Newton's Laws of Motion | 牛顿定律考点精讲

📚 Newton’s Laws of Motion | 牛顿定律考点精讲

Newton’s laws of motion form the foundation of classical mechanics. For CCEA IGCSE Physics, you must be able to state and apply all three laws, understand the concepts of inertia, resultant force, mass and weight, and analyse motion using free-body diagrams. This article covers key learning points, worked examples, and common exam pitfalls to help you master the topic.

牛顿运动定律是经典力学的基础。在 CCEA IGCSE 物理考试中，你需要能够陈述并应用三条定律，理解惯性、合力、质量和重量的概念，并能运用自由体图分析运动。本文涵盖核心考点、典型例题和常见考试误区，帮助你彻底掌握这一专题。

1. Introduction to Forces and Motion | 力与运动导论

A force is a push or a pull that can change an object’s shape or its state of motion. Forces are vector quantities – they have both magnitude and direction. When several forces act on an object, we can find their resultant (net) force by vector addition. The effect of a resultant force is to cause acceleration according to Newton’s laws.

力是一种推或拉的作用，可以改变物体的形状或运动状态。力是矢量，既有大小也有方向。当多个力作用在物体上时，我们可以通过矢量合成求出合力。根据牛顿定律，合力会使物体产生加速度。

2. Newton’s First Law – The Law of Inertia | 牛顿第一定律——惯性定律

Newton’s first law states: An object will remain at rest or continue to move at constant velocity in a straight line unless acted upon by a resultant external force. This natural tendency to resist changes in motion is called inertia. In the absence of a net force, an object’s velocity does not change – it is in equilibrium.

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。这种抵抗运动状态变化的固有属性称为惯性。在没有合力的情况下，物体的速度保持不变——它处于平衡状态。

For example, a cup sitting on a table has zero resultant force horizontally, so it stays at rest. A spacecraft drifting in deep space with no gravitational or frictional forces will continue moving at constant speed in a straight line indefinitely.

例如，静止在桌子上的杯子在水平方向合力为零，因此保持静止。在太空中远离任何引力和摩擦的航天器将会一直以恒定速度沿直线运动。

3. Understanding Inertia and Mass | 理解惯性与质量

Inertia is the resistance of an object to a change in its velocity. The larger the mass of an object, the larger its inertia. Mass is a scalar quantity measured in kilograms (kg) and indicates the amount of matter in an object. Crucially, mass does not depend on location – a 2 kg rock has the same mass on Earth, the Moon, or in deep space.

惯性是物体抵抗速度变化的性质。物体的质量越大，惯性就越大。质量是一个标量，单位是千克(kg)，表示物体所含物质的多少。关键的一点是：质量不随位置改变——一块 2 kg 的石头在地球、月球或太空中质量始终都是 2 kg。

You can experience inertia when standing on a bus: if the bus brakes suddenly, your body lurches forward because it tends to continue moving at the original speed. The larger your mass, the harder it is to stop you.

你可以在公交车上感受到惯性：如果公交车突然刹车，你的身体会向前倾，这是因为你的身体倾向于保持原来的速度。质量越大，让你停下来就越困难。

4. Balanced and Unbalanced Forces | 平衡力与非平衡力

When the forces acting on an object cancel each other out, the resultant force is zero. We say the forces are balanced. The object then either stays at rest or moves with constant velocity. This is direct consequence of Newton’s first law.

当作用在物体上的力相互抵消时，合力为零，我们称这些力是平衡力。此时物体要么保持静止，要么做匀速直线运动。这是牛顿第一定律的直接推论。

If the resultant force is not zero, the forces are unbalanced. An unbalanced resultant force always produces acceleration in the direction of the resultant force. The object may speed up, slow down, or change direction.

如果合力不为零，则力是非平衡的。非平衡合力总会在合力的方向上产生加速度。物体可能加速、减速或改变运动方向。

A book resting on a table: weight downwards is balanced by normal reaction upwards – balanced forces, no acceleration. A car with the engine exerting a larger driving force than friction: unbalanced forces, the car accelerates forward.

例子：放在桌上的书：向下的重力与向上的支持力平衡——平衡力，没有加速度。汽车发动机提供的牵引力大于摩擦力时：非平衡力，汽车向前加速。

5. Newton’s Second Law – F = ma | 牛顿第二定律——F = ma

Newton’s second law describes what happens when resultant force is not zero. The acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass. This is summarised in one of the most important equations in GCSE Physics:

牛顿第二定律描述了当合力不为零时会发生什么。物体的加速度与合外力成正比，与质量成反比。这可以用 GCSE 物理中最重要的公式之一总结：

F = m × a

where F is the resultant force in newtons (N), m is mass in kilograms (kg), and a is acceleration in metres per second squared (m/s²). To find acceleration, rearrange: a = F / m. To find mass: m = F / a.

其中 F 是合外力，单位牛顿 (N)；m 是质量，单位千克 (kg)；a 是加速度，单位米每二次方秒 (m/s²)。求加速度时变形为：a = F / m；求质量时：m = F / a。

Remember: F must be the resultant (net) force. If multiple forces act, you must first calculate the vector sum. The direction of acceleration is always the same as the direction of the resultant force.

切记：F 必须是合力。如果有多个力作用，需要先进行矢量合成。加速度的方向始终与合力的方向相同。

6. Applying F = ma: Worked Examples | F = ma 应用：例题精讲

Example 1: A trolley of mass 12 kg is pushed with a resultant force of 36 N. Calculate its acceleration. Solution: a = F / m = 36 / 12 = 3.0 m/s².

例题1：一辆质量为 12 kg 的小车受到 36 N 的合力推动。计算它的加速度。解：a = F / m = 36 / 12 = 3.0 m/s²。

Example 2: A car of mass 1000 kg accelerates at 4 m/s². Find the resultant force acting on it. Solution: F = m a = 1000 × 4 = 4000 N in the direction of acceleration.

例题2：一辆 1000 kg 的汽车以 4 m/s² 的加速度行驶。求作用在它上面的合力。解：F = m a = 1000 × 4 = 4000 N，方向与加速度方向相同。

Example 3 (two forces): A rocket of mass 8000 kg has engines producing a thrust of 100 000 N upwards. If its weight is 80 000 N downwards, find the resultant force and the initial acceleration. Resultant force = thrust − weight = 100 000 − 80 000 = 20 000 N upwards. a = F / m = 20 000 / 8000 = 2.5 m/s² upwards.

例题3（两个力）：一枚 8000 kg 的火箭，发动机产生向上的推力 100 000 N，火箭自身重量为 80 000 N 向下。求合力和初始加速度。合力 = 推力 − 重量 = 100 000 − 80 000 = 20 000 N 向上。a = F / m = 20 000 / 8000 = 2.5 m/s² 向上。

7. Weight, Mass and Gravitational Field Strength | 重量、质量与重力场强

Weight is the force of gravity acting on an object. It is a vector and always points towards the centre of the planet. Weight is calculated using:

重量是作用在物体上的重力，它是一个矢量，方向总是指向行星的中心。重量的计算公式是：

W = m × g

where W is weight in newtons (N), m is mass in kilograms (kg), and g is the gravitational field strength. On Earth, g ≈ 9.8 N/kg; in CCEA exam questions, g is often taken as 10 N/kg for simplicity unless stated otherwise.

其中 W 是重量，单位牛顿 (N)；m 是质量，单位千克 (kg)；g 是重力场强。在地球表面，g ≈ 9.8 N/kg；在 CCEA 的考试题中，为简化计算，g 通常取 10 N/kg，除非题目另有说明。

Key distinction: mass is a scalar and does not depend on gravity – a 1 kg object has a mass of 1 kg anywhere. Its weight, however, is only about 10 N on Earth, about 1.6 N on the Moon (where g ≈ 1.6 N/kg), and zero in deep space where g = 0. Do not confuse the two.

关键区别：质量是标量，不依赖于重力——1 kg 的物体在任何地方质量都是 1 kg。然而，它的重量在地球上约为 10 N，在月球上约为 1.6 N（月球 g ≈ 1.6 N/kg），而在深空重力场强为零时重量为零。切勿混淆二者。

8. 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: Whenever two objects interact, they exert equal and opposite forces on each other. In other words, if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These are often called action and reaction forces.

牛顿第三定律指出：每当两个物体相互作用时，它们彼此施加大小相等、方向相反的力。也就是说，如果物体 A 对物体 B 施加一个力，那么物体 B 也会对物体 A 施加一个大小相等、方向相反的力。这两个力通常被称为作用力与反作用力。

It is vital to remember that action and reaction forces always act on different objects. They never cancel each other out because they are not acting on the same body. They are also of the same type – for example, both are gravitational, both are normal contact forces, etc.

必须牢记：作用力与反作用力总是作用在不同的物体上。它们永远不会相互抵消，因为它们不作用在同一个物体上。它们还必须是同一性质的力——例如，同是引力、同是接触力等。

9. Identifying Action-Reaction Pairs | 识别作用力与反作用力对

Consider a book resting on a table. The Earth pulls down on the book with a gravitational force (weight). The action-reaction partner is the book pulling up on the Earth with an equal gravitational force. The table pushes up on the book with a normal contact force; the book pushes down on the table with an equal normal contact force. The weight and the normal force from the table are NOT an action-reaction pair – they act on the same object (the book) and are of different types (gravity versus contact). They can be balanced, but they are not Newton’s third law pairs.

以一本放在桌上的书为例。地球对书施加向下的引力（重力）。其反作用力是书对地球施加的大小相等的向上引力。桌面对书施加向上的支持力；书对桌面施加向下的压力。重力和支持力并不是一对作用力与反作用力——它们作用在同一物体（书）上，且属于不同类型（引力与接触力）。它们可以是平衡力，但不是牛顿第三定律里的力对。

Other examples: a swimmer pushes water backwards (action), water pushes swimmer forwards (reaction). A rocket expels gas downwards (action), gas pushes rocket upwards (reaction). When identifying pairs, always name the two objects and state the direction: ‘Object A exerts a force on B to the left; B exerts an equal force on A to the right.’

其他例子：游泳者向后推水（作用力），水向前推游泳者（反作用力）。火箭向下喷出燃气（作用力），燃气向上推火箭（反作用力）。在识别力对时，一定要指出两个物体和方向：“A 物体对 B 物体施加一个向左的力；B 物体对 A 物体施加一个大小相等的向右的力”。

10. Free-Body Diagrams | 受力分析图（自由体图）

A free-body diagram is a simplified sketch showing all the forces acting on a single object. The object is usually represented as a dot or a box. Each force is drawn as an arrow pointing in the direction it acts; the length of the arrow indicates the magnitude. Labelling each force (weight W, normal reaction N, friction F, thrust T, tension) is essential.

自由体图是一个简图，表示作用在单个物体上的所有力。物体通常用一个点或方框表示。每个力画作指向作用方向的箭头；箭头的长度表示力的大小。标注每个力（重量 W、法向反力 N、摩擦力 F、推力 T、拉力）至关重要。

Free-body diagrams are powerful tools for determining the resultant force. For example, a block sliding on a horizontal surface: weight downwards, normal reaction upwards, applied force to the right, friction to the left. If the vertical forces balance, resultant force = applied force − friction horizontally. Then F = m a can be applied.

自由体图是确定合力的强大工具。例如，一个在水平面上滑动的木块：重力向下，支持力向上，外加力向右，摩擦力向左。若竖直方向力平衡，则合力 = 外加力 − 摩擦力（水平方向），然后可以应用 F = m a。

In exam questions, always start by drawing a free-body diagram if one is not provided. It will help you see which forces must cancel and which contribute to acceleration.

在考试中，如果题目没有提供示意图，自己先画一个自由体图。它会帮助你理清哪些力相互抵消，哪些力产生加速度。

11. Friction and Terminal Velocity | 摩擦力与终极速度

Friction is a force that opposes the motion (or attempted motion) of two surfaces in contact. Air resistance (drag) is a type of friction that acts on objects moving through air. The magnitude of air resistance increases with the speed of the object. This leads to the concept of terminal velocity for a falling object.

摩擦力是一种阻碍两个接触表面相对运动或运动趋势的力。空气阻力（拖曳力）是物体在空气中运动时所受的一种摩擦力。空气阻力的大小随物体速度的增加而增大，这就引出了下落物体的终极速度概念。

When a skydiver first jumps, weight is greater than air resistance, so the resultant force is downward and she accelerates. As her speed increases, air resistance grows. Eventually, air resistance becomes equal to her weight. At this point, resultant force is zero, acceleration stops, and she continues to fall at a constant maximum speed – the terminal velocity. A velocity‑time graph would show a curve levelling off at terminal velocity.

跳伞者刚跳出时，重力大于空气阻力，合力向下，她加速下降。随着速度增加，空气阻力增大。最终空气阻力等于重力。此时合力为零，加速度消失，她以恒定的最大速度下落——即终极速度。速度‑时间图像将显示一条曲线，最后趋平于终极速度。

Understanding terminal velocity requires combining Newton’s first and second laws: unbalanced forces cause acceleration, balanced forces mean constant velocity. Similar reasoning applies to cars reaching a top speed when driving force equals resistive forces.

理解终极速度需要结合牛顿第一和第二定律：非平衡力导致加速，平衡力意味着速度恒定。类似的推理也适用于当汽车驱动力等于总阻力时达到最高速度的情形。

12. Common Misconceptions and Exam Tips | 常见误区与考试技巧

Students often make these mistakes. Myth 1: ‘A constant force is needed to keep an object moving.’ Truth: No, according to Newton’s first law, an object moves at constant velocity with zero resultant force. A force is needed only to change velocity (accelerate). Myth 2: ‘Mass and weight are the same thing.’ Truth: Mass is in kg, weight in N; weight = mg. Myth 3: ‘Action and reaction forces cancel.’ Truth: They act on different objects, so they never cancel. Myth 4: Forgetting to use resultant force in F = ma. Always find the net force first if multiple forces are present.

学生常犯这些错误。误区1：“物体运动需要恒力维持。” 事实：错，根据牛顿第一定律，合力为零时物体做匀速运动。力只用来改变速度（产生加速度）。误区2：“质量和重量是一回事。” 事实：质量单位是 kg，重量单位是 N；重量 = mg。误区3：“作用力与反作用力相互抵消。” 事实：它们作用在不同物体上，因此永远不会抵消。误区4：在 F = ma 中忘记使用合力。如果有多个力，一定要先求出合力。

Exam tips: Always read the question carefully to check whether you are given mass or weight. Write down the relevant formula (F = m a, W = m g). Substitute numbers with units

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Newton’s Laws of Motion | 牛顿定律考点精讲