📚 IB Edexcel Science: Forces and Motion Key Concepts | IB Edexcel 科学：力与运动 考点精讲
Forces and motion form the foundation of classical mechanics in the IB and Edexcel science curricula. Understanding how objects move, what causes changes in motion, and how to quantify these effects is essential for success in physics and combined science. This revision guide breaks down the key ideas into manageable sections, pairing English explanations with Chinese translations to reinforce learning.
力与运动是 IB 和 Edexcel 科学课程中经典力学的基础。理解物体如何运动、运动变化的原因以及如何量化这些效应，对于物理和综合科学的学习至关重要。本复习指南将核心概念分解成容易掌握的小节，用英文解释搭配中文翻译，帮助强化记忆。
1. Scalars and Vectors | 标量与矢量
Scalar quantities have only magnitude (size) with no direction. Examples include mass, time, temperature, speed, and distance. Vectors have both magnitude and direction, such as displacement, velocity, acceleration, and force. When adding vectors, direction must be considered; you can use the head-to-tail method or resolve into perpendicular components.
标量只有大小（量值）而没有方向。例如质量、时间、温度、速率和路程。矢量既有大小又有方向，如位移、速度、加速度和力。矢量相加时必须考虑方向；可以使用头尾相接法或分解为垂直分量。
- Distance vs. Displacement: Distance is the total length of the path travelled (scalar). Displacement is the straight-line distance from start to finish in a given direction (vector).
- 路程与位移：路程是运动路径的总长度（标量）。位移是从起点到终点的直线距离，带有方向（矢量）。
2. Speed, Velocity and Acceleration | 速率、速度与加速度
Speed is the rate of change of distance, while velocity is the rate of change of displacement. Average speed = total distance / total time. Acceleration is the rate of change of velocity: a = (v – u) / t, where u is initial velocity, v is final velocity, and t is time. Negative acceleration often indicates deceleration or retardation.
速率是路程的变化率，而速度是位移的变化率。平均速率 = 总路程 / 总时间。加速度是速度的变化率：a = (v – u) / t，其中 u 是初速度，v 是末速度，t 是时间。负加速度通常表示减速。
a = (v – u) / t
In a distance-time graph, the gradient gives speed. In a velocity-time graph, the gradient is acceleration, and the area under the graph gives displacement.
在路程-时间图中，斜率表示速率。在速度-时间图中，斜率表示加速度，图下的面积表示位移。
3. Newton’s First Law of Motion | 牛顿第一运动定律
An object will remain at rest or in uniform motion in a straight line unless acted upon by a resultant external force. This is the principle of inertia. If the resultant force on an object is zero, its velocity is constant (which includes being at rest).
物体将保持静止或匀速直线运动状态，除非受到合外力的作用。这就是惯性原理。如果作用在物体上的合力为零，物体的速度恒定（包括静止状态）。
This law explains why seatbelts are needed: a passenger continues moving forward when a car stops suddenly due to inertia.
这个定律解释了为什么需要安全带：当汽车突然停下时，乘客由于惯性会继续向前运动。
4. Newton’s Second Law of Motion | 牛顿第二运动定律
The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass. The equation is F = m × a, where F is resultant force in newtons (N), m is mass in kilograms (kg), and a is acceleration in metres per second squared (m s⁻²).
物体的加速度与作用在其上的合力成正比，与物体的质量成反比。公式为 F = m × a，其中 F 为合力，单位牛顿 (N)；m 为质量，单位千克 (kg)；a 为加速度，单位米每二次方秒 (m s⁻²)。
F = m × a
If mass is constant, doubling the force doubles the acceleration. If force is constant, doubling the mass halves the acceleration. Always remember that F is the net force.
如果质量恒定，力加倍则加速度加倍。如果力恒定，质量加倍则加速度减半。务必记住 F 是合力。
5. Newton’s Third Law of Motion | 牛顿第三运动定律
For every action force, there is an equal and opposite reaction force. These forces act on different objects and are of the same type. For example, when you push against a wall, the wall pushes back on you with an equal force in the opposite direction.
每一个作用力都有一个大小相等、方向相反的反作用力。这两个力作用在不同物体上，属于同种类型的力。例如，当你推墙时，墙也用同样大小的力反方向推你。
Action-reaction pairs never cancel each other out because they act on different bodies. This is why a rocket can accelerate in space: exhaust gases are pushed out backwards, and the rocket is pushed forwards.
作用力与反作用力不会相互抵消，因为它们作用在不同的物体上。这就是为什么火箭能在太空中加速：燃气向后喷出，火箭被向前推动。
6. Free-Body Diagrams and Resultant Force | 受力图与合力
A free-body diagram shows all the forces acting on a single object using arrows. Length of arrow represents magnitude, and direction indicates the force direction. Common forces include weight (W = m × g), normal reaction, friction, tension, and air resistance.
受力图用箭头表示作用在一个物体上的所有力。箭头的长度代表大小，方向指示力的方向。常见的力包括重力 (W = m × g)、法向反力、摩擦力、张力和空气阻力。
Resultant force is found by vector addition. If forces act along the same line, add or subtract them. For forces at an angle, resolve into perpendicular components (usually horizontal and vertical).
合力通过矢量合成求得。如果力在同一直线上，直接相加减。对于成角度的力，可分解为垂直分量（通常是水平和竖直方向）。
7. Mass, Weight and Gravitational Field Strength | 质量、重量与重力场强度
Mass is the amount of matter in an object and is measured in kilograms. It is a scalar and does not change with location. Weight is the gravitational force on an object: W = m × g, where g is gravitational field strength (on Earth ~9.8 N kg⁻¹). Weight is a vector directed towards the centre of the planet.
质量是物体所含物质的多少，单位为千克。质量是标量，不随位置改变。重量是作用在物体上的重力：W = m × g，其中 g 为重力场强度（地球表面约为 9.8 N kg⁻¹）。重量是矢量，方向指向地心。
W = m × g
On the Moon, g is about 1.6 N kg⁻¹, so an object’s weight is much less even though its mass remains the same.
在月球上，g 约为 1.6 N kg⁻¹，因此物体的重量远小于地球上的重量，尽管其质量保持不变。
8. Friction and Terminal Velocity | 摩擦力与终极速度
Friction is a force that opposes motion between two surfaces in contact. Air resistance (drag) is a type of friction that increases with speed. When an object falls, initially weight is greater than drag, so it accelerates. As speed increases, drag grows until it equals weight. At this point, resultant force is zero, and the object falls at a constant speed called terminal velocity.
摩擦力是阻碍接触面之间相对运动的力。空气阻力（曳力）是一种摩擦力，随速度增大而增大。物体下落时，起初重力大于阻力，因此加速。随着速度增加，阻力增大直到等于重力。此时合力为零，物体以恒定速度下落，这个速度称为终极速度。
Skydivers experience terminal velocity before opening the parachute, then a new lower terminal velocity after opening, due to increased surface area creating greater drag.
跳伞者在打开降落伞前会达到一个终极速度，打开伞后由于表面积增大产生更大的阻力，达到一个新的较低的终极速度。
9. Momentum and Impulse | 动量与冲量
Momentum (p) is the product of mass and velocity: p = m × v. It is a vector quantity with unit kg m s⁻¹. The principle of conservation of momentum states that in a closed system (no external forces), total momentum before a collision equals total momentum after.
动量 (p) 是质量与速度的乘积：p = m × v。动量是矢量，单位为 kg m s⁻¹。动量守恒定律指出，在封闭系统（无外力作用）中，碰撞前的总动量等于碰撞后的总动量。
Impulse is the change in momentum, and also equals force multiplied by time: Impulse = F × t = Δp. This is directly derived from Newton’s second law. Increasing the time of impact reduces the force for the same change in momentum — the principle behind crumple zones and air bags.
冲量是动量的变化量，也等于力乘以时间：冲量 = F × t = Δp。这直接由牛顿第二定律推导而来。在动量改变相同的情况下，延长碰撞时间可以减小力——这是汽车溃缩区和安全气囊背后的原理。
10. Work, Energy and Power in Motion | 运动中的功、能量与功率
Work is done when a force moves an object in the direction of the force: W = F × d (force times distance moved in direction of force). Energy is transferred. Gravitational potential energy (GPE) = m × g × h. Kinetic energy (KE) = ½ × m × v². In a frictionless system, mechanical energy is conserved.
当力使物体沿力的方向移动时，力做功：W = F × d（力乘以沿力方向移动的距离）。能量发生转移。重力势能 (GPE) = m × g × h。动能 (KE) = ½ × m × v²。在无摩擦系统中，机械能守恒。
KE = ½ × m × v²
Power is the rate of doing work or transferring energy: P = W / t, also P = F × v for an object moving at constant speed against a force. Unit: watt (W).
功率是做功或能量转移的速率：P = W / t，对于匀速运动的物体克服阻力时也有 P = F × v。单位：瓦特 (W)。
11. Circular Motion (Advanced) | 圆周运动（拓展）
An object moving at constant speed in a circular path is continuously changing direction, so its velocity is changing and it accelerates towards the centre. This centripetal acceleration requires a centripetal force: F = m × v² / r, where r is the radius of the circle. The centripetal force is not a new type of force but can be provided by tension, friction, or gravity.
物体以恒定速率沿圆周运动时，方向不断改变，因此速度在变化，并具有指向圆心的向心加速度。向心力由 F = m × v² / r 给出，其中 r 是圆周半径。向心力不是新型力，可以由拉力、摩擦力或重力提供。
For an object moving in a vertical circle, the magnitude of centripetal force varies, but the relationship v²/r still applies at any instant.
对于在竖直面内做圆周运动的物体，向心力的大小会变化，但在任意瞬时关系 v²/r 依然成立。
12. Experimental Skills and Graphs | 实验技能与图像分析
In forces and motion experiments, accurate measurement of time, distance, and mass is crucial. Use light gates or motion sensors to reduce human error in timing. When plotting graphs, draw a line of best fit and calculate gradient using a large triangle. Understand that the area under a velocity-time graph represents displacement, while gradient of position-time graph gives velocity.
在力与运动实验相关考题中，准确测量时间、路程和质量至关重要。使用光门或运动传感器可以减少计时的人为误差。绘制图像时，画出最佳拟合线，并用大三角形计算斜率。理解速度-时间图下的面积代表位移，位移-时间图的斜率代表速度。
Always check for proportional relationships: a straight line through the origin indicates direct proportionality, helping verify laws like F ∝ a (with constant mass).
务必检查比例关系：过原点的直线代表正比关系，有助于验证如 F ∝ a（质量恒定）等规律。
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