Year 12 Cambridge Physics Quick Formula & Principles Handbook | Year 12 剑桥物理公式定理速查手册

📚 Year 12 Cambridge Physics Quick Formula & Principles Handbook | Year 12 剑桥物理公式定理速查手册

This quick-reference guide summarises the essential formulae, definitions and physical principles required for Cambridge AS-Level Physics (Year 12). Each section provides the key relationships in a concise, exam-friendly format, with English and Chinese explanations side by side. Use it to review topics rapidly and to check that you can recall and apply every equation correctly.

本速查手册汇总了剑桥 AS 物理（Year 12）所要求的基本公式、定义和物理原理。每个部分以简洁、适合考试的格式呈现关键关系式，并提供中英双语对照说明。用它快速复习各章节，并确保你能准确回忆和运用每一个方程。

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1. Physical Quantities & SI Units | 物理量与SI单位

All physical quantities are expressed in terms of seven base SI units. Derived units are combinations of these bases. Homogeneity of equations means that the units on both sides must be equivalent.

所有物理量都可以用七个SI基本单位表示。导出单位是这些基本单位的组合。方程的量纲一致性意味着方程两边的单位必须相等。

Base Quantity (Base Unit)	基本量 (基本单位)
Length – metre (m)	长度 – 米 (m)
Mass – kilogram (kg)	质量 – 千克 (kg)
Time – second (s)	时间 – 秒 (s)
Electric current – ampere (A)	电流 – 安培 (A)
Temperature – kelvin (K)	热力学温度 – 开尔文 (K)
Amount of substance – mole (mol)	物质的量 – 摩尔 (mol)
Luminous intensity – candela (cd)	发光强度 – 坎德拉 (cd)

Common derived units include the newton (N = kg m s⁻²), joule (J = N m = kg m² s⁻²) and watt (W = J s⁻¹).

常见的导出单位包括牛顿 (N = kg m s⁻²)、焦耳 (J = N m = kg m² s⁻²) 和瓦特 (W = J s⁻¹)。

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2. Kinematics | 运动学

The suvat equations describe uniformly accelerated motion in a straight line. The symbols used are: s displacement, u initial velocity, v final velocity, a acceleration, t time.

suvat 方程描述匀加速直线运动。所用符号为：s 位移，u 初速度，v 末速度，a 加速度，t 时间。

v = u + a t

s = u t + ½ a t²

v² = u² + 2 a s

s = ½ (u + v) t

For free fall near the Earth’s surface, the acceleration due to gravity is g = 9.81 m s⁻², and air resistance is usually neglected.

在地球表面附近自由落体时，重力加速度为 g = 9.81 m s⁻²，通常忽略空气阻力。

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3. Dynamics & Newton’s Laws | 动力学与牛顿定律

Newton’s three laws of motion form the foundation of classical mechanics. The net force F acting on a body of mass m produces an acceleration a directly proportional to the force and inversely proportional to the mass.

牛顿运动三定律构成了经典力学的基础。作用在质量为 m 的物体上的净力 F 产生的加速度 a 与力成正比，与质量成反比。

F = m a

Weight is the force of gravity on a mass: W = m g. Frictional forces are often modelled by a coefficient of friction μ; for static friction f ≤ μₛ R and for dynamic friction f = μₖ R, where R is the normal reaction force.

重量是质量所受的重力：W = m g。摩擦力通常用摩擦系数 μ 来建模；静摩擦力 f ≤ μₛ R，滑动摩擦力 f = μₖ R，其中 R 为法向反作用力。

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4. Work, Energy & Power | 功、能量与功率

Work done by a constant force F acting over a displacement s at an angle θ to the displacement is:

恒力 F 沿位移 s 方向作功，当力与位移夹角为 θ 时，功为：

W = F s cos θ

Kinetic energy (Eₖ) and gravitational potential energy (Eₚ) near Earth’s surface are:

动能 (Eₖ) 和地表附近的重力势能 (Eₚ) 分别为：

Eₖ = ½ m v²

Eₚ = m g h

Power is the rate of doing work, and can also be expressed as the product of force and velocity:

功率是作功的速率，也可表示为力与速度的乘积：

P = W / t = F v

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another.

能量守恒定律指出：能量不能被创造或消灭，只能从一种形式转移或转化为另一种形式。

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5. Momentum & Impulse | 动量与冲量

Momentum is the product of mass and velocity. Impulse is the change in momentum caused by a force acting over a time interval.

动量是质量与速度的乘积。冲量是力在一段时间内产生的动量变化。

p = m v

Impulse = F Δ t = Δ p

In an isolated system, total momentum is conserved. For a two-body collision:

在孤立系统中，总动量守恒。对于两个物体的碰撞：

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

Elastic collisions conserve both momentum and kinetic energy. Inelastic collisions conserve momentum only.

弹性碰撞同时守恒动量和动能。非弹性碰撞仅守恒动量。

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6. Materials: Stress, Strain & Young Modulus | 材料：应力、应变与杨氏模量

Hooke’s law describes the linear extension of a spring subjected to a force, up to the limit of proportionality:

胡克定律描述弹簧在受力时的线性伸长，直到比例极限：

F = k x

Tensile stress and strain are defined for a wire of original length L₀ and cross-sectional area A:

对于原始长度为 L₀、横截面积为 A 的金属丝，拉伸应力和应变的定义为：

Stress σ = F / A

Strain ε = Δ L / L₀

The Young modulus E quantifies the stiffness of a material in the elastic region:

杨氏模量 E 量化材料在弹性范围内的刚性：

E = σ / ε

Elastic potential energy stored in a stretched spring or wire is given by the area under the force–extension graph:

储存在拉伸弹簧或金属丝中的弹性势能由力–伸长量图下的面积给出：

Eₑ = ½ k x²

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7. Waves: General Properties | 波：一般性质

The speed of a wave is related to its frequency and wavelength. For all wave motions:

波速与其频率和波长相关。对所有波动：

v = f λ

When a wave enters a different medium, its frequency remains unchanged while its speed and wavelength change. Refractive index n of a medium is the ratio of the speed of light in vacuum to that in the medium:

当波进入不同介质时，其频率保持不变，而波速和波长改变。介质的折射率 n 是真空中的光速与介质中的光速之比：

n = c / v

Snell’s law of refraction relates the angles of incidence and refraction to the refractive indices of the two media:

斯涅尔折射定律将入射角和折射角与两种介质的折射率联系起来：

n₁ sin θ₁ = n₂ sin θ₂

For total internal reflection to occur, the incident angle must exceed the critical angle C, given by:

发生全内反射时，入射角必须大于临界角 C，其满足：

sin C = 1 / n

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8. Superposition & Interference | 叠加与干涉

When two or more waves overlap, the resultant displacement is the vector sum of the individual displacements. For coherent sources of waves, interference produces a stable pattern of maxima and minima.

当两个或多个波重叠时，合位移是各波位移的矢量和。对于相干波源，干涉会产生稳定的明暗相间条纹。

In Young’s double-slit experiment, the fringe spacing Δx on a screen at distance D from slits of separation d is:

在杨氏双缝实验中，当屏幕与双缝距离为 D，双缝间距为 d 时，条纹间距 Δx 为：

Δ x = λ D / d

For a diffraction grating with slit spacing d, the condition for bright maxima is:

对于光栅常数为 d 的衍射光栅，亮纹条件为：

d sin θ = n λ

where n = 0, 1, 2, … is the order of the maximum.

其中 n = 0, 1, 2, … 为明纹级数。

Stationary (standing) waves are formed by the superposition of two identical progressive waves travelling in opposite directions. Nodes are points of zero amplitude; antinodes are points of maximum amplitude.

驻波由两列相同的行波沿相反方向叠加而成。波节是振幅为零的点；波腹是振幅最大的点。

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9. Electric Fields & Coulomb’s Law | 电场与库仑定律

Coulomb’s law gives the electrostatic force between two point charges Q₁ and Q₂ separated by a distance r in a vacuum:

库仑定律给出真空中相距 r 的两个点电荷 Q₁ 与 Q₂ 之间的静电力：

F = Q₁ Q₂ / (4π ε₀ r²)

where ε₀ =

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