📚 A-Level Physics Unit 1: Mechanics, Motion and Materials | A-Level 物理 Unit 1：运动、力学与材料
Unit 1 of A-Level Physics concentrates on the core principles of mechanics and materials. These topics form the foundation for later units such as fields, waves and thermal physics, and they are frequently examined through structured calculations, graph interpretation and practical scenario questions.
A-Level 物理第一单元聚焦力学与材料的核心原理。这些主题为后续的场、波和热物理等单元奠定基础，并且经常通过结构化计算、图像分析和实验情境题进行考查。
1. Understanding Scalars and Vectors | 理解标量与矢量
In A-Level Physics, physical quantities are divided into scalars and vectors. A scalar has magnitude only, while a vector has both magnitude and direction. This distinction matters because vector addition must account for direction, otherwise sign and angle errors become common.
在 A-Level 物理中，物理量分为标量和矢量。标量只有大小，矢量既有大小又有方向。这一区别很重要，因为矢量相加必须考虑方向，否则容易出现符号和角度的错误。
| Scalars | 标量 | Vectors | 矢量 |
|---|---|
| distance | 路程 | displacement | 位移 |
| speed | 速率 | velocity | 速度 |
| mass | 质量 | acceleration | 加速度 |
| energy | 能量 | force | 力 |
| time | 时间 | momentum | 动量 |
When resolving a vector at an angle θ to a chosen axis, the perpendicular components are given by:
当一个矢量与选定轴成 θ 角时，其垂直分量为：
Fₓ = F cos θ, Fᵧ = F sin θ
Always state the positive direction before using components in equations of motion or force calculations.
在运动方程或力的计算中使用分量前，一定要先规定正方向。
2. Equations of Motion (SUVAT) | 运动学方程（SUVAT）
The SUVAT equations describe uniformly accelerated motion in a straight line. The five variables are s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time). Each equation links four of the five variables.
SUVAT 方程描述匀加速直线运动。五个变量分别是 s（位移）、u（初速度）、v（末速度）、a（加速度）和 t（时间）。每个方程联系五个变量中的四个。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = (u + v)t / 2
These equations only apply when acceleration is constant. If acceleration varies, you must use graphical methods or calculus-based approaches. Also convert all quantities into SI units before substituting values.
这些方程仅适用于加速度恒定的情况。如果加速度变化，必须使用图像法或基于微积分的方法。此外，代入数值前要先把所有量换算成 SI 单位。
For free fall near the Earth' a = g = 9.81 m s⁻² and decide whether upward or downward is positive before writing signs.
对于地球表面附近的自由落体，取 a = g = 9.81 m s⁻²，并在写符号前先确定向上还是向下为正。
3. Forces, Newton's Laws and Free-Body Diagrams | 力、牛顿定律与受力图
Newton' gh F = ma. The third law states that forces occur in equal and opposite interaction pairs.
牛顿第一定律指出，除非受到合力作用，物体将保持静止或匀速直线运动。第二定律将合力、质量和加速度通过 F = ma 联系起来。第三定律指出力以大小相等、方向相反的相互作用对出现。
F = ma, W = mg
Free-body diagrams should show all forces acting on a single object: weight, normal contact force, friction, tension, air resistance and any applied forces. Do not include forces exerted by the object on its surroundings.
受力图应标出作用在单个物体上的所有力：重力、接触力、摩擦力、张力、空气阻力以及任何外力。不要把物体对外界施加的力画进去。
If several objects are connected, isolate each mass and write separate equations. This is a common method for pulley and tow-bar problems in Unit 1.
如果有多个物体连接，应对每个质量单独隔离并分别列方程。这是第一单元中滑轮和拖车问题的常用方法。
4. Energy, Work and Power | 能量、功与功率
Work is done when a force moves its point of application in the direction of the force. Work transfers energy, and the principle of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another.
当力的作用点沿力的方向移动时，力做功。功传递能量，而能量守恒定律指出能量不能被创造或消灭，只能从一种形式转化为另一种形式。
W = Fd cos θ, Eₖ = ½mv², ΔEₚ = mgΔh
e regularly tested in transport and lifting problems. Efficiency can be expressed as useful output energy divided by total input energy.
功率是做功的速率。P = W/t 和 P = Fv 这两个关系在交通和提升问题中经常考查。效率可以表示为有用输出能量除以总输入能量。
Be careful with units: energy and work are measured in joules (J), power in watts (W), and speed in metres per second (m s⁻¹).
注意单位：能量和功的单位是焦耳（J），功率的单位是瓦特（W），速度的单位是米每秒（m s⁻¹）。
5. Momentum and Impulse | 动量与冲量
Momentum is the product of mass and velocity, and it is a vector quantity. Impulse is the change in momentum caused by a resultant force acting over a time interval.
动量是质量与速度的乘积，是一个矢量。冲量是合力在一段时间内作用所引起的动量变化。
p = mv, FΔt = Δp = mv − mu
The principle of conservation of momentum states that in a closed system with no external resultant force, total momentum before a collision or explosion equals total momentum after the event. Collisions can be classified as elastic, where kinetic energy is conserved, or inelastic, where some kinetic energy is transferred to other forms.
动量守恒定律指出，在没有外部合力的封闭系统中，碰撞或爆炸前的总动量等于事件后的总动量。碰撞可分为弹性碰撞（动能守恒）和非弹性碰撞（部分动能转化为其他形式）。
In two-dimensional momentum problems, resolve the velocities into perpendicular components before applying conservation of momentum separately in each direction.
在二维动量问题中，应先将速度分解为垂直分量，然后在每个方向上分别应用动量守恒。
6. Moments, Equilibrium and Centre of Gravity | 力矩、平衡与重心
The moment of a force about a point is the product of the force and the perpendicular distance from the point to the line of action of the force. The principle of moments states that for an object in rotational equilibrium, the total clockwise moment equals the total anticlockwise moment about any pivot.
力对某点的力矩等于力与从该点到力作用线的垂直距离的乘积。力矩原理指出，处于转动平衡的物体，对任意支点的总顺时针力矩等于总逆时针力矩。
M = Fd
The centre of gravity is the point where the entire weight of an object may be considered to act. For a uniform regular object, it lies at the geometrical centre. If an object is suspended from a point, its centre of gravity lies directly below the point of suspension when at rest.
重心是物体全部重力可视为集中的作用点。对于均匀规则物体，重心位于几何中心。如果物体从某点悬挂，静止时其重心位于悬挂点的正下方。
A couple consists of two equal, opposite and parallel forces that produce rotation without translation. Its torque is one force multiplied by the perpendicular separation between the forces.
力偶由两个大小相等、方向相反且平行的力组成，产生转动而不产生平动。其力矩等于其中一个力乘以两力之间的垂直距离。
7. Materials: Stress, Strain and Young Modulus | 材料：应力、应变与杨氏模量
Stress is defined as the force applied per unit cross-sectional area. Strain is the extension per unit original length. Both definitions allow fair comparison between samples of different sizes.
应力定义为单位横截面积上所受的力。应变是单位原始长度的伸长量。这两个定义使得不同尺寸的样品之间可以公平比较。
σ = F / A, ε = ΔL / L₀
The Young modulus is the ratio of tensile stress to tensile strain within the limit of proportionality. It measures the stiffness of a material and has the unit pascal (Pa) or N m⁻².
杨氏模量是在比例极限内拉伸应力与拉伸应变之比。它衡量材料的刚度，单位为帕斯卡（Pa）或牛每平方米（N m⁻²）。
E = σ / ε = FL₀ / AΔL
In the standard experiment to determine Young modulus for a wire, measure the original length, diameter, extension and applied force. Plotting stress against strain gives a straight line through the origin whose gradient is the Young modulus.
在测定金属丝杨氏模量的标准实验中，需测量原始长度、直径、伸长量和施加的力。以应力对应变作图，得到一条过原点的直线，其斜率即为杨氏模量。
8. Stress-Strain Curves and Material Behaviour | 应力-应变曲线与材料行为
A stress-strain graph shows how a material responds to increasing tensile stress. The initial linear region obeys Hooke's law, and the gradient gives the Young modulus. The limit of proportionality marks the end of the linear relationship.
应力-应变图显示材料在逐渐增大的拉伸应力下的响应。初始线性区域遵循胡克定律，其斜率给出杨氏模量。比例极限标志着线性关系的结束。
The elastic limit is the maximum stress for which the material returns to its original length when the load is removed. Beyond this point, plastic deformation occurs and permanent extension remains. Ductile materials such as copper show a long plastic region, while brittle materials such as glass fail suddenly with little plastic flow.
弹性极限是卸载后材料能恢复原长的最大应力。超过该点后发生塑性变形，并保留永久伸长。铜等延性材料表现出较长的塑性区域，而玻璃等脆性材料几乎没有塑性流动便突然断裂。
Elastic strain energy = ½FΔL
The area under a stress-strain curve gives the strain energy stored per unit volume. This is useful for comparing toughness, where a larger area indicates greater energy absorption before failure.
应力-应变曲线下的面积表示单位体积储存的应变能。这有助于比较韧性，面积越大表明材料在破坏前吸收的能量越多。
9. Projectile Motion | 抛体运动
Projectile motion is analysed by separating horizontal and vertical components. Horizontally, there is no acceleration if air resistance is ignored, so horizontal velocity remains constant. Vertically, the motion has constant acceleration due to gravity.
抛体运动通过分解水平分量和竖直分量来分析。如果忽略空气阻力，水平方向没有加速度，因此水平速度保持不变。竖直方向则为重力作用下的匀加速运动。
vₓ = u cos θ, vᵧ = u sin θ − gt
The time of flight depends only on the vertical motion, while the horizontal range is the constant horizontal velocity multiplied by the time of flight. Maximum height occurs when the vertical velocity component becomes zero.
飞行时间只取决于竖直运动，而水平射程等于恒定的水平速度乘以飞行时间。最大高度出现在竖直速度分量为零的时刻。
Range = u² sin 2θ / g
This formula for range applies only for level ground and no air resistance. For a given launch speed, maximum range is achieved at an angle of 45°.
该射程公式仅适用于水平地面且无空气阻力的情况。对于给定的发射速度，发射角为 45° 时射程最大。
10. Common Exam Mistakes and Data Analysis | 常见考试错误与数据分析
Many Unit 1 marks are lost through avoidable errors: using the wrong sign convention, mixing units, forgetting vector directions, misreading graph axes and quoting final answers to an inappropriate number of significant figures.
第一单元中很多失分来自可避免的错误：正负号规定错误、单位混用、忘记矢量方向、看错图像坐标轴，以及最终答案有效数字位数不当。
When interpreting motion graphs, recall that the gradient of a displacement-time graph gives velocity, the gradient of a velocity-time graph gives acceleration, and the area under a velocity-time graph gives displacement. In force-extension graphs, the gradient gives the stiffness constant and the area gives elastic strain energy.
在解读运动图像时，位移-时间图斜率表示速度，速度-时间图斜率表示加速度，速度-时间图下的面积表示位移。在力-伸长图中，斜率给出劲度系数，面积给出弹性应变能。
Always show the units in tables and axis labels. In calculations, write the equation first, substitute values with units, and then rearrange. This makes method marks easier to earn even if the final answer is wrong.
表格和坐标轴标签中要始终标明单位。计算时应先写公式，代入带单位的数值，再进行整理。这样即使最终答案错误，也更容易获得方法分。
11. Practical Skills: Measurements and Uncertainties | 实验技能：测量与不确定度
Accuracy describes how close a measurement is to the true value, while precision describes how repeatable the measurements are. Random errors reduce precision, whereas systematic errors reduce accuracy and shift all readings in one direction.
准确度描述测量值与真实值的接近程度，而精密度描述测量值的可重复性。随机误差降低精密度，系统误差降低准确度并使所有读数向同一方向偏移。
The absolute uncertainty of a measurement is usually half the smallest scale division for analogue instruments, or the resolution stated for digital instruments. Percentage uncertainty is calculated as absolute uncertainty divided by the measured value, multiplied by 100%.
测量值的绝对不确定度对于模拟仪器通常是其最小分度值的一半，对于数字仪器则是其标称分辨率。百分比不确定度等于绝对不确定度除以测量值再乘以 100%。
When quantities are added or subtracted, add absolute uncertainties. When multiplied or divided, add percentage uncertainties. If a quantity is raised to a power n, multiply the percentage uncertainty by n.
当物理量相加或相减时，应相加绝对不确定度。当物理量相乘或相除时，应相加百分比不确定度。如果物理量被乘方 n 次，则百分比不确定度乘以 n。
12. Revision Checklist | 复习清单
Use this checklist to confirm that each core Unit 1 skill is secure before the exam.
在考试前，用下面的清单确认第一单元每一项核心技能都已掌握。
- Define scalar and vector quantities and give examples | 定义标量与矢量并给出实例
- Resolve vectors into perpendicular components and add vectors correctly | 将矢量分解为垂直分量并正确进行矢量加法
- Select and apply the correct SUVAT equation for constant acceleration | 选择并应用正确的 SUVAT 方程处理匀加速运动
- Draw free-body diagrams and apply Newton's laws to connected masses | 画受力图并将牛顿定律应用于连接体
- Calculate work, energy, power and efficiency in mechanical systems | 计算机械系统中的功、能量、功率和效率
- Apply conservation of momentum to collisions and explosions | 将动量守恒应用于碰撞和爆炸
- Use moments to solve equilibrium and centre of gravity problems | 利用力矩求解平衡和重心问题
- Calculate stress, strain and Young modulus from experimental data | 根据实验数据计算应力、应变和杨氏模量
- Describe stress-strain curves for ductile, brittle and polymeric materials | 描述延性、脆性和高分子材料的应力-应变曲线
- Analyse projectile motion by separating horizontal and vertical components | 通过分离水平与竖直分量分析抛体运动
- Interpret motion graphs and calculate gradient and area accurately | 准确解读运动图像并计算斜率和面积
- Estimate uncertainties and combine them using the correct rules | 估计不确定度并使用正确规则进行合成
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图