Momentum | 动量

📚 Momentum | 动量

Momentum is a fundamental concept in physics that describes the quantity of motion an object possesses. It depends on both the mass and the velocity of the object, and it plays a key role in understanding collisions, explosions, and the effect of forces over time. In your Edexcel IGCSE Science course, momentum appears under the Physics section, linking Newton's laws to real-world applications such as car safety and rocket propulsion.

动量是物理学中一个基本概念，用来描述物体运动的“量”。它既取决于物体的质量，也取决于其速度，在理解碰撞、爆炸以及力在一段时间内产生的效果时起着关键作用。在 Edexcel IGCSE 科学课程中，动量出现在物理部分，它将牛顿定律与汽车安全、火箭推进等实际应用紧密联系起来。

1. What is Momentum? | 什么是动量？

Momentum is defined as the product of an object's mass and its velocity. Any moving object has momentum, and the greater its mass or the faster it moves, the more momentum it carries. Because velocity includes direction, momentum is a vector quantity — it has both magnitude and direction.

动量定义为物体的质量与其速度的乘积。任何运动的物体都具有动量，物体的质量越大，或运动得越快，它所携带的动量就越大。由于速度包含方向，动量是一个矢量——既有大小，也有方向。

Imagine a heavy lorry and a bicycle both moving at the same speed. The lorry has much more mass, so its momentum is far greater, making it harder to stop. This simple idea helps us understand why momentum is conserved in closed systems.

想象一下，一辆重型卡车和一辆自行车以相同速度行驶。卡车的质量大得多，因此其动量也大得多，更难停下来。这个简单的思路有助于我们理解为什么在封闭系统中动量是守恒的。

---

2. The Momentum Equation | 动量公式

You are required to recall and use the equation that links mass, velocity and momentum. In symbols, the relationship is written as:

你需要记住并运用联系质量、速度和动量的公式。用符号表示如下：

p = m × v

where p represents momentum (in kilogram metres per second, kg·m/s or kg m s⁻¹), m stands for mass (in kilograms, kg) and v is velocity (in metres per second, m/s). Make sure you can rearrange this to find mass or velocity when the other quantities are given.

其中 p 表示动量（单位为千克米每秒，kg·m/s 或 kg m s⁻¹），m 代表质量（单位千克，kg），v 是速度（单位米每秒，m/s）。你要能够通过变形求出质量或速度。

000 kg·m/s. If the velocity doubles to 30 m/s, the momentum also doubles to 36 000 kg·m/s, showing the direct proportionality between velocity and momentum when mass is constant.

例如，一辆 1200 kg 的汽车以 15 m/s 行驶，其动量为 1200 × 15 = 18 000 kg·m/s。如果速度加倍到 30 m/s，动量也加倍至 36 000 kg·m/s，表明在质量不变时速度与动量成正比。

---

3. Units of Momentum | 动量单位

se momentum is mass × velocity, its SI unit is kilogram metre per second (kg·m/s or kg m s⁻¹). In IGCSE exams it is common to see answers left in this combined unit; there is no special name for the unit of momentum.

因为动量是质量 × 速度，其国际单位是千克米每秒（kg·m/s 或 kg m s⁻¹）。在 IGCSE 考试中，答案通常保留这个复合单位，动量单位没有专门的名字。

You may sometimes need to convert masses from grams to kilograms or speeds from km/h to m/s before calculating. Always check that your units are consistent, otherwise your momentum value will be incorrect.

有时你需要先把质量由克换算成千克，或把速度由 km/h 换算成 m/s，然后再计算。务必保证单位一致，否则动量值会是错误的。

---

4. Momentum as a Vector | 动量是矢量

Since velocity is a vector, momentum is also a vector. This means that when you consider momentum, the direction of motion matters. A positive direction is chosen, and any velocity in the opposite direction is treated as negative.

由于速度是矢量，动量也是矢量。这意味着考虑动量时运动方向很重要。我们会选择一个正方向，与之相反的速度就是负的。

rs: −1.5 − (+2.0) = −3.5 kg·m/s. Getting the sign right is crucial for collision problems.

例如，一个质量为 0.5 kg 的小球以 4 m/s 向右运动，动量为 +2.0 kg·m/s。如果它以 3 m/s 向左反弹，动量就变为 −1.5 kg·m/s。动量的变化就是末动量与初动量之差：−1.5 − (+2.0) = −3.5 kg·m/s。在碰撞问题中正确处理正负号至关重要。

---

5. Newton’s Second Law and Momentum | 牛顿第二定律与动量

terms of momentum. The resultant force acting on an object is equal to the rate of change of its momentum. Mathematically:

牛顿第二定律通常表述为 F = m a，但也可以用动量来表述：作用在物体上的合力等于其动量的变化率。数学表达式为：

F = Δp / Δt

where Δp is the change in momentum and Δt is the time taken for that change. This version is particularly useful when a force acts for a very short time, such as in kicks, collisions or hitting a ball.

其中 Δp 是动量变化量，Δt 是发生变化所用的时间。当一个力作用时间很短时（例如踢球、碰撞或击球），这种表述尤其有用。

e change in momentum can be achieved by a large force over a short time, or a small force over a longer time — an idea that underpins many safety features.

由 F = Δp/Δt 可以看出，相同的动量变化可以通过短时间内的大力，或较长时间内的小力来实现——这正是许多安全设计背后的原理。

---

6. Impulse | 冲量

Impulse is defined as the product of the resultant force and the time for which it acts. Impulse equals the change in momentum produced:

冲量定义为合力与作用时间的乘积。冲量等于产生的动量变化：

Impulse = F × Δt = Δp

This relationship is extremely helpful when analysing forces in collisions. For a given change in momentum, increasing the collision time reduces the force experienced.

这个关系在分析碰撞中的力时非常有用。若动量变化一定，延长碰撞时间可以减小所受到的力。

−35 N. The negative sign shows the force is opposite to the original direction of motion.

以前面提到的小球为例，若动量变化为 −3.5 kg·m/s，与墙壁接触时间为 0.10 s，那么作用在小球上的平均力为 F = −3.5 / 0.10 = −35 N。负号表示力的方向与最初运动方向相反。

---

广告 / Sponsored

7. Impulse from Force–Time Graphs | 力-时间图中的冲量

When a force varies with time, the impulse can be found by calculating the area under a force–time graph. This area represents the change in momentum. In your exam, you may be asked to estimate the area by counting squares or using simple geometry if the graph is made up of straight lines.

当力随时间变化时，可以通过计算力-时间图下方的面积来求冲量。这个面积就代表动量的变化。在考试中，你可能会被要求通过数格子或简单几何方法估算面积。

A common graph shape is a triangle or a trapezium, corresponding to a force that increases or decreases steadily. The area under the graph, in newton-seconds (N·s), gives the impulse, which is numerically equal to the change in momentum in kg·m/s.

常见的图形是三角形或梯形，对应力稳步增大或减小的情况。图线下的面积以牛顿秒（N·s）为单位，就表示冲量，其数值等于以 kg·m/s 为单位的动量变化。

---

8. Conservation of Momentum | 动量守恒

In a closed system where no external forces act, the total momentum before an event (such as a collision or explosion) is equal to the total momentum after the event. This is the principle of conservation of momentum, a fundamental law of physics.

在没有外力作用的封闭系统中，事件（例如碰撞或爆炸）前的总动量等于事件后的总动量。这就是动量守恒原理，一个基本的物理定律。

Mathematically, for two objects A and B:

对于两个物体 A 和 B，可用公式表示：

mₐ uₐ + m_b u_b = mₐ vₐ + m_b v_b

where u represents initial velocities and v represents final velocities. You must assign a positive direction and treat velocities in the opposite direction as negative to apply the principle correctly.

其中 u 表示初速度，v 表示末速度。你必须规定一个正方向，并将反方向的速度视为负值，才能正确应用该原理。

Conservation of momentum is why a gun recoils when fired — the forward momentum of the bullet is matched by an equal and opposite momentum of the gun.

动量守恒说明了为什么开枪时枪会后退——子弹向前的动量与枪向后的动量大小相等、方向相反。

---

9. Collisions and Explosions | 碰撞与爆炸

There are two main types of events you will work with: collisions, where objects come together, and explosions, where objects move apart. In both cases, the total momentum remains constant, provided no external forces interfere.

你主要会接触到两类事件：碰撞——物体碰到一起；爆炸——物体分离开来。在这两种情况下，只要没有外力干扰，总动量都保持不变。

the calculation straightforward: total momentum before = (combined mass) × final velocity.

在碰撞中，物体可能粘在一起（变成一个整体）或彼此弹开。当它们粘在一起时，会共享相同的末速度，这使计算变得简单：碰撞前的总动量 = （总质量）× 末速度。

In an explosion, a stationary object breaks into fragments that fly apart. The initial momentum is zero, so the vector sum of the momenta of the fragments after the explosion must also equal zero. This is why the fragments move in opposite directions with momenta that cancel each other out.

在爆炸中，原本静止的物体崩裂成多个碎片向四周飞散。初动量为零，因此爆炸后各碎片的动量矢量和也必须为零。这就是碎片向相反方向运动且动量相互抵消的原因。

---

10. Elastic and Inelastic Collisions | 弹性与非弹性碰撞

Collisions can be classified by whether kinetic energy is conserved. In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved but some kinetic energy is transformed into heat, sound or deformation energy.

碰撞可以根据动能是否守恒来分类。在弹性碰撞中，动量和动能都守恒。在非弹性碰撞中，动量守恒，但一部分动能转变为热能、声能或形变能。

Most real-world collisions are inelastic. For IGCSE, you are not required to do detailed energy calculations for collisions, but you should understand the difference and recognise that momentum is always conserved in isolated systems, while kinetic energy is only conserved in perfectly elastic collisions.

现实世界中的大多数碰撞都是非弹性的。在 IGCSE 阶段，你不需要对碰撞进行详细的能量计算，但应该理解两者区别，并认识到在孤立系统中动量始终守恒，而动能只有在完全弹性碰撞中才守恒。

---

11. Solving Momentum Problems | 动量问题求解

When tackling momentum questions, follow a clear method: choose a positive direction; write down the masses and velocities of all objects before and after the event; set up the conservation equation; substitute values, using negative signs where velocities are opposite to the chosen direction; and solve for the unknown.

解答动量问题时，请遵循清晰的步骤：选定正方向；写出事件前后所有物体的质量和速度；建立守恒方程；代入数值，与所选方向相反的速度用负号；然后求解未知量。

Always check that your answer is sensible — final speeds should not exceed realistic values, and the direction of motion should match the situation (e.g. a heavier object will usually continue in its original direction after a collision with a lighter one).

务必检查答案是否合理——末速度不应超出实际范围，运动方向也应符合情景（例如，较重的物体与较轻的物体碰撞后通常会保持原来的方向）。

momentum conservation: (2.0 × 3.0) + (1.0 × 0) = 3.0 × v, giving v = 2.0 m/s to the right.

举例：一辆 2.0 kg 的小车以 3.0 m/s 向右运动，撞上一辆静止的 1.0 kg 小车。碰撞后它们粘在一起。总质量为 3.0 kg。根据动量守恒：(2.0 × 3.0) + (1.0 × 0) = 3.0 × v，得出 v = 2.0 m/s 向右。

---

12. Safety Applications | 安全应用

The impulse–momentum relationship explains many safety features in vehicles. Crumple zones, airbags and seat belts all increase the time over which a person’s momentum changes during a crash. By extending the impact time, the average force experienced is reduced, lowering the risk of serious injury.

冲量–动量关系可以解释汽车中的许多安全设计。吸能区、安全气囊和安全带都延长了碰撞过程中人体动量改变的时间。通过延长撞击时间，所受到的平均力减小，从而降低严重受伤的风险。

driver’s momentum to drop to zero. Both design features follow directly from F = Δp / Δt.

汽车前后部的吸能区会逐步变形，吸收能量并延长碰撞时间。安全气囊快速充气，提供柔软的缓冲，再次延长驾驶员动量降至零的时间。这两种设计都直接源自 F = Δp / Δt。

Even crash mats in gymnastics and cushioned soles in sports shoes apply the same principle — spreading impact over a longer time to reduce the force on the body.

即使是体操比赛中的防摔垫和运动鞋的缓冲鞋底，也应用了同一条原理——将冲击分散到更长的时间内，以减小作用在身体上的力。

---

Published by TutorHao | Science Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）