AS Physics: Understanding the Unit 1 Formula Sheet (June 2019) | AS 物理：理解单元1 公式表 (2019年6月)

📚 AS Physics: Understanding the Unit 1 Formula Sheet (June 2019) | AS 物理：理解单元1 公式表 (2019年6月)

The June 2019 AS Unit 1 Physics data sheet provides a concise reference of essential formulae, constants and relationships that span mechanics, materials, waves and quantum phenomena. Mastering this sheet is not just about memorising symbols — it is about understanding when and how to apply each equation in problem-solving contexts. This article breaks down the key concepts behind every group of equations, enabling you to use the data sheet as a powerful tool in your revision and examinations.

2019 年 6 月 AS 单元 1 物理数据手册简要列出了力学、材料、波和量子现象的核心公式、常数与关系。掌握这份表格不只是记住符号，更意味着理解在解题中何时以及如何应用每一组方程。本文深入剖析各组公式背后的关键概念，帮助你将数据手册转化为复习和考试中的有力工具。

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1. Navigating the Data Sheet Layout | 熟悉数据手册的结构

The data sheet is grouped by topic, often starting with mechanics, moving through materials, waves and finally quantum phenomena. Recognising these clusters saves time in exams, as you can quickly locate the right formula without second-guessing. Each section also includes diagrams that illustrate variable definitions, such as forces on a slope or wavefronts in refraction.

数据手册按主题分组，通常从力学开始，依次覆盖材料、波，最后是量子现象。认识这些分类能节省考试时间，你可以迅速定位正确公式，无需反复确认。每个部分还配有示意图来说明变量定义，比如斜面上的受力或折射中的波阵面。

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2. Kinematic Equations of Motion | 运动学方程

v = u + at

This equation calculates final velocity when initial velocity u, constant acceleration a and time t are known. It underpins any scenario with uniform acceleration, such as free-fall or a car accelerating along a straight road.

该方程在已知初速度 u、恒定加速度 a 和时间 t 时计算末速度。它适用于所有匀加速场景，如自由落体或汽车沿直线加速行驶。

s = ut + ½at²

Use this to find displacement s when the object starts with initial velocity u and moves under constant acceleration a for a time t. Be careful with the sign of a if the object is decelerating.

当物体以初速度 u 开始运动，并在恒定加速度 a 下持续时间 t 时，用该式求位移 s。如果物体在减速，注意 a 的符号。

v² = u² + 2as

Linking final velocity directly to displacement without involving time, this equation is perfect for problems where time is not given. It is often used in collision analysis or stopping-distance calculations.

该式直接将末速度与位移联系起来而不涉及时间，非常适合未给出时间的题目，常用于碰撞分析或制动距离计算。

s = ½(u + v)t

This formula expresses displacement as the average velocity multiplied by time. It is especially handy when acceleration is constant and the initial and final velocities are known.

该公式将位移表示为平均速度乘以时间，当加速度恒定且已知初、末速度时特别实用。

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3. Newton’s Laws and Momentum | 牛顿定律与动量

F = m a

Newton’s second law states that the resultant force acting on a body equals the product of its mass and acceleration. Always consider the vector nature of force and acceleration — both are in the same direction as the net force.

牛顿第二定律指出作用于物体的合力等于其质量与加速度的乘积。始终牢记力与加速度的矢量性——两者都与合力的方向相同。

p = m v

Linear momentum is defined as mass times velocity. It is a vector quantity, conserved in all collisions and explosions provided no external resultant force acts.

线动量定义为质量乘以速度。它是矢量，只要没有外合力作用，在所有碰撞与爆炸中动量守恒。

Δp = F Δt

The impulse-momentum theorem tells us that the change in momentum equals the average force multiplied by the time for which it acts. This explains the effectiveness of crumple zones and airbags in extending impact time and reducing force.

冲量—动量定理表明动量的变化等于平均力乘以作用时间。这解释了为何汽车溃缩区与安全气囊通过延长撞击时间减小作用力。

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4. Work, Energy and Power | 功、能与功率

W = F s cosθ

Work done is the product of the force component in the direction of motion and the displacement. When the force is perpendicular to motion (θ = 90°), no work is done — for example, the normal force on a horizontal surface.

功等于力在位移方向上的分量乘以位移大小。当力与运动方向垂直时（θ = 90°），不做功——例如水平面上的法向力。

Eₖ = ½ m v²

Kinetic energy depends on mass and the square of speed. Doubling the speed quadruples the kinetic energy, a fact critical in road safety discussions about braking distances.

动能取决于质量与速度的平方。速度翻倍将使动能变为原来的四倍，这一关系在讨论制动距离的交通安全中至关重要。

Eₚ = m g Δh

Gravitational potential energy gain or loss equals weight (mg) multiplied by the change in vertical height. Choose a consistent reference level to define Δh correctly.

重力势能的增减等于重力 (mg) 乘以垂直高度的变化。选择一个一致的参考水平以正确定义 Δh。

P = ΔW / Δt and P = F v

Power is the rate of energy transfer or work done. The second form, P = F v, applies when a constant force moves an object at a constant speed against resistive forces, such as driving a car at steady speed.

功率是能量转换或做功的速率。第二个形式 P = F v 适用于恒力推动物体以恒定速度克服阻力的情形，比如汽车匀速行驶。

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

σ = F / A

Tensile or compressive stress is the force applied per unit cross-sectional area. It is measured in pascals (Pa). Understanding stress is essential for determining whether a material will deform or fracture under a given load.

拉伸或压缩应力是单位横截面积上所施加的力，单位为帕斯卡 (Pa)。理解应力对于判断材料在给定载荷下是否会变形或断裂至关重要。

ε = ΔL / L

Strain is the fractional extension — the ratio of the change in length to the original length. Being dimensionless, it directly indicates how much a material has stretched relative to its initial size.

应变是长度变化的分数——即伸长量与原始长度之比。由于无量纲，它直接表示材料相对于初始尺寸的拉伸程度。

E = σ / ε

The Young modulus measures the stiffness of a material within its elastic limit. A high Young modulus means the material resists deformation; it is a fundamental property used in selecting materials for construction and engineering.

杨氏模量衡量材料在弹性极限内的刚度。高杨氏模量意味着材料抵抗形变的能力强；它是建筑与工程选材时用到的基本性质。

F = k ΔL and Elastic potential energy = ½ F ΔL = ½ k (ΔL)²

Hooke’s law states that the extension is proportional to the applied force up to the limit of proportionality. The stored elastic energy is the area under the force–extension graph, which is a triangle for materials obeying Hooke’s law.

胡克定律指出，在比例极限内伸长量与所施加的力成正比。储存的弹性能量等于力—伸长图下方的面积，对于遵守胡克定律的材料，该面积为三角形。

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6. Wave Properties: Speed and Refraction | 波的性质：波速与折射

v = f λ

The wave speed equation links frequency, wavelength and speed. In vacuum, all electromagnetic waves travel at the same speed c. For sound and water waves, the speed depends on the medium’s properties.

波速方程将频率、波长与波速联系起来。在真空中，所有电磁波以同一速度 c 传播。对于声波和水波，波速取决于介质的性质。

n = sin i / sin r (or n₁ sin θ₁ = n₂ sin θ₂)

Snell’s law describes how a wavefront changes direction when crossing a boundary between two media of different optical densities. The refractive index n is the ratio of the sine of the angle of incidence to the sine of the angle of refraction; it can also be used to compare wave speeds in the two media.

斯涅尔定律描述波阵面穿越两种光密度不同的介质界面时方向如何改变。折射率 n 是入射角正弦与折射角正弦之比，也可以用来比较两种介质中的波速。

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