Year 12 AQA Physics: Formula & Theorem Quick Reference | AQA 物理公式定理速查手册

📚 Year 12 AQA Physics: Formula & Theorem Quick Reference | AQA 物理公式定理速查手册

This concise handbook gathers the essential formulas and theorems required for Year 12 AQA Physics (AS level). Each section presents the key relationships alongside brief explanations to reinforce conceptual understanding and support efficient revision. Whether used alongside past papers or as a pre-exam checklist, this resource helps you build confidence in applying the right equation in the right context.

这份速查手册汇集了 AQA 物理 Year 12（AS 阶段）的核心公式和定理。每个小节都列出了关键关系式，并配有简要说明，以强化概念理解、支持高效复习。无论是配合历年真题使用，还是作为考前清单，都能帮助你更有把握地在合适的情境中套用正确的方程。

1. Kinematics and Motion | 运动学公式

The SUVAT equations apply to uniformly accelerated motion along a straight line. You must define a positive direction and remember that acceleration is constant. The displacement-time, velocity-time and acceleration-time graphs are interlinked: slope of an s-t graph gives velocity, slope of a v-t graph gives acceleration, and the area under a v-t graph gives displacement.

SUVAT 方程适用于匀加速直线运动。必须规定正方向，且注意加速度为恒定值。位移-时间图、速度-时间图和加速度-时间图相互关联：s-t 图的斜率表示速度，v-t 图的斜率表示加速度，v-t 图下方的面积表示位移。

v = u + at

Relates final velocity to initial velocity, acceleration and time.

将末速度与初速度、加速度和时间联系起来。

s = ut + ½ at²

Displacement as a function of initial velocity, time and constant acceleration.

位移表示为初速度、时间和恒定加速度的函数。

v² = u² + 2as

Links the square of the final speed directly to the displacement, independent of time.

将末速度的平方直接与位移关联，与时间无关。

s = ½ (u + v) t

Uses the average velocity to find displacement when acceleration is uniform.

利用平均速度求出匀加速情况下的位移。

For projectile motion, resolve the initial velocity into horizontal and vertical components. The horizontal component is constant; the vertical motion obeys the SUVAT equations with a = g downward. The time of flight is determined by the vertical motion, while the horizontal range is vₓ × t.

处理抛体运动时，将初速度分解为水平和竖直分量。水平分量保持不变；竖直运动遵守 SUVAT 方程，且 a = g 向下。飞行时间由竖直运动决定，水平射程为 vₓ × t。

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2. Newton’s Laws and Forces | 牛顿定律与力

Newton’s three laws form the foundation of classical mechanics. The first law describes inertia; the second law quantifies it as F = ma; the third law emphasizes that forces always come in action-reaction pairs acting on different bodies.

牛顿三定律是经典力学的基础。第一定律描述惯性；第二定律将其量化为 F = ma；第三定律强调力总是成对出现，作用在不同的物体上。

F = m a

The resultant force on an object equals its mass times its acceleration. Remember that F and a are vectors and must be in the same direction.

物体所受合力等于其质量乘以加速度。注意 F 和 a 是矢量，方向必须一致。

W = m g

Weight is the gravitational force on a mass near the Earth’s surface. g is taken as 9.81 N kg⁻¹ on Earth.

重力是地球表面附近物体所受的引力。地球上的 g 通常取 9.81 N kg⁻¹。

For equilibrium, the vector sum of forces must be zero. Resolve forces into perpendicular components; the sum of horizontal components and the sum of vertical components are both zero. Free-body diagrams are essential tools for analysing forces.

处于平衡状态时，力的矢量和必须为零。将力分解为垂直方向的分量；水平方向分量的代数和为零，竖直方向分量的代数和也为零。受力分析图是分析力的重要工具。

The maximum static friction is fₘₐₓ = μₛ R, and kinetic friction is fₖ = μₖ R, where R is the normal reaction force.

最大静摩擦力为 fₘₐₓ = μₛ R，动摩擦力为 fₖ = μₖ R，其中 R 为法向反作用力。

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3. Work, Energy and Power | 功、能与功率

Work is done when a force moves its point of application in the direction of the force. Energy is the capacity to do work, and power is the rate at which work is done. The principle of conservation of energy states that energy cannot be created or destroyed, only transferred between forms.

力使其作用点沿力的方向移动时做功。能量表示做功的本领，功率则是做功的速率。能量守恒原理指出，能量不能凭空产生或消失，只能在不同形式之间传递。

W = F s cos θ

Work done by a constant force F acting over a displacement s, where θ is the angle between the force and the displacement direction. When the force is parallel, W = F s.

恒力 F 在位移 s 上所做的功，θ 为力与位移方向之间的夹角。若力与位移平行，则 W = F s。

Eₖ = ½ m v²

Kinetic energy of an object of mass m moving at speed v.

质量为 m、速度为 v 的物体的动能。

Eₚ = m g h

Change in gravitational potential energy near the Earth’s surface, with h measured vertically.

地球表面附近的重力势能变化量，其中 h 为竖直高度。

P = ΔW / Δt = F v

Power is the work done per unit time. For an object moving at constant speed against a constant resistive force, the useful power output is the product of the driving force and speed.

功率定义为每单位时间所做的功。对于以恒定速度克服恒定阻力运动的物体，有效输出功率为驱动力与速度的乘积。

Efficiency of a system is the ratio of useful output power (or energy) to total input power (or energy), often expressed as a percentage.

系统的效率是有用输出功率（或能量）与总输入功率（或能量）之比，常用百分比表示。

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4. Momentum and Impulse | 动量与冲量

Momentum is a vector quantity defined as the product of mass and velocity. In a closed system with no external forces, total momentum is conserved. Collisions can be elastic (kinetic energy conserved) or inelastic (kinetic energy not conserved), but momentum is always conserved in the absence of external resultant forces.

动量是矢量，定义为质量与速度的乘积。在无外力的封闭系统中，总动量守恒。碰撞可分为弹性碰撞（动能守恒）和非弹性碰撞（动能不守恒），但若没有合外力作用，动量始终守恒。

p = m v

Linear momentum of a body. The direction of p is the same as that of v.

物体的线动量。p 的方向与 v 相同。

Impulse = F Δt = Δp

The impulse of a force equals the change in momentum of the body on which it acts. The area under a force-time graph gives the impulse.

力的冲量等于它所作用的物体的动量变化量。力-时间图下方的面积代表冲量。

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

Conservation of linear momentum for a two-body system with no external resultant forces.

无合外力的二体系统线动量守恒。

For a perfectly elastic collision in one dimension, relative speed of approach equals relative speed of separation: u₁ – u₂ = v₂ – v₁. In inelastic collisions, objects may stick together and share a common final velocity.

对于一维完全弹性碰撞，接近的相对速度等于分离的相对速度：u₁ – u₂ = v₂ – v₁。在非弹性碰撞中，物体可能粘在一起并具有共同的末速度。

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

The mechanical properties of materials are described by stress and strain. Hooke’s law applies up to the limit of proportionality, where extension is proportional to applied force. The Young modulus characterises the stiffness of a material and is independent of sample dimensions.

材料的力学性质用应力和应变来描述。在比例极限以内，胡克定律成立，此时伸长量与施加的力成正比。杨氏模量表征材料的刚度，与试样的尺寸无关。

σ = F / A

Tensile stress σ is the force applied per unit cross-sectional area.

拉伸应力 σ 是单位横截面积上所施加的力。

ε = ΔL / L₀

Tensile strain ε is the extension per unit original length.

拉伸应变 ε 是单位原始长度的伸长量。

E = σ / ε

The Young modulus E is the ratio of tensile stress to tensile strain within the linear elastic region. The SI unit is Pa or N m⁻².

杨氏模量 E 是线弹性区内拉伸应力与拉伸应变的比值，SI 单位为 Pa 或 N m⁻²。

F = k ΔL

Hooke’s law for a spring or wire within its elastic limit, where k is the spring constant (N m⁻¹). The gradient of a force-extension graph gives k.

弹簧或金属丝在其弹性极限内遵守胡克定律，k 为劲度系数（弹簧常数，单位 N m⁻¹）。力-伸长量图的斜率给出 k 值。

The elastic strain energy stored in a deformed object is the area under the force-extension graph: for linear behaviour, U = ½ F ΔL = ½ k (ΔL)².

变形物体储存的弹性应变能等于力-伸长量图下方的面积：对于线性行为，U = ½ F ΔL = ½ k (ΔL)²。

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6. Electricity: Circuits and Components | 电学：电路与元件

Electric circuits transfer energy from a source to components. Basic quantities are current, potential difference and resistance. Ohm’s law is a special case, not a universal rule. Circuit rules include Kirchhoff’s current law at junctions and the voltage divider principle for series resistors.

电路将能量从电源传输给元件。基本物理量包括电流、电势差和电阻。欧姆定律是一个特例，并非普遍规律。电路规则包括节点处的基尔霍夫电流定律以及串联电阻的分压原理。

I = ΔQ / Δt

Electric current is the rate of flow of charge. The conventional current direction is from positive to negative.

电流是电荷流动的速率。常规电流方向从正到负。

V = I R

Ohm’s law holds for an ohmic conductor at constant temperature. For a non-ohmic component, the I-V characteristic is non-linear.

欧姆定律对恒温下的欧姆导体成立。对于非欧姆元件，I-V 特性曲线是非线性的。

R = ρ L / A

Resistance of a uniform conductor depends on its resistivity ρ, length L and cross-sectional area A. Resistivity is a material property and depends on temperature.

均匀导体的电阻取决于其电阻率 ρ、长度 L 和横截面积 A。电阻率是材料属性，并随温度变化。

Rₛ = R₁ + R₂ + …

For resistors in series, the total resistance is the sum of individual resistances.

串联电阻的总电阻等于各电阻之和。

1/Rₚ = 1/R₁ + 1/R₂ + …

For resistors in parallel, the reciprocal of the total resistance is the sum of reciprocals of individual resistances.

并联电阻总电阻的倒数等于各电阻倒数之和。

V = ε – I r

The terminal potential difference of a cell equals its emf minus the voltage drop across the internal resistance r when a current flows.

电池的端电压等于电动势减去电流流过时内阻 r 上的压降。

P = I V = I² R = V² / R

Electrical power dissipated in a component can be expressed in three equivalent forms, valid for any component if V and I refer to that component.

元件消耗的电功率可用三种等价形式表示，对任何元件都成立，只要 V 和 I 是该元件两端的电压和流过的电流。

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7. Waves: Properties and Behaviour | 波：性质与行为

Waves transfer energy without transferring matter. All waves exhibit reflection, refraction, diffraction and interference. The speed, frequency and wavelength are linked by the wave equation. Phase difference and path difference determine whether waves superpose constructively or destructively.

波传递能量而不传递物质。所有波都会发生反射、折射、衍射和干涉。波速、频率和波长由波动方程联系在一起。相位差和路程差决定了波是相长叠加还是相消叠加。

v = f λ

The wave speed v equals the product of frequency f and wavelength λ.

波速 v 等于频率 f 与波长 λ 的乘积。

T = 1 / f

The period T is the time for one complete oscillation and is the reciprocal of the frequency.

周期 T 是完成一次完整振动所需的时间，是频率的倒数。

Δφ = (2π / λ) × Δx

The phase difference Δφ between two points separated by path difference Δx on a progressive wave. For constructive interference, Δφ =0, 2π, 4π … (path difference = nλ); for destructive interference, Δφ = π, 3π … (path difference = (n+½)λ).

行进波上相距路程差 Δx 的两点之间的相位差 Δφ。相长干涉条件：Δφ = 0, 2π, 4π …（路程差 = nλ）；相消干涉条件：Δφ = π, 3π …（路程差 = (n+½)λ）。

d sin θ = n λ

For a diffraction grating, the angle θ to the nth-order maximum is given by this equation, where d is the slit spacing. The same formula applies to the path difference for Young’s double-slit experiment, but with d as slit separation.

对于衍射光栅，第 n 级明纹的角度 θ 由此式给出，其中 d 是光栅刻线间距。同样的公式也适用于杨氏双缝干涉实验的路程差，此时 d 为双缝间距。

w = λ D / s

In the double-slit experiment, fringe spacing w (distance between adjacent bright or dark fringes) is related to wavelength λ, slit separation s and slit-to-screen distance D.

在双缝实验中，条纹间距 w（相邻明纹或暗纹之间的距离）与波长 λ、双缝间距 s 及缝到屏幕距离 D 之间的关系。

Standing waves form when two identical progressive waves travel in opposite directions. Nodes are points of zero displacement; antinodes are points of maximum amplitude. For a string fixed at both ends, the first harmonic has wavelength λ = 2L.

当两列相同的行进波沿相反方向传播时，形成驻波。波节是位移为零的点；波腹是振幅最大的点。对于两端固定的弦，基频的波长 λ = 2L。

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8. Quantum Phenomena: Photoelectric Effect and Atomic Spectra | 量子现象：光电效应与原子光谱

Quantum physics reveals that light behaves as both a wave and a particle, and that energy in atoms is quantised. The photoelectric effect provides evidence for the particle nature of light, while emission and absorption spectra support the discrete energy level model of atoms.

量子物理揭示光既具有波动性又具有粒子性，且原子中的能量是量子化的。光电效应为光的粒子性提供了证据，而发射光谱和吸收光谱则支持原子的分立能级模型。

E = h f

The energy of a photon is directly proportional to its frequency f, where h is Planck’s constant (6.63 × 10⁻³⁴ J s).

光子的能量与其频率 f 成正比，h 为普朗克常数 (6.63 × 10⁻³⁴ J s)。

h f = φ + Eₖ,ₘₐₓ

Einstein’s photoelectric equation: the energy of an incident photon is used to overcome the work function φ of the metal and to provide the maximum kinetic energy of the emitted electron. The stopping potential Vₛ is related by Eₖ,ₘₐₓ = e Vₛ.

爱因斯坦光电方程：入射光子的能量一部分用于克服金属的逸出功 φ，剩下的转换为逸出电子的最大动能。遏止电势 Vₛ 满足 Eₖ,ₘₐₓ = e Vₛ。

The threshold frequency f₀ = φ / h. Below this frequency, no photoelectrons are emitted, regardless of intensity. Above f₀, increasing intensity increases the rate of emission, not the maximum kinetic energy.

截止频率 f₀ = φ / h。低于该频率，无论光强多大，都不会有光电子发射。高于 f₀ 时，增大光强会增加发射速率，但不会改变最大动能。

ΔE = h f = h c / λ

When an electron transitions between energy levels in an atom, a photon of energy equal to the difference is emitted or absorbed. This explains line spectra, with each line corresponding to a specific ΔE.

当电子在原子能级之间跃迁时，会发射或吸收一个能量等于能级差的光子。这解释了线状光谱，每条谱线对应一个特定的 ΔE。

λ = h / p

de Broglie wavelength of a matter particle with momentum p. This wave nature is demonstrated by electron diffraction, where a beam of electrons passing through a crystal or graphite produces a diffraction pattern.

动量为 p 的物质粒子的德布罗意波长。电子衍射实验证实了这种波动性，电子束通过晶体或石墨后产生衍射图样。

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9. Measurements and Errors | 测量与误差

All experimental data carry uncertainty. Distinguishing between precision and accuracy is crucial. You need to be able to propagate absolute, fractional and percentage uncertainties through calculations and express final results with appropriate significant figures.

所有实验数据都带有不确定度。区分精密度与准确度至关重要。你需要能够传递绝对、相对和百分比不确定度，并以合适的有效数字表示最终结果。

Absolute uncertainty: the ± value in a measurement, e.g. 5.0 ± 0.2 cm. Fractional uncertainty = absolute uncertainty / measured value. Percentage uncertainty = (absolute uncertainty / measured value) × 100%.

绝对不确定度：测量值中的 ± 数值，例如 5.0 ± 0.2 cm。相对不确定度 = 绝对不确定度 / 测量值。百分比不确定度 =（绝对不确定度 / 测量值）× 100%。

For addition or subtraction, add absolute uncertainties. For multiplication or division, add percentage uncertainties. For a power, multiply the percentage uncertainty by the power. These rules give the maximum possible uncertainty.

进行加减运算时，将 绝对不确定度相加。进行乘除运算时，将 百分比不确定度相加。对于乘方运算，将百分比不确定度乘以指数。这些规则给出的是最大可能不确定度。

Reading uncertainty from an analogue scale is ± half the smallest scale division; for a digital meter it is ± the resolution unless otherwise stated. Systematic errors affect accuracy; random errors affect precision. Repeating readings and averaging reduces random error but not systematic error.

模拟刻度的读数不确定度为 ± 最小刻度值的一半；对于数字仪表，若无特别说明，不确定度为 ± 分辨率。系统误差影响准确度；随机误差影响精密度。重复读数并取平均值可以减少随机误差，但不能消除系统误差。

Plotting graphs can help identify anomalies, find lines of best fit and determine gradients with uncertainty bars. The uncertainty in the gradient can be estimated from the worst acceptable line.

绘图有助于识别异常值、确定最佳拟合线并通过误差棒求出斜率。斜率的不确定度可以通过最差可接受线进行估算。

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