📚 Formula & Theorems Quick Reference Handbook | 公式定理速查手册
This quick reference handbook contains all the essential formulas and theorem statements you need to master Year 8 Cambridge Physics. Each section presents the key relationships in a clear, symmetrical format so you can revise efficiently.
本速查手册涵盖 Year 8 剑桥物理所有核心公式与定理陈述。每一节都以清晰对照的形式给出关键关系，帮助你高效复习。
1. Speed, Distance and Time | 速度、距离与时间
Average speed is the distance travelled divided by the time taken. The formula triangle helps rearrange the three quantities.
平均速度等于移动距离除以所用时间。利用公式三角形可以灵活变换三个物理量。
Average Speed = Total Distance ÷ Total Time
平均速度 = 总距离 ÷ 总时间
v = s ÷ t, s = v × t, t = s ÷ v
v = s ÷ t, s = v × t, t = s ÷ v
Units: speed in m/s, distance in m, time in s. Always check unit consistency before calculating.
单位：速度 m/s，距离 m，时间 s。计算前务必保持单位一致。
2. Acceleration | 加速度
Acceleration is the rate of change of velocity. If the direction or speed of a moving object changes, it accelerates.
加速度是速度的变化率。物体运动方向或速率发生变化时，就具有加速度。
Acceleration = Change in Velocity ÷ Time Taken
加速度 = 速度变化量 ÷ 所用时间
a = (v - u) ÷ t
a = (v - u) ÷ t
v is final velocity, u is initial velocity. Unit: m/s².
v 是末速度，u 是初速度。单位：m/s²。
Negative acceleration (deceleration) occurs when v is smaller than u.
当 v 小于 u 时，加速度为负值（减速）。
3. Forces and Newton's Laws | 力与牛顿定律
Newton's Second Law is the foundation of dynamics. An unbalanced force produces an acceleration proportional to the force and inversely proportional to the mass.
牛顿第二定律是动力学的基础。不平衡的力产生的加速度与力成正比，与质量成反比。
Resultant Force = Mass × Acceleration (F = m × a)
合力 = 质量 × 加速度 (F = m × a)
First Law: An object stays at rest or moves with constant velocity unless a resultant force acts.
第一定律：若无合力作用，物体保持静止或匀速直线运动。
Third Law: When body A exerts a force on body B, body B exerts an equal and opposite force on body A.
第三定律：作用力与反作用力大小相等、方向相反，分别作用在不同物体上。
Weight = Mass × Gravitational Field Strength (W = m × g). g ≈ 10 N/kg on Earth.
重量 = 质量 × 重力场强度 (W = m × g)。地球上 g≈10 N/kg。
4. Pressure | 压强
Pressure quantifies how concentrated a force is. The same force spread over a larger area produces lower pressure.
压强衡量力的集中程度。同样大小的力分散在更大面积上，产生的压强更小。
Pressure = Force ÷ Area (P = F ÷ A)
压强 = 力 ÷ 面积 (P = F ÷ A)
Unit: pascal (Pa). 1 Pa = 1 N/m².
单位：帕斯卡 (Pa)。1 Pa = 1 N/m²。
In liquids: Pressure increases with depth, and is equal at the same horizontal level regardless of container shape.
液体压强随深度增大，同种液体同一水平面上压强处处相等，与容器形状无关。
5. Density | 密度
Density describes how much mass is packed into a given volume. It is an intrinsic property of materials.
密度描述单位体积所包含的质量，是物质的固有属性。
Density = Mass ÷ Volume (ρ = m ÷ V)
密度 = 质量 ÷ 体积 (ρ = m ÷ V)
Unit: kg/m³ or g/cm³. 1 g/cm³ = 1000 kg/m³.
单位：kg/m³ 或 g/cm³。1 g/cm³ = 1000 kg/m³。
An object floats if its average density is less than that of the fluid; it sinks if greater.
物体平均密度小于液体密度时上浮，大于时下沉。
6. Energy, Work and Power | 能量、功和功率
When a force moves an object, work is done and energy is transferred. Power tells us how quickly that transfer happens.
力使物体移动时，就做了功，能量发生转移。功率表示能量转移的快慢。
Work Done = Force × Distance moved in direction of force (W = F × d)
做功 = 力 × 在力的方向上移动的距离 (W = F × d)
Power = Work Done ÷ Time Taken (P = W ÷ t)
功率 = 做功 ÷ 所用时间 (P = W ÷ t)
Kinetic Energy = ½ × m × v². Gravitational Potential Energy = m × g × h.
动能 = ½ × m × v²。重力势能 = m × g × h。
Energy is measured in joules (J), power in watts (W). 1 W = 1 J/s.
能量单位焦耳 (J)，功率单位瓦特 (W)。1 W = 1 J/s。
Principle of Conservation of Energy: Energy cannot be created or destroyed, only transferred or transformed.
能量守恒定律：能量既不能凭空产生，也不能凭空消失，只能转移或转化。
7. Electrical Circuits | 电路
Electric current, potential difference and resistance are linked by Ohm's Law. Charge, voltage and energy relationships complete the picture.
电流、电压和电阻由欧姆定律联系。电荷、电压与能量的关系构成完整电路知识。
Current = Charge ÷ Time (I = Q ÷ t)
电流 = 电荷 ÷ 时间 (I = Q ÷ t)
Voltage = Energy Transferred ÷ Charge (V = E ÷ Q)
电压 = 转移能量 ÷ 电荷 (V = E ÷ Q)
Resistance = Voltage ÷ Current (R = V ÷ I)
电阻 = 电压 ÷ 电流 (R = V ÷ I)
ircuits: Current is the same everywhere; total resistance = sum of individual resistances.
串联电路：电流处处相等；总电阻等于各电阻之和。
circuits: Voltage is the same across each branch; total current = sum of branch currents.
并联电路：各支路电压相同；总电流等于各支路电流之和。
8. Wave Properties | 波的性质
Waves transfer energy without transferring matter. The speed, frequency and wavelength of any wave are linked by a simple equation.
波传递能量但不传递物质。波速、频率和波长由一个简单方程联系在一起。
Wave Speed = Frequency × Wavelength (v = f × λ)
波速 = 频率 × 波长 (v = f × λ)
Frequency (f) in hertz (Hz), wavelength (λ) in m, speed (v) in m/s.
频率 (f) 单位 Hz，波长 (λ) 单位 m，波速 (v) 单位 m/s。
Transverse waves: oscillations perpendicular to wave direction (light, water waves). Longitudinal waves: oscillations parallel to direction (sound).
横波：振动方向与传播方向垂直（如光波、水波）。纵波：振动方向与传播方向平行（如声波）。
9. Thermal Energy and States of Matter | 热能及物质状态
Heating a substance can change its internal energy and eventually its state. Latent heat is absorbed or released without temperature change during a change of state.
加热物体可改变其内能，最终改变物态。物态变化过程中，吸收或释放潜热而温度保持不变。
Change in Thermal Energy = Mass × Specific Heat Capacity × Temperature Change
热能变化 = 质量 × 比热容 × 温度变化 (ΔE = m × c × Δθ)
Energy to change state = Mass × Specific Latent Heat
物态变化所需能量 = 质量 × 比潜热 (E = m × L)
During melting or boiling, temperature remains constant while energy continues to be supplied.
熔化或沸腾期间，虽持续供热，温度保持恒定。
Conduction, convection and radiation are three methods of thermal energy transfer. Radiation does not require a medium.
热传导、热对流和热辐射是三种热能传递方式。热辐射不需要介质。
10. Light: Reflection and Refraction | 光的反射与折射
Light obeys exact geometric laws when it strikes a surface or crosses into a new medium. These laws are the basis for image formation and lenses.
光遇到界面或进入新介质时严格遵循几何定律，这是成像和透镜工作的基础。
Law of Reflection: Angle of incidence (i) = Angle of reflection (r)
反射定律：入射角 = 反射角
Snell's Law for Refraction: n₁ × sin θ₁ = n₂ × sin θ₂
折射定律（斯涅尔定律）：n₁ × sin θ₁ = n₂ × sin θ₂
When light enters a denser medium, it bends towards the normal; when it enters a less dense medium, it bends away from the normal.
光进入更密介质时向法线偏折；进入更疏介质时偏离法线。
Critical angle and total internal reflection occur when light travels from denser to less dense medium and the angle of incidence exceeds the critical angle.
光从光密介质射向光疏介质，入射角大于临界角时发生全内反射。
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