Mass and Inertia | 质量与惯性

📚 Mass and Inertia | 质量与惯性

In A-level Physics, mass and inertia are foundational concepts that explain why objects resist changes in their state of motion. Mass is a measure of the amount of matter in an object, while inertia is the property that makes an object continue doing what it is already doing unless an external force acts on it. Understanding the relationship between mass and inertia is essential for mastering Newton’s laws of motion and for analysing the behaviour of objects from everyday life to space travel.

在 A-level 物理中，质量与惯性是解释物体为何抵抗运动状态变化的基础概念。质量是物体所含物质多少的量度，而惯性是使物体保持原有运动状态的性质，除非受到外力作用。理解质量与惯性之间的关系对于掌握牛顿运动定律以及分析从日常生活到航天飞行中物体的行为至关重要。

1. Introduction to Mass and Inertia | 质量与惯性概述

Mass is a scalar quantity that measures the amount of matter in a body. In the International System of Units (SI), mass is measured in kilograms (kg). Inertia, on the other hand, is not a quantity that can be measured directly with a single instrument; it is a property of matter that describes the resistance of an object to any change in its velocity. The concept of inertia was formalised by Galileo and later incorporated into Newton’s first law of motion.

质量是一个标量，用于衡量物体所含物质的多少。在国际单位制（SI）中，质量的单位是千克（kg）。而惯性并不是一个可以用单一仪器直接测量的量；它是物质的一种属性，描述物体对其速度任何变化的抵抗能力。惯性的概念由伽利略正式提出，后来被纳入牛顿第一运动定律。

In classical mechanics, mass is constant for a given object and does not depend on location, velocity or temperature, provided the object is not travelling at relativistic speeds. Inertia is directly related to mass: the greater the mass of an object, the greater its inertia.

在经典力学中，对于一个给定的物体，只要其速度不接近相对论速度，质量就是恒定的，与位置、速度或温度无关。惯性与质量直接相关：物体的质量越大，其惯性就越大。

2. Defining Inertia | 惯性的定义

Inertia is the tendency of an object to resist any change in its state of rest or uniform motion in a straight line. This means that a stationary object will remain stationary, and a moving object will continue moving at the same speed and in the same direction, unless acted upon by a net external force.

惯性是物体抵抗其静止状态或匀速直线运动状态发生任何变化的趋势。这意味着静止的物体会保持静止，运动的物体会以相同的速度沿相同方向继续运动，除非受到净外力作用。

Inertia is often described as a ‘laziness’ of matter, but it is more accurately understood as a fundamental property of mass. It does not require any energy to maintain motion; energy is only required to change the state of motion. For example, a spacecraft travelling through deep space continues moving without any engine thrust because there is no external force to stop it.

惯性常被描述为物质的“惰性”，但更准确地说，它是质量的一种基本属性。维持运动不需要任何能量；改变运动状态才需要能量。例如，一艘在深空中飞行的航天器不需要发动机推力就能继续运动，因为没有外力使它停下来。

3. Mass as a Measure of Inertia | 质量作为惯性的量度

Mass is the quantitative measure of inertia. If two objects are subjected to the same net force, the object with the larger mass will experience a smaller acceleration. This is because a larger mass has more inertia and therefore resists the change in motion more strongly.

质量是惯性的定量量度。如果两个物体受到相同的净力，质量较大的物体加速度较小。这是因为较大的质量具有更大的惯性，因此更强烈地抵抗运动状态的变化。

Consider pushing a shopping trolley and a loaded lorry with the same force. The trolley accelerates easily, while the lorry barely moves. The lorry has much greater mass and therefore much greater inertia. In this sense, mass tells us how hard it is to change an object’s velocity.

考虑用同样的力推动一辆购物车和一辆满载的卡车。购物车很容易加速，而卡车几乎不动。卡车质量大得多，因此惯性也大得多。从这个意义上说，质量告诉我们改变物体速度有多困难。

Inertia depends only on mass, not on the object’s current velocity. A fast-moving bullet has a small mass and therefore small inertia, whereas a slow-moving oil tanker has enormous mass and enormous inertia, even though its speed may be low.

惯性只取决于质量，而不取决于物体当前的速度。高速飞行的子弹质量小，因此惯性小；而缓慢航行的油轮质量巨大，惯性也巨大，尽管其速度可能很低。

4. Newton’s First Law of Motion | 牛顿第一运动定律

Newton’s first law of motion, often called the law of inertia, states that an object will remain at rest or move with constant velocity in a straight line unless acted upon by a net external force. This law provides a qualitative definition of force: a force is that which changes the state of motion of an object.

牛顿第一运动定律，通常称为惯性定律，指出：除非受到净外力作用，否则物体将保持静止或沿直线做匀速运动。该定律给出了力的定性定义：力是改变物体运动状态的原因。

Mathematically, if the net external force on an object is zero, then the acceleration is zero:

如果物体所受的净外力为零，则加速度为零：

ΣF = 0 ⇒ a = 0

This means that when forces are balanced, there is no change in velocity. The object may be at rest (v = 0) or moving with constant velocity (v = constant). Many students mistakenly believe that a constant force is needed to keep an object moving at constant velocity; in reality, when friction is negligible, no force is needed to maintain uniform motion.

这意味着当力平衡时，速度没有变化。物体可能静止（v = 0），也可能以恒定速度运动（v = 常数）。许多学生错误地认为需要恒定的力来维持物体做匀速运动；实际上，当摩擦可以忽略

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