📚 Motion, Forces and Energy | 运动、力与能量
This revision guide covers the essential concepts of motion, forces, and energy for the Cambridge IGCSE Physics syllabus. You will explore how objects move, why they move, and how energy is transferred in mechanical systems. A clear understanding of these foundational topics is crucial for tackling both theory and practical questions in your examination.
本复习指南涵盖了剑桥 IGCSE 物理教学大纲中运动、力与能量的核心概念。你将探究物体如何运动、为何运动以及能量如何在力学系统中传递。透彻理解这些基础主题对于应对考试中的理论与实验题目至关重要。
1. Scalars and Vectors | 标量与矢量
Scalar quantities have magnitude only. Examples include distance, speed, mass, time, energy, and temperature. When you add scalars, you simply use ordinary arithmetic.
标量只有大小。例子包括距离、速率、质量、时间、能量和温度。对标量进行加法运算时，直接使用普通的算术运算即可。
Vector quantities have both magnitude and direction. Displacement, velocity, acceleration, force, weight, and momentum are all vectors. The direction of a vector is often shown using an arrow, where the length represents the magnitude and the arrowhead indicates the direction. Adding vectors requires considering their directions; if they act along the same line, assign positive and negative signs.
矢量既有大小又有方向。位移、速度、加速度、力、重量和动量都是矢量。矢量的方向通常用箭头表示，箭头长度代表大小，箭头指向表示方向。将矢量相加时必须考虑方向；如果它们沿同一直线作用，则赋予正负号。
A resultant vector is the single vector that has the same effect as two or more vectors acting together. You can find the resultant of perpendicular vectors using Pythagoras’ theorem.
合矢量是一个单一的矢量，其作用效果与两个或多个矢量共同作用的效果相同。你可以使用勾股定理求出相互垂直的矢量的合矢量。
2. Speed and Velocity | 速率与速度
Speed is the rate at which distance is covered. It is a scalar: average speed = total distance ÷ total time. The SI unit is metres per second (m/s). In everyday life, speed may also be given in kilometres per hour (km/h).
速率是距离变化的快慢。它是一个标量：平均速率 = 总距离 ÷ 总时间。国际单位是米每秒（m/s）。在日常生活中，速率也可能用千米每小时（km/h）表示。
Velocity is the rate of change of displacement. It is a vector, so direction matters. Average velocity = total displacement ÷ total time. If an object moves in a straight line without turning, its speed and the magnitude of its velocity are equal.
速度是位移的变化率。它是一个矢量，因此方向很重要。平均速度 = 总位移 ÷ 总时间。如果一个物体沿直线运动且不转弯，其速率与速度大小相等。
Constant velocity means both constant speed and constant direction. Any change in speed or direction results in a change in velocity.
匀速意味着速率和方向均不变。速率或方向的任何改变都会导致速度发生变化。
3. Acceleration | 加速度
Acceleration is the rate of change of velocity. It is a vector: a = Δv ÷ t, where Δv is the change in velocity. Acceleration occurs when an object speeds up, slows down (deceleration/negative acceleration) or changes direction.
加速度是速度的变化率。它是一个矢量：a = Δv ÷ t，其中 Δv 是速度的变化量。当物体加速、减速（负加速度）或改变方向时，都在发生加速度。
The SI unit of acceleration is m/s² (metres per second squared). An acceleration of 3 m/s² means the velocity increases by 3 m/s every second.
加速度的国际单位是 m/s²（米每二次方秒）。加速度为 3 m/s² 意味着速度每秒增加 3 m/s。
a = (v – u) ÷ t
where u is initial velocity, v is final velocity and t is time taken.
其中 u 是初速度，v 是末速度，t 是所用时间。
4. Distance-Time Graphs | 距离-时间图
A distance-time graph shows how an object’s distance from a starting point changes with time. The gradient of the graph represents the object’s speed.
距离-时间图显示物体离起点的距离如何随时间变化。图的斜率表示物体的速率。
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A straight, sloping line indicates constant speed. The steeper the slope, the greater the speed.
一条倾斜的直线表示匀速。斜率越陡，速率越大。
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A horizontal line means the object is stationary (distance does not change).
水平线表示物体静止（距离不变）。
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A curved line shows changing speed. If the curve is getting steeper, the object is accelerating.
曲线表示速率在变化。如果曲线变得越来越陡，物体正在加速。
To determine instantaneous speed from a curve, draw a tangent at the point of interest and calculate its gradient.
要从曲线上确定瞬时速率，在感兴趣的点处画一条切线，并计算其斜率。
5. Velocity-Time Graphs | 速度-时间图
A velocity-time graph plots velocity on the vertical axis and time on the horizontal axis. The gradient gives the acceleration, and the area under the graph gives the displacement (distance moved in a given direction).
速度-时间图以纵轴表示速度，横轴表示时间。斜率给出加速度，图线下的面积表示位移（在给定方向上移动的距离）。
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A sloping straight line indicates constant acceleration.
倾斜直线表示匀加速度。
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A horizontal line indicates constant velocity.
水平线表示匀速。
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A line sloping downwards represents deceleration (negative acceleration).
向下倾斜的线表示减速（负加速度）。
For an object starting from rest and accelerating uniformly, the area under the v-t graph forms a triangle. The displacement can be found using area = ½ × base × height.
对于从静止开始均匀加速的物体，v-t 图下的面积构成一个三角形。位移可通过 面积 = ½ × 底 × 高 计算。
6. Equations of Motion | 运动方程
For uniformly accelerated motion in a straight line, you can use the SUVAT equations. These link displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t).
对于直线上的匀加速运动，可以使用 SUVAT 方程。它们将位移（s）、初速度（u）、末速度（v）、加速度（a）和时间（t）联系起来。
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = (u + v) t ÷ 2
Remember that these equations only apply when acceleration is constant and motion is in a straight line.
请记住，这些方程仅在加速度恒定且运动沿直线时才适用。
When using these equations, always define the positive direction first. A negative value for a, v or u indicates the opposite direction.
使用这些方程时，务必先规定正方向。a、v 或 u 为负值表示反向。
7. Forces and Newton’s Laws | 力与牛顿定律
A force is a push or pull that can change an object’s shape, speed or direction. Force is a vector quantity measured in newtons (N).
力是一种推或拉，可以改变物体的形状、速率或方向。力是矢量，单位为牛顿（N）。
Newton’s first law states that an object remains at rest or moves with constant velocity unless acted upon by a resultant external force. This is also called the law of inertia.
牛顿第一定律指出，除非受到合外力的作用，否则物体将保持静止或匀速直线运动状态。这也称为惯性定律。
Newton’s second law describes the relationship between force, mass and acceleration: the acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass.
牛顿第二定律描述了力、质量与加速度之间的关系：物体的加速度与合外力成正比，与其质量成反比。
F = m a
Newton’s third law says that when object A exerts a force on object B, object B simultaneously exerts an equal and opposite force on object A. These action-reaction pairs act on different bodies.
牛顿第三定律指出，当物体 A 对物体 B 施加一个力时，物体 B 同时会对物体 A 施加一个大小相等、方向相反的力。这些作用力与反作用力作用在不同物体上。
8. Mass, Weight and Gravity | 质量、重量与重力
Mass is the amount of matter in an object. It is a scalar, measured in kilograms (kg), and does not change with location.
质量是物体所含物质的多少。它是标量，单位为千克（kg），不随位置变化。
Weight is the gravitational force acting on an object. Weight is a vector and is measured in newtons. It always acts towards the centre of the Earth (or other massive body).
重量是作用在物体上的重力。重量是矢量，单位为牛顿。它始终指向地球（或其他大质量天体）的中心。
W = m g
On Earth, the gravitational field strength g is approximately 9.8 N/kg (often rounded to 10 N/kg in IGCSE problems). The Moon has a much smaller g (about 1.6 N/kg), so an object’s weight is much less there, even though its mass is unchanged.
在地球上，引力场强度 g 约为 9.8 N/kg（IGCSE 题目中常取 10 N/kg）。月球上的 g 小得多（约 1.6 N/kg），因此物体在月球上的重量小得多，尽管其质量不变。
9. Friction and Drag | 摩擦与阻力
Friction is a force that opposes motion between two surfaces in contact. It arises from the interlocking of microscopic irregularities. Friction can be useful (e.g. walking, braking) or a hindrance (causing wear and energy loss).
摩擦力是一种阻碍接触表面之间相对运动的力。它源于微观不平整表面的相互咬合。摩擦可能是有益的（如行走、刹车），也可能是不利的（导致磨损和能量损失）。
Drag is the resistive force experienced by an object moving through a fluid (liquid or gas). Air resistance is a common example. Drag increases with speed; for many situations, drag is proportional to speed².
阻力是物体在流体（液体或气体）中运动时所受到的抗拒力。空气阻力是一个常见例子。阻力随速度增大而增大；在许多情况下，阻力与速度的平方成正比。
When an object falls through a fluid, it eventually reaches terminal velocity: the constant speed at which the upward drag force exactly balances the downward weight. At terminal velocity, the resultant force is zero and acceleration ceases.
当物体在流体中下落时，最终会达到终极速度：此时向上的阻力恰好与向下的重力平衡，物体以恒定速度下落。在终极速度下，合力为零，加速度为零。
10. Work, Energy and Power | 功、能量与功率
Work is done when a force moves an object in the direction of the force. Work is a scalar quantity measured in joules (J).
当力使物体沿力的方向移动时，就做了功。功是标量，单位为焦耳（J）。
W = F d
where F is the magnitude of the force and d is the distance moved in the direction of the force. If the force is at an angle, only the component of the force parallel to the displacement does work.
其中 F 是力的大小，d 是沿力的方向移动的距离。如果力有角度，则只有与位移平行的分力做功。
Energy is the capacity to do work. Kinetic energy (Ek) is the energy of motion: Ek = ½ m v². Gravitational potential energy (Ep) is the energy stored due to an object’s position in a gravitational field: Ep = m g h, where h is the height above a reference level.
能量是做功的能力。动能（Ek）是运动的能量：Ek = ½ m v²。重力势能（Ep）是由于物体在重力场中的位置而储存的能量：Ep = m g h，其中 h 是相对于某一参考水平的高度。
Power is the rate of doing work or transferring energy: P = W ÷ t, measured in watts (W). One watt is one joule per second.
功率是做功或转化能量的快慢：P = W ÷ t，单位为瓦特（W）。一瓦特等于每秒一焦耳。
11. Conservation of Energy | 能量守恒
The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transferred from one form to another, or moved from one place to another. The total energy of a closed system remains constant.
能量守恒原理指出，能量既不能被创造也不能被消灭；它只能从一种形式转化为另一种形式，或从一个地方转移到另一个地方。封闭系统的总能量保持不变。
In a pendulum swinging in a vacuum, energy continuously converts between gravitational potential energy and kinetic energy. At the highest points, Ep is maximum and Ek is zero; at the lowest point, Ek is maximum and Ep is minimum. In reality, some energy is dissipated as thermal energy due to air resistance.
在真空中摆动的摆锤，能量在重力势能和动能之间不断转换。在最高点，Ep 最大而 Ek 为零；在最低点，Ek 最大而 Ep 最小。现实中，由于空气阻力，部分能量会以热能的形式耗散。
Energy efficiency is given by: useful output energy ÷ total input energy × 100%. Many systems waste energy as heat; designing low-friction components improves efficiency.
能量效率由下式给出：有效能量输出 ÷ 总能量输入 × 100%。许多系统以热能形式浪费能量；设计低摩擦部件可以提高效率。
12. Momentum | 动量
Momentum is a property of moving objects and is defined as the product of mass and velocity. It is a vector: p = m v, with units kg m/s.
动量是运动物体的属性，定义为质量与速度的乘积。它是矢量：p = m v，单位为 kg m/s。
The law of conservation of momentum states that in a closed system, the total momentum before a collision or explosion equals the total momentum after the event, provided no external resultant force acts.
动量守恒定律指出，在封闭系统中，如果没有外部合力作用，碰撞或爆炸前的总动量等于事件后的总动量。
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
Force is also related to the rate of change of momentum: F = Δp ÷ t. This explains why crumple zones in cars and airbags reduce injury – they increase the time over which momentum changes, reducing the force.
力还与动量的变化率有关：F = Δp ÷ t。这解释了为何汽车的碰撞褶皱区和安全气囊能减少伤害——它们延长了动量变化的时间，从而减小了力。
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