📚 GCSE OCR Physics: Momentum – Revision Guide | GCSE OCR 物理：动量考点精讲
Welcome to this comprehensive revision guide on momentum for OCR GCSE Physics. Momentum helps explain how objects interact during collisions, explosions, and when forces act over time. Mastering this topic is essential for tackling calculation questions and understanding real-world safety applications.
欢迎阅读这篇面向OCR GCSE物理的动量综合复习指南。动量帮助我们解释物体在碰撞、爆炸以及力持续作用时的相互作用。掌握这一主题对于解答计算题和理解现实世界中的安全应用至关重要。
1. What is Momentum? | 什么是动量？
In physics, momentum is a measure of the motion of an object and depends on both its mass and velocity. It tells us how hard it is to stop a moving object – a heavy lorry has more momentum than a bicycle at the same speed.
在物理中，动量是描述物体运动量的指标，它取决于质量和速度。动量表明让运动的物体停下来有多困难——与自行车相比，以相同速度行驶的重型卡车具有更大的动量。
Momentum (symbol p) is a vector quantity, meaning it has both magnitude and direction. The direction of momentum is always the same as the direction of the object’s velocity.
动量（符号 p）是一个矢量，既有大小也有方向。动量的方向总是与物体速度的方向相同。
The equation for momentum is:
p = m × v
动量的计算公式为：
p = m × v
where p is momentum in kilogram metres per second (kg·m/s), m is mass in kilograms (kg), and v is velocity in metres per second (m/s).
式中 p 为动量，单位是千克·米/秒（kg·m/s），m 为质量，单位为千克（kg），v 为速度，单位为米/秒（m/s）。
2. Momentum as a Vector | 动量——矢量
Because velocity is a vector, momentum also has direction. When solving problems, we must assign positive and negative signs to represent opposite directions. For example, moving to the right could be positive, and moving to the left negative.
由于速度是矢量，动量也具有方向。在解题时，我们必须用正负号表示相反的方向。例如，向右运动可以定为正，向左运动定为负。
If a 2 kg ball moves to the right at 3 m/s, its momentum is +6 kg·m/s. If it bounces back to the left at 3 m/s, its momentum becomes –6 kg·m/s. The change in momentum is therefore –6 – (+6) = –12 kg·m/s, with the negative sign showing the change is opposite to the initial direction.
如果一个2 kg的小球以3 m/s向右运动，其动量为 +6 kg·m/s。如果它以3 m/s的速度弹回向左，动量变为 –6 kg·m/s。因此动量的变化量为 –6 – (+6) = –12 kg·m/s，负号表示变化方向与初始方向相反。
3. Calculating Momentum | 动量计算
A car of mass 1200 kg travels at 15 m/s. Its momentum is calculated as:
p = 1200 kg × 15 m/s = 18 000 kg·m/s
一辆质量为 1200 kg 的汽车以 15 m/s 的速度行驶。其动量计算如下：
p = 1200 kg × 15 m/s = 18 000 kg·m/s
If a bus has a momentum of 60 000 kg·m/s and its mass is 8000 kg, its velocity is v = p / m = 60 000 / 8000 = 7.5 m/s.
如果一辆公共汽车的动量为 60 000 kg·m/s，质量为 8000 kg，则其速度为 v = p / m = 60 000 / 8000 = 7.5 m/s。
Always remember to use SI units: mass in kg and velocity in m/s. Convert grams to kilograms and km/h to m/s before substituting into the formula.
务必始终使用国际单位制：质量用千克，速度用米/秒。代入公式前，先将克转换为千克，千米/时转换为米/秒。
4. Conservation of Momentum | 动量守恒
In a closed system (no external forces act), the total momentum before an event is equal to the total momentum after the event. This is called the principle of conservation of momentum.
在封闭系统（无外力作用）中，事件发生前的总动量等于事件发生后的总动量。这就是动量守恒定律。
For two objects colliding, the conservation can be written as:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
对于两个物体发生碰撞，动量守恒可写作：
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where m₁ and m₂ are masses, u₁ and u₂ are initial velocities, and v₁ and v₂ are final velocities. Remember that velocities can be positive or negative depending on direction.
式中 m₁ 和 m₂ 为质量，u₁ 和 u₂ 为初速度，v₁ 和 v₂ 为末速度。注意速度根据方向可正可负。
5. Collisions and Momentum Conservation | 碰撞与动量守恒
When two objects collide, they exert equal and opposite forces on each other. If no external forces act, the total momentum is conserved. This allows us to find unknown velocities after the collision.
两个物体碰撞时，它们相互施加大小相等、方向相反的力。如果没有外力作用，总动量守恒。这使我们能够求出碰撞后的未知速度。
Consider a 2 kg trolley moving at 4 m/s rightwards colliding with a stationary 1 kg trolley. After the collision they stick together. Total momentum before: 2×4 + 1×0 = 8 kg·m/s. Combined mass = 3 kg, so v = 8 / 3 ≈ 2.67 m/s to the right.
m₁u₁ + m₂u₂ = (m₁ + m₂)v
假设一辆 2 kg 的小车以 4 m/s 向右运动，撞上静止的 1 kg 小车，碰撞后两车粘在一起。碰撞前总动量为：2×4 + 1×0 = 8 kg·m/s。总质量为 3 kg，因此 v = 8 / 3 ≈ 2.67 m/s，方向向右。
m₁u₁ + m₂u₂ = (m₁ + m₂)v
If the trolleys bounce apart, the same conservation equation applies, but you must assign positive and negative signs to velocities in opposite directions.
如果小车碰后分开，动量守恒方程同样适用，但你必须对相反方向的速度赋予正负号。
6. Explosions and Recoil | 爆炸与反冲
An explosion is essentially a collision in reverse. Initially, the total momentum of the system is zero because the objects are at rest. After the explosion, they move apart with equal and opposite momentum.
爆炸本质上是碰撞的反过程。最初系统的总动量为零，因为物体静止。爆炸后它们分开运动，且动量大小相等、方向相反。
For two fragments of masses m₁ and m₂ ejected in opposite directions:
0 = m₁v₁ + m₂v₂
对于质量分别为 m₁ 和 m₂ 的两个碎片向相反方向飞出：
0 = m₁v₁ + m₂v₂
This means m₁v₁ = –m₂v₂. If a 5 kg cannon fires a 0.1 kg cannonball at 100 m/s to the right, what is the recoil velocity of the cannon? 5×v_cannon + 0.1×100 = 0, so v_cannon = –2 m/s (to the left).
这意味着 m₁v₁ = –m₂v₂。如果一个 5 kg 的大炮向右发射一个 0.1 kg 的炮弹，速度为 100 m/s，大炮的反冲速度是多少？由 5×v_炮 + 0.1×100 = 0 得 v_炮 = –2 m/s（向左）。
7. Force and Rate of Change of Momentum | 力与动量变化率
A resultant force acting on an object causes its momentum to change. Newton’s second law can be expressed in terms of momentum:
F = Δp / Δt
作用在物体上的合力会导致其动量发生变化。牛顿第二定律可以用动量表示为：
F = Δp / Δt
Here Δp is the change in momentum (impulse), and Δt is the time over which the change occurs. This formula shows that for a given change in momentum, increasing the time reduces the force experienced.
式中 Δp 为动量的变化量（冲量），Δt 为变化发生的时间。该公式表明，对于给定的动量变化，延长作用时间可以减小所受到的力。
Alternatively, using final and initial velocities:
F = (mv – mu) / t
也可用初末速度表示为：
F = (mv – mu) / t
where u is initial velocity and v is final velocity. This relationship explains why crumple zones and airbags save lives: they increase the stopping time and thus decrease the force on occupants.
其中 u 为初速度，v 为末速度。这一关系式解释了为何褶皱区和安全气囊能挽救生命：它们增加了停止时间，从而减小了乘员受到的力。
8. Car Safety Features | 汽车安全装置
Modern vehicles use several devices designed around the principle that extending impact time reduces force. Here is a summary:
现代汽车采用多种基于延长碰撞时间以减小力这一原理的装置。以下是总结：
| Safety Feature | 安全装置 | How it works – principle | 作用原理 |
|---|---|
| Crumple zones 褶皱区 |
They deform and crush on impact, increasing the time for the car to stop. This reduces the force on passengers. 在碰撞时变形和溃缩，延长汽车停止所需的时间，从而减小乘客受到的力。 |
| Airbags 安全气囊 |
They inflate rapidly during a crash, providing a cushion that increases the time for the driver’s momentum to change to zero, decreasing the
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