Momentum for GCSE WJEC Physics | GCSE WJEC 物理：动量考点精讲

📚 Momentum for GCSE WJEC Physics | GCSE WJEC 物理：动量考点精讲

Momentum is a fundamental concept in the WJEC GCSE Physics specification. It explains how objects behave in collisions and explosions, and it provides the scientific basis for understanding car safety features. A solid grasp of momentum, its conservation, and its relationship with force will help you tackle calculations and descriptive questions confidently.

动量是 WJEC GCSE 物理考试大纲中的基础概念。它解释物体在碰撞和爆炸中的行为，并为理解汽车安全装置提供科学依据。牢固掌握动量、动量守恒及其与力的关系，将帮助你自信地应对计算题和描述性问题。

1. What is Momentum? | 什么是动量？

Momentum is a property that all moving objects possess. It is defined as the product of an object’s mass and its velocity.

动量是所有运动物体都拥有的一种属性。它被定义为物体的质量与速度的乘积。

The symbol for momentum is p, and it is measured in kilogram metres per second (kg m/s). A stationary object has zero momentum because its velocity is zero.

动量的符号是 p，单位为千克米每秒（kg m/s）。静止的物体动量为零，因为它的速度为零。

Momentum is a vector quantity. This means it has both magnitude and direction. The direction of the momentum is the same as the direction of the object’s velocity. When solving problems, you must assign a positive direction and treat opposite directions as negative.

动量是矢量。这意味着它既有大小也有方向。动量的方向与物体速度的方向一致。解题时，你必须规定一个正方向，并将相反方向视为负方向。

2. Calculating Momentum | 动量计算

The momentum of an object can be calculated using the equation:

物体的动量可以用以下公式计算：

p = m × v

where p is momentum (kg m/s), m is mass (kg) and v is velocity (m/s).

其中 p 是动量（kg m/s），m 是质量（kg），v 是速度（m/s）。

For example, a car of mass 1200 kg moving at a velocity of 15 m/s has a momentum of p = 1200 × 15 = 18 000 kg m/s.

例如，一辆质量为 1200 kg、速度为 15 m/s 的汽车，其动量为 p = 1200 × 15 = 18 000 kg m/s。

If the same car travels in the opposite direction at the same speed, its velocity is −15 m/s if we define the original direction as positive. Its momentum would then be −18 000 kg m/s, clearly showing the directional nature of momentum.

如果同一辆车以相同速率向相反方向行驶，并规定原来方向为正，则其速度为 −15 m/s。此时动量变为 −18 000 kg m/s，清楚地显示出动量的方向性。

3. Newton’s Second Law in Terms of Momentum | 用动量表述牛顿第二定律

Newton’s Second Law can be written in terms of momentum. The resultant force acting on an object is equal to the rate of change of its momentum.

牛顿第二定律可以用动量表述。作用在物体上的合力等于其动量的变化率。

F = Δp / Δt

where F is the resultant force (N), Δp is the change in momentum (kg m/s), and Δt is the time taken for the change (s).

其中 F 是合力（N），Δp 是动量的变化量（kg m/s），Δt 是变化所用的时间（s）。

If the mass of the object remains constant, Δp = m × (v − u), where u is initial velocity and v is final velocity. Substituting this gives the familiar F = m × a, because acceleration a = (v − u) / Δt. This shows that the momentum form is a more general statement of the law.

如果物体质量恒定，则 Δp = m × (v − u)，其中 u 为初速度，v 为末速度。代入后可得熟悉的公式 F = m × a，因为加速度 a = (v − u) / Δt。这说明动量形式是牛顿第二定律更普适的表述。

4. Force, Time and Change in Momentum | 力、时间与动量变化

The equation F = Δp / Δt can be rearranged to Δp = F × Δt. The product of force and the time for which it acts is equal to the change in momentum. This quantity is sometimes referred to as impulse.

公式 F = Δp / Δt 可变形为 Δp = F × Δt。力与其作用时间的乘积等于动量的变化量。这个量有时被称为冲量。

A larger force applied over a short time can cause the same change in momentum as a smaller force acting over a longer time. This idea is crucial for understanding safety features.

在短时间内施加较大的力，与在较长时间内施加较小的力，可以引起相同的动量变化。这一概念对理解安全装置至关重要。

On a force–time graph, the area under the curve represents the change in momentum (impulse). In many GCSE questions, you simply use F = (mv − mu) / t.

在力–时间图上，曲线下的面积代表动量的变化量（冲量）。在多数 GCSE 考题中，你只需直接使用 F = (mv − mu) / t 计算。

5. Conservation of Momentum | 动量守恒

In a closed system where no external forces act, the total momentum before an event is equal to the total momentum after the event. This is the principle of conservation of momentum.

在没有外力作用的封闭系统中，事件发生前的总动量等于事件发生后的总动量。这就是动量守恒原理。

For two objects, A and B, the conservation law is written as:

对两个物体 A 和 B，动量守恒定律写作：

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

where m₁ and m₂ are masses, u₁ and u₂ are initial velocities, and v₁ and v₂ are final velocities. All velocities must be taken with their correct signs.

其中 m₁ 和 m₂ 为质量，u₁ 和 u₂ 为初速度，v₁ 和 v₂ 为末速度。所有速度必须带上正确的正负号。

This principle applies to collisions and explosions. The total momentum vector is conserved, so you must consider direction when adding momenta.

该原理适用于碰撞和爆炸。总动量矢量是守恒的，因此在累加动量时必须考虑方向。

6. Collisions | 碰撞

When two objects collide, they exert equal and opposite forces on each other for the same time. As a result, the total momentum of the system remains constant.

当两个物体碰撞时，它们在相同时间内对彼此施加大小相等、方向相反的力。因此，系统的总动量保持不变。

If the two objects join together after the collision, it is a completely inelastic collision. The final combined mass moves with a common velocity v. The momentum equation becomes:

如果碰撞后两个物体粘在一起，则为完全非弹性碰撞。合并后的整体以共同速度 v 运动。动量方程变为：

m₁ u₁ + m₂ u₂ = (m₁ + m₂) v

In WJEC questions, you will be given three of the variables and asked to calculate the fourth. Always identify the positive direction before substituting values.

在 WJEC 考题中，通常会给出四个变量中的三个，要求你计算第四个。代入数值前务必先确定正方向。

7. Explosions | 爆炸

An explosion is the opposite of a perfectly inelastic collision. Initially, the parts are together with zero total momentum. After the explosion, they fly apart. By conservation of momentum, the total final momentum must also be zero.

爆炸与完全非弹性碰撞相反。最初，各部分连在一起，总动量为零。爆炸后，它们向各个方向飞出。根据动量守恒，末总动量也必定为零。

For two fragments:

对于两个碎片：

0 = m₁ v₁ + m₂ v₂

which leads to m₁ v₁ = −m₂ v₂. This means the fragments move in opposite directions, and the heavier fragment recoils more slowly.

由此可得 m₁ v₁ = −m₂ v₂。这意味着两个碎片沿相反方向运动，且质量较大的碎片反冲速度更慢。

This explains why a cannon recoils when firing a cannonball, and why a rocket moves forward by expelling gas backwards.

这就解释了为什么大炮发射炮弹时会后退，以及为什么火箭向后喷射气体而向前运动。

8. Elastic and Inelastic Collisions | 弹性碰撞与非弹性碰撞

Collisions can also be classified by whether kinetic energy is conserved.

碰撞还可根据动能是否守恒进行分类。

Elastic collision	Kinetic energy is conserved. Momentum is conserved. Objects bounce apart without permanent deformation or heat generation. Examples: collisions of ideal gas molecules, nearly elastic bounces of hard steel balls.
Inelastic collision	Kinetic energy is NOT conserved. Some kinetic energy is transformed into heat, sound or internal energy. Momentum is still conserved. Most everyday collisions are inelastic. A completely inelastic collision is one where objects stick together, losing the maximum possible kinetic energy.

弹性碰撞：动能守恒，动量守恒。物体弹开，不发生永久形变或生热。例如理想气体分子的碰撞、硬钢球近乎弹性的碰撞。

非弹性碰撞：动能不守恒，部分动能转化为热能、声能或内能。动量仍然守恒。大多数日常碰撞都是非弹性的。完全非弹性碰撞是指物体粘在一起，损失最大可能的动能。

In WJEC GCSE, you are not required to perform detailed kinetic energy calculations for every collision, but you should understand that in an elastic collision total KE is the same before and after.

在 WJEC GCSE 考试中，不要求每次碰撞都进行详细的动能计算，但你应当理解，在弹性碰撞中总动能前后相等。

9. Safety Features: Crumple Zones, Airbags and Seatbelts | 安全装置：溃缩区、安全气囊与安全带

Modern vehicles include safety features designed to reduce the forces acting on occupants during a crash. They all work on the principle of increasing the time over which the change in momentum occurs.

现代车辆包含旨在减少碰撞中乘员所受力度的安全装置。它们的工作原理都是延长动量变化发生的时间。

Crumple zones at the front and rear of a car are designed to collapse in a controlled way. They increase the collision time, and since Δp is fixed for a given crash, the force F = Δp / Δt is reduced.

汽车前后端的溃缩区设计为以受控方式塌陷，延长碰撞时间。对于给定碰撞，Δp 是固定的，所以力 F = Δp / Δt 就会减小。

Airbags inflate rapidly and provide a soft cushion. They increase the time it takes for the driver’s head and chest to come to rest, spreading the force over a larger area and reducing the peak force.

安全气囊在碰撞瞬间迅速充气，提供柔软缓冲。它延长了驾驶员头部和胸部减速至静止的时间，将力分散到更大面积，从而降低峰值力。

Seatbelts restrain passengers and also give a little stretch. This stretch slightly increases the stopping time for the wearer, decreasing the force experienced. They also prevent secondary collisions with the dashboard or windscreen.

安全带约束乘客，并且有少量拉伸。这种拉伸略微增加了佩戴者停止的时间，减小了受力。同时，它们还能防止与仪表盘或挡风玻璃的二次碰撞。

All these features demonstrate the practical importance of the relationship F = Δp / Δt.

所有这些装置都体现了 F = Δp / Δt 这一关系在实际中的重要应用。

10. Key Equations and Exam Tips | 核心公式与考试技巧

Essential equations you must recall:

必须记住的关键公式：

p = m × v

p = m × v
F = Δp / Δt and Δp = F × Δt

F = Δp / Δt 以及 Δp = F × Δt
F = (mv − mu) / t

F = (mv − mu) / t
Conservation of momentum: total p before = total p after

动量守恒：碰撞前总 p = 碰撞后总 p

Common pitfalls and tips:

常见错误与建议：

Always assign a positive direction and stick to it. Velocities in the opposite direction must be negative.

一定要规定正方向并始终遵循，相反方向的速度必须为负值。
Check that all mass units are in kg and velocity units in m/s before calculating. Momentum is in kg m/s.

计算前检查所有质量单位是否为 kg，速度单位是否为 m/s。动量单位是 kg m/s。
When an object sticks to another, use the combined mass. When it bounces back, the final velocity sign may reverse.

当物体粘在一起时，使用合并后的质量。当物体反弹时，末速度的符号可能要反号。
In explanation questions, always link back to the idea that increasing collision time reduces the force for a given change in momentum.

在解释类问题中，始终要联系到“对于给定的动量变化，延长碰撞时间可以减小力”这一思路。
Practice rearranging the momentum equations quickly and accurately.

练习快速、准确地变形动量方程。

Momentum questions in WJEC GCSE Physics often combine calculations with written explanations. Mastering both the mathematical and conceptual sides will help you achieve the highest marks.

WJEC GCSE 物理中的动量考题往往将计算与文字解释相结合。同时掌握数学计算和概念理解，将帮助你取得最高分。

Published by TutorHao | GCSE Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Momentum for GCSE WJEC Physics | GCSE WJEC 物理：动量考点精讲