
物体被加热时，其内能增加。使一定质量物体升温所需的热能用公式 Q = mcΔθ 计算，其中 Q 为能量，m 为质量，c 为比热容，Δθ 为温度变化。
Q = mcΔθ
Specific heat capacity c is the energy required to raise the temperature of 1 kg of a substance by 1 °C. Its unit is J/(kg °C). Water has a high specific heat capacity, so it heats up and cools down slowly, making it useful for thermal storage.
比热容 c 是使 1 kg 物质温度升高 1 °C 所需的能量，单位是 J/(kg °C)。水的比热容较大，因此升温慢，降温也慢，适合用作热能储存介质。
When energy is transferred from a hotter object to a cooler one, conservation of energy requires that the thermal energy lost by the hot object equals the energy gained by the cold object, provided no energy is lost to the surroundings.
能量从高温物体传向低温物体时，根据能量守恒，如果没有能量散失到环境中，高温物体损失的热能等于低温物体获得的热能。
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