📚 IGCSE CIE Physics Momentum Revision | IGCSE CIE 物理动量考点精讲
Momentum is one of the most fundamental quantities in IGCSE CIE Physics. It appears in topics ranging from simple collisions to car safety designs. This article covers every key point you need for the exam: definition, formula, vector nature, conservation law, impulse, and the link between force and rate of change of momentum. Worked examples will help you apply the concepts confidently.
动量是 IGCSE CIE 物理中最基本的概念之一，出现在从简单碰撞到汽车安全设计的多个主题中。本文涵盖考试所需的每个关键点：定义、公式、矢量性质、守恒定律、冲量以及力与动量变化率之间的联系。典型例题将帮助你自信地应用这些概念。
1. What is Momentum? | 什么是动量？
Momentum is a measure of 'how much motion' an object has. It depends on both the mass of the object and its velocity. A heavy lorry moving slowly can have the same momentum as a light car moving quickly. In everyday language we might call it 'oomph' – the greater the momentum, the harder it is to stop the object.
动量是衡量一个物体“运动量”大小的物理量。它取决于物体的质量和速度。一辆缓慢行驶的重型卡车可能与一辆快速行驶的小汽车具有相同的动量。用日常语言来说，我们可以称它为“冲劲”——动量越大，物体越难停下来。
2. Momentum Formula and Units | 动量公式与单位
Momentum is calculated using the equation:
动量用以下公式计算：
p = m × v
动量 = 质量 × 速度
where p is momentum, m is mass (kg) and v is velocity (m/s). The SI unit of momentum is kilogram metre per second, written as kg m/s. Since velocity has direction, momentum is also a vector, but we will treat that as a separate point.
其中 p 是动量，m 是质量（千克），v 是速度（米/秒）。动量的国际单位是千克米每秒，写作 kg m/s。由于速度有方向，动量也是矢量，这一点我们将单独讨论。
3. Momentum as a Vector | 动量是矢量
Like velocity, momentum has both magnitude and direction. If we define 'to the right' as positive, then an object moving to the right has positive momentum, while an object moving to the left has negative momentum. In collision problems we often use positive and negative signs to keep track of direction before and after the impact.
和速度一样，动量既有大小也有方向。如果我们定义“向右”为正，那么向右运动的物体具有正动量，而向左运动的物体具有负动量。在碰撞问题中，我们经常用正负号来记录碰撞前后的方向。
4. Conservation of Momentum | 动量守恒
The principle of conservation of momentum states that in a closed system (no external forces acting), the total momentum before an event (like a collision or an explosion) is equal to the total momentum after the event. This is one of the most powerful tools in physics for solving collision problems.
动量守恒定律指出：在一个封闭系统（没有外力作用）中，事件（如碰撞或爆炸）前的总动量等于事件后的总动量。这是物理学中解决碰撞问题最有力的工具之一。
- total momentum before = total momentum after
- 碰撞前总动量 = 碰撞后总动量
Mathematically, for two objects A and B:
用公式表示，对于两个物体 A 和 B：
mₐ uₐ + mₙ uₙ = mₐ vₐ + mₙ vₙ
where u stands for initial velocities and v for final velocities. The equation works with vector signs – be careful with direction.
其中 u 代表初速度，v 代表末速度。该方程使用矢量符号——注意方向。
5. Elastic and Inelastic Collisions | 弹性碰撞与非弹性碰撞
Collisions can be divided into two types: elastic and inelastic. In an elastic collision, both momentum and kinetic energy are conserved. This means the total kinetic energy before equals the total kinetic energy after. An ideal example is a collision between atomic particles, but in the macroscopic world perfectly elastic collisions are rare – a bouncy ball hitting a hard floor comes close.
碰撞可以分为两种类型：弹性碰撞和非弹性碰撞。在弹性碰撞中，动量和动能都守恒。这意味着碰撞前的总动能等于碰撞后的总动能。理想例子是原子粒子之间的碰撞，但在宏观世界中完全弹性碰撞很少见——弹性球撞击硬地板近似于弹性碰撞。
In an inelastic collision, momentum is conserved but kinetic energy is not – some energy is transferred to other forms such as heat, sound, or deformation. In a completely inelastic collision, the two objects stick together after impact and move with a common velocity.
在非弹性碰撞中，动量守恒但动能不守恒——部分能量转化为其他形式，如热能、声能或形变能。在完全非弹性碰撞中，两个物体在碰撞后粘在一起并以共同的速度运动。
6. Impulse | 冲量
Impulse is defined as the product of the average force acting on an object and the time for which it acts. It is also equal to the change in momentum of the object.
冲量定义为作用在物体上的平均力与力作用时间的乘积。它也等于物体动量的变化量。
Impulse = F × Δt = Δp
冲量 = 力 × 时间 = 动量变化量
The unit of impulse is newton second (N s), which is equivalent to kg m/s. This theorem explains why a large force applied for a very short time can produce the same change in momentum as a smaller force applied for a longer time.
冲量的单位是牛顿秒（N s），与 kg m/s 等效。这个定理解释了一个很大的力作用很短时间，可以产生与较小的力作用较长时间相同的动量变化。
7. Force and Rate of Change of Momentum | 力与动量变化率
Newton's second law is often written as F = m a, but its more general form is:
牛顿第二定律通常写作 F = m a，但更普遍的形式是：
F = Δp / Δt
力 = 动量变化量 / 时间
en expects you to explain situations using the idea of changing momentum over time, for example in car crashes.
这意味着作用在物体上的合力等于其动量变化率。如果质量恒定，就简化为 F = m a。CIE 经常要求你用动量随时间变化的概念来解释一些情形，比如汽车碰撞。
8. Safety Applications – Increasing Collision Time | 安全应用——延长碰撞时间
e can see that for a given change in momentum (like when a car stops), the force experienced is smaller if the time taken is longer. This is the principle behind many safety features:
从冲量公式 F = Δp / Δt 可以看出，对于给定的动量变化（如汽车停止时），如果所用时间越长，则受到的力越小。这是许多安全装置背后的原理：
- Crumple zones – the front of a car is designed to collapse gradually, increasing the time of impact and reducing the force on passengers.
- Air bags – they inflate and provide a soft cushion that slows the body down over a longer time.
- Seat belts – they stretch slightly, again extending the stopping time for the occupant.
- Crash mats in sports – gymnasts land on thick mats that increase stopping time and reduce the peak force.
- 吸能区（褶皱区）——汽车前部设计成逐步塌陷，延长碰撞时间，减少乘客受力。
- 安全气囊——气囊充气后提供柔软的缓冲，使人身体在更长时间内减速。
- 安全带——略微伸展，同样延长了乘员的停止时间。
- 运动中的防摔垫——体操运动员落在厚垫子上，增加停止时间，减小峰值力。
9. Worked Examples | 典型例题
Example 1: Basic momentum calculation – A tennis ball of mass 0.06 kg moves at 25 m/s. Find its momentum.
例题1：基础动量计算——一个质量为0.06 kg 的网球以 25 m/s 的速度运动。求其动量。
p = m v = 0.06 × 25 = 1.5 kg m/s
Example 2: Conservation of momentum in a collision – A toy car of mass 2 kg moving at 3 m/s to the right collides with a stationary car of mass 1 kg. After the collision they stick together. Find their common velocity.
例题2：碰撞中的动量守恒——一辆质量为2 kg的玩具车以3 m/s的速度向右运动，与一辆静止的质量为1 kg的小车相撞。碰撞后它们粘在一起。求共同速度。
ntum before = 2×3 + 1×0 = 6 kg m/s. After, combined mass = 3 kg. Let v be common velocity.
取向右为正。碰撞前总动量 = 2×3 + 1×0 = 6 kg m/s。碰撞后总质量 = 3 kg。设共同速度为 v。
6 = 3 v ⇒ v = 2 m/s (to the right)
Example 3: Impulse and force – A 0.15 kg cricket ball is bowled at 20 m/s and hit back at 30 m/s in the opposite direction. The bat is in contact with the ball for 0.05 s. Calculate the average force exerted by the bat.
例题3：冲量与力——一个0.15 kg 的板球以20 m/s投出，被反向击回时速度为30 m/s。球拍与球接触时间为0.05 s。计算球拍施加的平均力。
(-30) = -4.5 kg m/s. Change in momentum Δp = -4.5 - 3 = -7.5 kg m/s. Impulse = F Δt = -7.5 ⇒ F = -7.5 / 0.05 = -150 N. The force is 150 N opposite to the initial direction.
初动量 = 0.15×20 = 3 kg m/s（设为正）。末动量 = 0.15×(-30) = -4.5 kg m/s。动量变化 Δp = -4.5 - 3 = -7.5 kg m/s。冲量 F Δt = -7.5 ⇒ F = -7.5/0.05 = -150 N。力大小为150 N，方向与初始方向相反。
Published by TutorHao | Physics Revision Series | aleveler.com
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