📚 IGCSE Physics: Momentum Revision Guide | IGCSE 物理：动量 考点精讲
Momentum is a fundamental concept in IGCSE Physics, linking mass and velocity to describe the 'quantity of motion' of an object. This revision guide covers everything you need: definition, impulse, conservation, collisions, explosions, and real-world safety applications. Let's get started!
动量是IGCSE物理的一个核心概念，它将质量和速度联系起来，描述物体的“运动量”。这份考点精讲涵盖了你需要掌握的全部内容：定义、冲量、守恒、碰撞、爆炸以及现实中的安全应用。我们开始吧！
1. Definition of Momentum | 动量的定义
Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). It tells us how difficult it is to stop a moving object. A heavy truck moving slowly can have the same momentum as a light car moving quickly.
动量(p)的定义是物体的质量(m)与其速度(v)的乘积。它告诉我们让一个运动的物体停下来有多难。一辆缓慢行驶的重型卡车可能与一辆快速行驶的轻型轿车具有相同的动量。
2. Momentum as a Vector | 动量是矢量
Momentum is a vector quantity, meaning it has both magnitude and direction. The direction of momentum is always the same as the direction of the velocity. When solving problems, you must take account of the signs to indicate direction (e.g., positive to the right, negative to the left).
动量是矢量，既有大小也有方向。方向总是与速度的方向相同。解题时必须用正负号表示方向（例如向右为正，向左为负）。
For example, if a ball of mass 2 kg moves to the right at 3 m s⁻¹, its momentum is +6 kg m s⁻¹. If it moves to the left at 3 m s⁻¹, its momentum is -6 kg m s⁻¹.
例如，一个质量为2 kg的球以3 m s⁻¹向右运动，其动量为+6 kg m s⁻¹；如果以3 m s⁻¹向左运动，动量为-6 kg m s⁻¹。
3. Formula and Units | 公式与单位
The formula for momentum is:
p = m × v
where p is momentum (kg m s⁻¹), m is mass (kg), and v is velocity (m s⁻¹). The SI unit of momentum is kilogram metre per second (kg m s⁻¹). Momentum has no separate named unit; it is a compound unit. Another equivalent unit is newton second (N s), which appears in the impulse-momentum relationship.
动量的公式为：p = m × v，其中p为动量（单位kg m s⁻¹），m为质量（kg），v为速度（m s⁻¹）。动量的国际单位是千克米每秒（kg m s⁻¹），没有单独的名称，是复合单位。另一个等效单位是牛顿秒（N s），出现在冲量与动量的关系中。
4. Impulse and Change in Momentum | 冲量与动量变化
Impulse is defined as the product of the net force acting on an object and the time for which it acts. Impulse is a vector. Mathematically:
Impulse = F × Δt
The impulse-momentum theorem states that the impulse applied to an object equals its change in momentum:
F Δt = Δp = m v – m u
where u is initial velocity and v is final velocity. This is the most important equation in momentum topics, linking force, time, and change in motion.
冲量定义为作用在物体上的净力与作用时间的乘积，是矢量。数学表达式为：冲量 = F × Δt。冲量-动量定理指出，施加于物体的冲量等于其动量的变化量：F Δt = Δp = m v – m u，其中u为初速度，v为末速度。这是动量主题中最重要的方程，将力、时间和运动变化联系起来。
5. Impulse-Momentum Theorem in Action | 冲量-动量定理的应用
This theorem explains why crumple zones in cars increase collision time, reducing the force experienced by passengers. For the same change in momentum, increasing the time Δt decreases the average force F. Similarly, bending your knees when landing from a jump extends the stopping time, reducing the force on your legs.
该定理解释了为什么汽车的溃缩区能增加碰撞时间，从而减小乘客受到的力。对于相同的动量变化，延长作用时间Δt会减小平均力F。同样，跳落后屈膝能延长停止时间，减小腿部受力。
- Example: A 0.5 kg ball hits a wall at 10 m s⁻¹ and rebounds at 8 m s⁻¹ in the opposite direction. If the contact time is 0.1 s, find the average force on the ball.
Change in momentum = final momentum – initial momentum = (0.5 × -8) – (0.5 × 10) = -4 – time = -9 / 0.1 = -90 N (the negative sign means force is opposite to initial direction). - 例子：一个0.5 kg的球以10 m s⁻¹撞墙，并以8 m s⁻¹反向弹回。若接触时间为0.1 s，求球受到的平均力。
动量变化 = 末动量 – 初动量 = (0.5 × -8) – (0.5 × 10) = -4 – 5 = -9 kg m s⁻¹。冲量 = -9 N s。平均力 = 冲量/时间 = -9/0.1 = -90 N（负号表示力与初速反向）。
6. Newton's Second Law in Terms of Momentum | 牛顿第二定律的动量形式
Newton's second law originally stated that the net force is equal to the rate of change of momentum:
F = Δp / Δt
). The momentum form is more general and works even when mass changes (e.g., a rocket ejecting fuel).
牛顿第二定律最初表述为净力等于动量的变化率：F = Δp / Δt。在质量恒定时，简化为F = m a（因为Δp = m Δv，故F = m Δv/Δt = m a）。动量形式更为普遍，即使质量变化（如火箭喷射燃料）也适用。
7. Conservation of Momentum | 动量守恒定律
The principle of conservation of momentum states that in a closed system (no external forces), the total momentum before an interaction equals the total momentum after the interaction. Mathematically:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where subscripts 1 and 2 refer to two objects, u represents initial velocities, and v represents final velocities. This principle is derived from Newton's third law and is fundamental to collision and explosion analysis.
动量守恒定律指出，在一个封闭系统（无外力）中，相互作用前的总动量等于相互作用后的总动量。数学表示为：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂，其中下标1和2代表两个物体，u为初速度，v为末速度。该原理源于牛顿第三定律，是分析碰撞和爆炸的基础。
8. Elastic and Inelastic Collisions | 弹性与非弹性碰撞
Collisions are classified based on whether kinetic energy is conserved:
- Elastic collision: Both momentum and kinetic energy are conserved. Objects bounce apart without loss of kinetic energy. Examples: collisions between billiard balls (idealised), gas molecules.
- Inelastic collision: Momentum is conserved but kinetic energy is not (some is converted to heat, sound, or deformation). Most real collisions are inelastic. A perfectly inelastic collision is one where the objects stick together after impact and move with a common velocity.
碰撞根据动能是否守恒进行分类：
- 弹性碰撞：动量和动能都守恒。物体弹开时没有动能损失。例如：台球碰撞（理想化）、气体分子。
- 非弹性碰撞：动量守恒但动能不守恒（部分转化为热能、声能或形变）。大多数真实碰撞是非弹性的。完全非弹性碰撞是指碰撞后物体粘在一起并以共同速度运动。
To solve problems, use conservation of momentum first. If the collision is elastic, you can also equate total kinetic energy before and after.
解题时先使用动量守恒。如果是弹性碰撞，还可以令碰撞前后的总动能相等。
9. Explosions | 爆炸
An explosion is the reverse of a collision. Initially, the total momentum is zero (objects stationary). According to conservation of momentum, after an explosion the total momentum must remain zero. This means the fragments move apart with momenta that are equal in magnitude but opposite in direction. Example: a gun firing a bullet – the bullet gains forward momentum, and the gun recoils backward with equal and opposite momentum.
爆炸是碰撞的逆过程。初始时总动量为零（物体静止）。根据动量守恒，爆炸后总动量必须保持为零。这意味着碎片以大小相等、方向相反的动量分离。例如：枪发射子弹——子弹获得向前的动量，枪则向后反冲，动量大小相等方向相反。
mₚvₚ + mₓvₓ = 0 ⇒ mₓvₓ = - mₚvₚ
Subscripts p for projectile, g for gun.
其中p代表子弹，g代表枪。
10. Safety Features and Momentum | 安全设计与动量原理
Many vehicle safety devices are designed using momentum principles to reduce force on occupants during a crash:
- Seat belts: Restrain passengers, so they decelerate with the car, increasing stopping time and reducing force. Seat belts also stretch slightly to extend the time.
- Airbags: Inflate rapidly to provide a cushion, increasing the time over which the passenger's momentum changes, thus lowering the force.
- Crumple zones: Front and rear sections of a car are designed to crumple in a controlled way, increasing collision time and absorbing energy.
- Cycle helmets: Soft foam inside a helmet compresses during impact, increasing the stopping time for the head, hence lowering the force.
许多车辆安全装置利用动量原理来减少碰撞时乘员受到的力：
- 安全带：约束乘客，使其随车减速，增加停止时间从而减小力。安全带还能轻微拉伸以延长时间。
- 安全气囊：快速充气形成缓冲，延长乘客动量变化的时间，从而降低力。
- 溃缩区：汽车前后部设计为可控变形，增加碰撞时间并吸收能量。
- 自行车头盔：头盔内的软泡沫在撞击时被压缩，延长头部停止时间，从而减小力。
11. Worked Example: Collision Problem | 计算例题：碰撞问题
A trolley A of mass 2 kg moving at 4 m s⁻¹ collides with a stationary trolley B of mass 3 kg. After the collision, they stick together. Find the common velocity after collision.
tial momentum = 2 × 4 + 3 × 0 = 8 kg m s⁻¹. Total mass after sticking = 5 kg. So 5 × v = 8 ⇒ v = 1.6 m s⁻¹ in the same direction as A's original motion.
一辆质量为2 kg的小车A以4 m s⁻¹的速度运动，撞上静止的、质量为3 kg的小车B。碰撞后它们粘在一起。求碰撞后的共同速度。
解：根据动量守恒，总初动量 = 2×4 + 3×0 = 8 kg m s⁻¹。粘合后的总质量 = 5 kg。故5×v = 8 ⇒ v = 1.6 m s⁻¹，方向与A原来运动方向相同。
12. Exam Tips | 考试技巧
1. Always state the conservation of momentum when solving collision or explosion problems – it is often a mark point.
2. Assign positive and negative directions for velocities; momentum is a vector, and signs matter.
se = change in momentum = F Δt. Use this to explain safety features or to calculate force.
4. In collision calculations where objects stick together, the final velocity is common. Write: (m₁ + m₂)v.
5. For elastic collisions, mention that kinetic energy is conserved, but you rarely need the kinetic energy equation at IGCSE unless specifically asked.
6. Be familiar with the unit kg m s⁻¹ and its equivalence to N s.
7. Read questions carefully: 'rebound' implies velocity changes sign; 'at rest' means zero velocity; 'combine' means they stick together.
1. 解碰撞或爆炸问题时一定要先陈述动量守恒定律，这通常是得分点。
2. 为速度规定正负方向；动量是矢量，符号至关重要。
3. 记住冲量=动量变化=FΔt，用它来解释安全设计或计算力。
4. 在物体粘在一起的碰撞计算中，末速度相同。要写出：(m₁+m₂)v。
5. 对于弹性碰撞，要说明动能守恒，但IGCSE很少需要你使用动能方程，除非特别要求。
6. 熟悉单位kg m s⁻¹及其与N s的等价关系。
7. 仔细审题：“反弹”意味着速度变号；“静止”意味着速度为零；“结合在一起”意味着它们粘在一起。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图