📚 Newton’s Laws Revision Guide for Edexcel A-Level Physics | A-Level Edexcel 物理：牛顿定律考点精讲
Newton’s laws of motion form the bedrock of classical mechanics and are essential for any Edexcel A‑Level Physics student. This revision guide walks you through each law, common applications, and the key equations that you must master for the exams. We will also explore momentum, impulse, connected particles, circular motion, and gravitation — all rooted in Newton’s powerful principles.
牛顿运动定律是经典力学的基石，也是每一位 Edexcel A‑Level 物理学生必须掌握的核心内容。本篇考点精讲将逐一梳理三大定律，解析常见应用与必考方程，帮助你牢牢把握考试重点。我们还会深入动量、冲量、连接体、圆周运动以及万有引力等内容——它们全都植根于牛顿的伟大原理。
1. Newton’s First Law: Inertia | 牛顿第一定律：惯性
Newton’s First Law states that an object will remain at rest or move with a constant velocity unless acted upon by a resultant external force. This property of matter is called inertia. The law implies that if the vector sum of forces on a body is zero, the body is in equilibrium: it may be stationary or moving at a steady speed in a straight line.
牛顿第一定律指出，除非受到合外力的作用，物体将保持静止或匀速直线运动状态。这一性质称为惯性。该定律说明，若作用于物体的力矢量和为零，物体就处于平衡状态：它可能静止，也可能沿直线以恒定速率运动。
A common misconception is that a constant force is needed to maintain motion. In fact, when there is no net force (e.g., an ice hockey puck sliding on frictionless ice), the object continues moving indefinitely at constant velocity. Recognising when a body is in equilibrium is crucial for solving statics problems.
一个常见的误解是认为维持运动需要恒定的力。实际上，当合外力为零时（例如冰球在无摩擦的冰面上滑动），物体会无限期地以恒定速度运动下去。在解决静力学问题时，能识别物体是否处于平衡态至关重要。
2. Mass, Inertial Mass and Gravitational Mass | 质量、惯性质量与引力质量
Mass is a measure of an object’s inertia — its resistance to change in velocity. The inertial mass m of a body is defined by the ratio of the net force applied to the resulting acceleration: m = Fₙₑₜ / a. In Edexcel Physics, you are also expected to distinguish between inertial mass and gravitational mass. Gravitational mass determines the strength of the gravitational force on an object, and experiments show that the two are equivalent; this equivalence underpins Einstein’s general relativity.
质量是物体惯性的量度——即物体对速度变化的抗拒程度。物体的惯性质量 m 由合外力与产生的加速度之比定义：m = Fₙₑₜ / a。在 Edexcel 物理中，你还需要区分惯性质量与引力质量。引力质量决定物体所受引力的大小，实验表明两者是等价的；这一等价性正是爱因斯坦广义相对论的基石。
In most A‑Level problems, we simply use ‘mass’ and apply Newton’s Second Law without distinguishing the two. However, a common exam question asks students to explain how mass can be measured using an inertial balance or how to compare masses via their accelerations under the same force.
在大多数 A‑Level 问题中，我们直接使用“质量”并应用牛顿第二定律，无需区分两者。但常见的考题会要求学生解释如何用惯性天平测量质量，或如何通过相同力作用下的加速度来比较质量。
3. Newton’s Second Law: F = ma | 牛顿第二定律：F = ma
The Second Law quantifies the effect of a resultant force: the acceleration a of an object is directly proportional to the net force Fₙₑₜ acting on it and inversely proportional to its mass m. In its simplest form, it is written as:
第二定律定量描述了合外力的作用效果：物体的加速度 a 与所受合外力 Fₙₑₜ 成正比，与质量 m 成反比。最简单的形式表示为：
Fₙₑₜ = m a
When using this equation, always ensure that you are working with the resultant force in a given direction. In Edexcel exams, you will often need to resolve forces into perpendicular components and apply F = ma along each axis separately, especially on inclined planes.
使用该方程时，务必确保你使用的是某一方向上的合力。在 Edexcel 考试中，常需要将力沿垂直方向分解，并分别沿每个轴应用 F = ma，特别是在斜面问题中。
For a body on a smooth inclined plane at angle θ, the component of weight down the slope is mg sin θ. The acceleration down the plane, in the absence of friction, is a = g sin θ.
对于放在光滑斜面上、倾角为 θ 的物体，重力沿斜面的分量是 mg sin θ。无摩擦时，物体沿斜面的加速度为 a = g sin θ。
4. Momentum and Newton’s Second Law in Terms of Momentum | 动量与动量形式的第二定律
Momentum p is defined as the product of mass and velocity: p = m v. It is a vector quantity with units kg m s⁻¹ or N s. Newton’s Second Law can be expressed in a more general form: the rate of change of momentum of an object is directly proportional to the resultant force acting on it, and takes place in the direction of that force.
动量 p 定义为质量与速度的乘积：p = m v。它是矢量，单位为 kg m s⁻¹ 或 N s。牛顿第二定律可以用更一般的形式表述：物体动量的变化率与其所受合外力成正比，且变化发生在该力的方向上。
Fₙₑₜ = Δp / Δt
For a system of constant mass, this reduces to F = m a. However, when mass changes (e.g., rocket propulsion), you must use the momentum form. Edexcel often tests your ability to link force and momentum in collision problems.
对于质量不变的系统，该式可简化为 F = m a。然而，当质量变化时（如火箭推进），必须使用动量形式。Edexcel 常在碰撞问题中考查你对力与动量关系的理解。
5. Impulse and Change in Momentum | 冲量与动量变化
Impulse J is defined as the product of the average force acting on an object and the time interval for which it acts: J = Fₐₗ₉ Δt. From the momentum form of the Second Law, impulse is equal to the change in momentum:
冲量 J 定义为作用在物体上的平均力与作用时间间隔的乘积：J = Fₐₗ₉ Δt。根据第二定律的动量形式，冲量等于动量的变化量：
J = Δp = m v − m u
The impulse–momentum relationship is especially useful when analysing collisions, safety features like airbags, and sporting actions. The area under a force–time graph also gives the impulse experienced by an object.
冲量-动量关系在分析碰撞、安全气囊等安全设施以及体育运动时特别有用。力–时间图下的面积也表示物体受到的冲量。
In Edexcel papers, you are often asked to use this theorem to find the average force during a collision, such as a ball bouncing off a wall, or to explain how crumple zones reduce injury by increasing the impact time and thus reducing the force.
在 Edexcel 试卷中，常要求运用该定理计算碰撞过程中的平均力，例如球撞墙反弹，或者解释溃缩区如何通过延长撞击时间而减小受力，从而降低伤害。
6. Newton’s Third Law: Action and Reaction | 牛顿第三定律：作用力与反作用力
Newton’s Third Law states that if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. These forces are of the same type, act on different bodies, and are equal in magnitude but opposite in direction:
牛顿第三定律指出，若物体 A 对物体 B 施加一个力，则物体 B 同时对物体 A 施加一个大小相等、方向相反的力。这两个力类型相同、作用在不同物体上，大小相等、方向相反：
Fₐₚₒₙₙ Fₐₚₒₙₙ = – Fₐₚₒₙₙ (i.e., Fₐ on B = – F_B on A)
Common exam mistakes include pairing forces that act on the same body (e.g., weight and normal reaction on a book resting on a table) as a Third Law pair. The correct pair for the book’s weight is the gravitational pull of the book on the Earth, not the normal force from the table.
常见考试误区是将作用在同一物体上的力（例如书本放在桌上时的重力和支持力）错误地当作第三定律中的一对力。书本重力的正确配对是书本对地球的引力，而不是桌面的支持力。
Understanding the Third Law is vital for analysing the motion of connected objects, rockets, and forces on inclined planes with pulleys. Always ask: “What is the other body?” to verify a Third Law pair.
理解第三定律对于分析连接体运动、火箭以及含滑轮的斜面问题至关重要。总是要问：“另一个物体是谁？”来验证一对力是否满足第三定律。
7. Free-body Diagrams and Resolving Forces | 受力分析与力的分解
Drawing a clear free-body diagram is the first step to solving any force problem. Isolate the body, draw all forces acting on it as arrows originating from its centre of mass, and label them clearly: weight (mg), normal reaction (R or N), tension (T), friction (f or F_f), and any applied forces.
绘制清晰的受力分析图是解决任何力学问题的第一步。将物体隔离，把所有作用力画成从质心出发的箭头，并清楚标记：重力 (mg)、法向反作用力 (R 或 N)、拉力 (T)、摩擦力 (f 或 F_f) 以及任何外加力。
Forces that act at an angle, such as a pull at 30° to the horizontal, must be resolved into perpendicular components. Using trigonometry, the horizontal component is F cos θ and the vertical component is F sin θ. Apply Newton’s Second Law independently along each axis.
与水平方向成角度的力（如 30° 的拉力）必须分解为垂直分量。利用三角函数，水平分量为 F cos θ，竖直分量为 F sin θ。分别在每个轴上独立应用牛顿第二定律。
Equilibrium conditions are often tested: for a body at rest or moving with constant velocity, the net force in any direction is zero. This allows you to set up simultaneous equations to find unknown forces.
平衡条件常受考核：对于静止或匀速运动的物体，任何方向上的合外力均为零。这使你能够列方程组求解未知力。
8. Connected Particles: Pulleys and Tension | 连接体问题：滑轮与张力
When two objects are connected by a light inextensible string passing over a smooth pulley, they share the same magnitude of tension and acceleration. Treat each mass separately: draw free-body diagrams, write down F = ma for each, and solve the resulting equations simultaneously.
当两个物体由一根轻质且不可伸长的绳子相连，并跨过一个光滑滑轮时，它们具有大小相同的拉力和加速度。分别处理每个物体：画受力图，对每个物体列出 F = ma，然后联立求解方程。
T − m₁g = m₁a (for the lighter mass being lifted)
m₂g − T = m₂a (for the heavier mass falling)
Adding the two equations eliminates T and gives the acceleration: a = (m₂ − m₁)g / (m₂ + m₁). Such problems, known as Atwood machine problems, are classic Edexcel A‑Level questions and may include friction or an inclined table.
两式相加消去 T 可得加速度：a = (m₂ − m₁)g / (m₂ + m₁)。这类问题称为阿特伍德机问题，是 Edexcel A‑Level 的经典题型，可能包含摩擦或倾斜桌面等情况。
9. Circular Motion and Centripetal Force | 圆周运动与向心力
When an object moves in a circle at constant speed, its velocity is changing direction, so it experiences an acceleration towards the centre. This centripetal acceleration a_c = v² / r = ω² r. By Newton’s Second Law, there must be a resultant centripetal force:
当物体以恒定速率沿圆周运动时，其速度方向不断改变，因此它具有指向圆心的加速度。该向心加速度 a_c = v² / r = ω² r。根据牛顿第二定律，必然存在指向圆心的合力：
F_c = m v² / r = m ω² r
The centripetal force is not a new type of force; it is provided by tension, gravity, friction, or the normal reaction. For a car rounding a bend, friction provides the centripetal force; for a satellite, it is gravity.
向心力并非一种新型力；它由拉力、重力、摩擦力或法向反作用力提供。汽车转弯时，摩擦力充当向心力；卫星运动中则是引力提供向心力。
Exam questions often require you to analyse situations like a bucket swinging in a vertical circle or a car on a banked track. Here you must resolve forces and apply F = ma in the radial direction.
考题常要求分析水桶在竖直面内摇转或汽车在倾斜轨道上行驶的情形。此时需要分解力并在径向应用 F = ma。
10. Newton’s Law of Universal Gravitation | 牛顿万有引力定律
Newton’s Law of Universal Gravitation states that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation:
牛顿万有引力定律指出，任意两个质点都相互吸引，引力的大小与两质点质量的乘积成正比，与它们之间距离的平方成反比：
F = G M m / r²
where G is the gravitational constant, 6.67 × 10⁻¹¹ N m² kg⁻². Although this is not one of the three laws of motion, it is an extension of Newtonian mechanics and a key part of the Edexcel specification, especially for satellite motion, Kepler’s laws, and gravitational field strength g = GM / r².
其中 G 是引力常量，6.67 × 10⁻¹¹ N m² kg⁻²。虽然万有引力定律不属于三大运动定律，但它是牛顿力学的延伸，也是 Edexcel 考纲的重要组成部分，尤其在卫星运动、开普勒定律和引力场强度 g = GM / r² 方面。
Combining this law with centripetal force allows you to derive the orbital period of a satellite, showing that T² ∝ r³. Such derivations are common in A‑Level exams.
将该定律与向心力结合，可以推导卫星的轨道周期，证明 T² ∝ r³。这类推导在 A‑Level 考试中十分常见。
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