📚 IGCSE Edexcel Maths: Mechanics Key Points | IGCSE Edexcel 数学：力学考点精讲
Welcome to our focused revision guide for the Mechanics topics within the Edexcel IGCSE Mathematics specification. Here, we break down the essential concepts and formulae you need to master – from SUVAT equations and motion graphs to forces, momentum, and connected particles. Work through each section, pairing the English explanations with their Chinese translations to reinforce your understanding.
欢迎阅读针对 Edexcel IGCSE 数学力学部分的核心考点复习指南。我们在此分解你必须掌握的基本概念与公式——从 SUVAT 方程和运动图像，到力、动量以及连接体。逐一学习各小节的英文详解与中文翻译，巩固你的理解。
1. Constant Acceleration Equations (SUVAT) | 匀加速运动方程 (SUVAT)
When an object moves in a straight line with constant acceleration, the five quantities – initial velocity (u), final velocity (v), acceleration (a), displacement (s) and time (t) – are linked by four equations. Choose the one that contains the three known variables and the one unknown you wish to find.
当物体以恒定加速度沿直线运动时，五个量——初速度 (u)、末速度 (v)、加速度 (a)、位移 (s) 和时间 (t)——通过四个方程联系在一起。选择包含三个已知量和所求未知量的那个方程即可。
The four SUVAT equations are:
四个 SUVAT 方程为：
v = u + at
s = ut + ½ at²
v² = u² + 2as
s = ½ (u + v) t
Remember to use consistent units (usually metres and seconds) and to take direction into account when assigning signs to velocity and acceleration.
请记住使用一致的单位（通常为米和秒），并且在赋予速度和加速度正负号时要考虑方向。
2. Displacement–Time Graphs | 位移–时间图
A displacement–time (s–t) graph shows how the distance from a fixed origin changes over time. The gradient of the graph represents the velocity of the object. A straight line indicates constant velocity, while a curved line indicates changing velocity (acceleration or deceleration).
位移–时间 (s–t) 图显示与固定原点的距离如何随时间变化。图像的斜率代表物体的速度。直线表示匀速，而曲线表示速度变化（加速或减速）。
If the graph is a horizontal line, the object is stationary. A positive gradient means motion away from the origin; a negative gradient means motion towards it.
若图像为水平线，则物体静止。斜率为正表示远离原点运动；斜率为负表示朝向原点运动。
3. Velocity–Time Graphs | 速度–时间图
A velocity–time (v–t) graph provides two key pieces of information: the gradient gives the acceleration, and the area under the graph gives the displacement (distance if direction ignored) during that time interval.
速度–时间 (v–t) 图提供两个关键信息：斜率表示加速度，图像下方的面积表示该时间区间内的位移（若忽略方向则为路程）。
For a straight sloping line, acceleration is constant. The area can often be split into rectangles and triangles for easy calculation. Take care with negative velocities: areas below the time axis represent motion in the opposite direction and contribute negatively to displacement.
对于倾斜直线，加速度恒定。面积通常可分割为矩形和三角形以便计算。注意负速度：时间轴下方的面积代表反向运动，对位移的贡献为负。
4. Newton’s Laws of Motion | 牛顿运动定律
Newton’s first law states that an object remains at rest or moves with constant velocity unless a resultant force acts on it. The second law quantifies this: the resultant force acting on an object equals its mass multiplied by its acceleration, expressed as F = ma.
牛顿第一定律指出，除非受到合外力作用，否则物体将保持静止或匀速直线运动状态。第二定律则定量描述：作用在物体上的合外力等于物体质量乘以其加速度，即 F = ma。
Newton’s third law reminds us that forces come in pairs: if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. In problem solving, always identify the object you are considering and draw a clear force diagram.
牛顿第三定律提醒我们力成对出现：若物体 A 对物体 B 施加力，则物体 B 同时对物体 A 施加大小相等、方向相反的力。解题时，始终明确所考虑的对象并画出清晰的受力图。
5. Mass, Weight and Gravity | 质量、重量与重力
Mass (m) is a measure of the amount of matter in an object and is measured in kilograms (kg). Weight (W) is the gravitational force acting on that mass. Near the Earth’s surface, weight is calculated using W = mg, where g is the acceleration due to gravity (approximately 9.8 m/s², often taken as 10 m/s² in IGCSE problems).
质量 (m) 是物体所含物质的量度，单位为千克 (kg)。重量 (W) 是作用在该质量上的引力。在地球表面附近，重量由 W = mg 计算，其中 g 为重力加速度（约 9.8 m/s²，IGCSE 题目中常取 10 m/s²）。
Weight always acts vertically downwards. Do not confuse mass and weight: mass is scalar and constant everywhere, while weight is a vector and depends on the local gravitational field strength.
重量始终竖直向下。切勿混淆质量和重量：质量是标量，处处恒定；而重量是矢量，取决于当地的引力场强度。
6. Resultant Force and Equilibrium | 合力与平衡
The resultant force is the single force that has the same effect as all the individual forces acting on an object combined. You can find it by vector addition: forces in the same direction add, forces in opposite directions subtract.
合力是能与物体所受所有力作用效果相同的单一力。可通过矢量加法求得：同向力相加，反向力相减。
An object is in equilibrium when the resultant force on it is zero. In this state, it will either remain at rest or continue moving with constant velocity. For problems involving equilibrium, set the sum of forces in each perpendicular direction to zero.
当物体所受合外力为零时，物体处于平衡状态。此时物体要么静止，要么继续匀速运动。涉及平衡的问题，需将各正交方向的合力设为零。
7. Resolving Forces into Components | 力的分解
A force acting at an angle can be split into two perpendicular components, usually horizontal and vertical. If a force F makes an angle θ with the horizontal, its components are F cos θ horizontally and F sin θ vertically.
以某个角度作用的力可分解为两个正交分量，通常为水平分量和竖直分量。若力 F 与水平方向夹角为 θ，则其水平分量为 F cos θ，竖直分量为 F sin θ。
Resolving forces makes it easier to apply F = ma or equilibrium conditions along two independent directions. Always label your components clearly and use a sketch.
力的分解使得沿两个独立方向应用 F = ma 或平衡条件更为简便。务必清楚标注各个分量并画出草图。
8. Friction and Limiting Friction | 摩擦力与最大静摩擦力
Friction is a force that opposes motion or attempted motion between two surfaces in contact. On a rough surface, the frictional force F can range from zero up to a maximum value given by F_max = μR, where μ is the coefficient of friction and R is the normal reaction force.
摩擦力是阻碍接触表面之间运动或相对运动趋势的力。在粗糙表面上，摩擦力 F 的取值范围从零到最大值 F_max = μR，其中 μ 为摩擦系数，R 为法向反作用力。
If the applied force is less than F_max, the object does not move and the friction adjusts exactly to balance the applied force. When motion is just about to occur, friction reaches its limiting value. Always draw the friction force parallel to the surfaces and opposite to the direction of motion or tendency.
若施加的力小于 F_max，物体静止，摩擦力恰好与外力平衡。当物体即将运动时，摩擦力达到最大值。作图时务必让摩擦力平行于接触面，并指向与运动或运动趋势相反的方向。
9. Motion on an Inclined Plane | 斜面上的运动
When a particle is placed on a smooth inclined plane at angle θ to the horizontal, its weight mg can be resolved into components parallel and perpendicular to the plane: mg sin θ down the slope, and mg cos θ perpendicular to the slope.
当质点置于与水平面成 θ 角的光滑斜面上时，其重量 mg 可分解为沿斜面和垂直于斜面的分量：沿斜面向下的 mg sin θ，以及垂直于斜面的 mg cos θ。
The perpendicular component is balanced by the normal reaction R, so R = mg cos θ. The acceleration of the particle down the slope is then a = g sin θ, assuming no other forces. If friction is present, the net force down the slope becomes mg sin θ – F, and you must also ensure R = mg cos θ.
垂直分量由法向反作用力 R 平衡，故 R = mg cos θ。若无其他力，质点沿斜面的加速度为 a = g sin θ。若存在摩擦力，则沿斜面的净力为 mg sin θ – F，同时仍需满足 R = mg cos θ。
10. Connected Particles | 连接体
Two or more objects connected by a light inextensible string or tow-bar experience the same acceleration and, in the case of a string, the same tension. To solve such problems, first apply Newton’s second law to the whole system to find the acceleration. Then consider one particle separately to find the tension or other internal forces.
两个或多个通过轻质且不可伸长的绳或牵引杆连接的物体具有相同的加速度，并且对于绳子，张力处处相等。解决这类问题，首先对整个系统应用牛顿第二定律求出加速度，然后单独分析其中一个物体以求出张力或其他内力。
For example, a car of mass 1200 kg towing a trailer of mass 800 kg with a driving force of 3000 N: the total mass is 2000 kg, so the acceleration is a = 3000 ÷ 2000 = 1.5 m/s². The tension T in the tow-bar can be found by considering the trailer alone: T = 800 × 1.5 = 1200 N.
例如，一辆质量为 1200 kg 的汽车以 3000 N 的驱动力牵引质量为 800 kg 的拖车：总质量为 2000 kg，加速度 a = 3000 ÷ 2000 = 1.5 m/s²。牵引杆中的张力 T 可单独分析拖车求得：T = 800 × 1.5 = 1200 N。
11. Momentum and Collisions | 动量与碰撞
Momentum (p) is the product of mass and velocity: p = mv. It is a vector quantity, so direction must be accounted for. In a closed system with no external forces, the total momentum before a collision or explosion equals the total momentum after: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
动量 (p) 是质量与速度的乘积：p = mv。它是矢量，因此必须考虑方向。在没有外力的封闭系统中，碰撞或爆炸前的总动量等于碰撞或爆炸后的总动量：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
In IGCSE questions, you may be asked to find an unknown velocity after a collision or to determine the impulse exerted on a particle. Remember that impulse is the change in momentum: impulse = mv – mu.
IGCSE 题目可能要求你求碰撞后的未知速度，或者确定作用于质点的冲量。记住冲量是动量的变化量：冲量 = mv – mu。
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