Momentum and Impulse: Key Points for IGCSE OCR Maths | IGCSE OCR 数学：动量与冲量考点精讲

📚 Momentum and Impulse: Key Points for IGCSE OCR Maths | IGCSE OCR 数学：动量与冲量考点精讲

In IGCSE OCR Mathematics, the topic of momentum and impulse appears in the applied module. Understanding these concepts is essential for solving collision and explosion problems, as well as interpreting force–time graphs. This article covers all key points with clear explanations, worked examples, and exam tips.

在IGCSE OCR数学中，动量与冲量出现在应用数学模块。理解这些概念对解决碰撞和爆炸问题以及解读力-时间图至关重要。本文涵盖所有考点，包括清晰解释、例题和考试技巧。

1. Introduction to Linear Momentum | 线动量简介

Linear momentum (often simply called momentum) is the product of an object’s mass and its velocity. It is a vector quantity, so it has both magnitude and direction. The direction of the momentum vector is the same as the direction of the velocity. Momentum is denoted by p and its SI unit is kilogram metre per second (kg m s⁻¹).

线动量（通常简称动量）是物体质量与速度的乘积。动量是矢量，既有大小又有方向；其方向与速度方向相同。动量用符号 p 表示，国际单位是千克·米每秒 (kg m s⁻¹)。

Because momentum is a vector, two objects moving in opposite directions can have momenta that cancel each other out when added. This property is crucial in conservation problems.

由于动量是矢量，两个沿相反方向运动的物体，其动量相加时可以相互抵消。这一性质在守恒问题中至关重要。

The formula for linear momentum is:

线动量的公式为：

p = m v

where m is mass in kilograms and v is velocity in metres per second. Always convert mass to kilograms before calculating.

其中 m 为质量（千克），v 为速度（米/秒）。计算前务必先将质量转换为千克。

2. Impulse and Change in Momentum | 冲量与动量变化

Impulse measures the effect of a force acting over a time interval. For a constant force F applied for a time Δt, the impulse J is given by:

冲量是力在一段时间内作用的累积效应。对于恒力 F 作用时间 Δt，冲量 J 的定义为：

J = F Δt

The unit of impulse is newton-second (N s), which is equivalent to kg m s⁻¹. The impulse imparted to an object equals its change in momentum. This is the impulse–momentum theorem:

冲量的单位是牛·秒 (N s)，与 kg m s⁻¹ 等价。物体所受冲量等于其动量的变化量，这就是冲量–动量定理：

F Δt = Δp = m v − m u

where u is initial velocity and v is final velocity. This theorem is a direct consequence of Newton’s second law: F = m a = m (Δv/Δt). Rearranging gives F Δt = m Δv.

其中 u 为初速度，v 为末速度。该定理是牛顿第二定律 F = m a = m (Δv/Δt) 的直接结果，整理后即得 F Δt = m Δv。

Impulse is a vector; its direction is the same as the change in velocity. When a collision involves a change in direction, you must assign positive and negative signs to velocities according to a chosen positive direction.

冲量也是矢量，方向与速度变化量相同。当碰撞涉及方向改变时，必须按选定的正方向赋予速度正确的正负号。

3. Impulse from Force–Time Graphs | 力-时间图的冲量

For a variable force,

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