📚 IGCSE OCR Physics: Kinematics and Dynamics Key Concepts | IGCSE OCR 物理：动力学 考点精讲
Mastering the principles of motion and forces is essential for IGCSE OCR Physics. This comprehensive guide breaks down every critical topic in kinematics and dynamics, from scalars and vectors to momentum conservation. Clear explanations, practical graphs and worked examples will help you build a strong foundation for exam success.
掌握运动和力的原理是 IGCSE OCR 物理的关键。这份全面的考点精讲将逐一分解运动学和动力学的每个重要主题——从标量与矢量到动量守恒。清晰的解释、实用的图表和例题将帮助你打下扎实的基础，在考试中取得成功。
1. Scalars and Vectors | 标量与矢量
Scalars are physical quantities that have magnitude only. Common examples include mass, distance, speed, energy and time. When you say a mass is 5 kg, no direction is needed — that makes it a scalar. Scalars are added or subtracted using ordinary arithmetic, which simplifies many calculations.
标量是只有大小的物理量。常见的例子包括质量、距离、速率、能量和时间。当你说一个质量是 5 千克，不需要方向——这就使它成为标量。标量用普通算术加减，这简化了许多计算。
Vectors, on the other hand, possess both magnitude and direction. Displacement, velocity, acceleration, force and momentum are all vectors. Representing a vector requires an arrow where the length indicates magnitude and the arrowhead shows direction. Vector addition must consider direction; for forces acting along a straight line, you can assign positive and negative signs to opposite directions.
矢量则同时具有大小和方向。位移、速度、加速度、力和动量都是矢量。表示矢量需要一根箭头，长度代表大小，箭头表示方向。矢量加法必须考虑方向；对于沿直线作用的力，你可以用正负号来表示相反的方向。
2. Distance and Displacement | 距离与位移
Distance is the total length of the path travelled by an object, regardless of direction. It is a scalar quantity measured in metres (m). If a runner completes one lap of a 400 m track, the distance covered is 400 m. Distance can never be negative and always increases as the object moves.
距离是物体所经过路径的总长度，不考虑方向。它是一个标量，单位为米 (m)。如果一个跑者跑完一圈 400 米的跑道，经过的距离是 400 米。距离永远不为负值，且随着物体移动而不断增加。
Displacement is the straight-line distance from the starting point to the finishing point in a specified direction. It is a vector. For the same lap, if the runner returns exactly to the start, the displacement is zero because the overall change in position is zero. Displacement can be positive, negative or zero, depending on the chosen reference direction.
位移是从起点指向终点的直线距离，并带有指定的方向。它是一个矢量。同样的一圈，如果跑者精确地回到起点，位移为零，因为位置的总变化为零。位移可以是正、负或零，取决于所选的参考方向。
3. Speed and Velocity | 速率与速度
Speed is the rate at which distance is covered. It is a scalar calculated as speed = distance / time. The SI unit is m/s, but km/h is often used in everyday life. Average speed ignores any variations during the journey and is simply total distance divided by total time.
速率是经过距离的快慢程度。它是一个标量，计算公式为 速率 = 距离 / 时间。SI 单位是 m/s，但日常生活中常用 km/h。平均速率忽略行程中的任何变化，只是总距离除以总时间。
Velocity is the rate of change of displacement, so it is a vector: velocity = displacement / time. Constant velocity means both constant speed and constant direction. If an object moves in a circle at constant speed, its velocity is not constant because the direction is continuously changing. Instantaneous velocity is the velocity at a particular moment, which can be found from the gradient of a displacement-time graph.
速度是位移变化的快慢，因此它是一个矢量：速度 = 位移 / 时间。匀速意味着速率和方向都恒定。如果一个物体以恒定速率做圆周运动，它的速度并不是恒定的，因为方向在不断变化。瞬时速度是某一特定时刻的速度，可以从位移-时间图的斜率求得。
4. Acceleration | 加速度
Acceleration is the rate of change of velocity. It is a vector quantity given by the equation: a = (v − u) / t, where u is initial velocity, v is final velocity and t is the time taken. The unit is m/s². If the velocity of an object increases, acceleration is positive in the direction of motion; if it decreases, the object decelerates and acceleration is negative relative to the initial direction.
加速度是速度变化的快慢。它是一个矢量，计算公式为：a = (v − u) / t，其中 u 是初速度，v 是末速度，t 是所用时间。单位是 m/s²。如果物体的速度增加，加速度在运动方向上为正；如果速度减小，则物体减速，加速度相对于初始方向为负。
An object falling freely near the Earth’s surface experiences a uniform acceleration of about 9.8 m/s², called the acceleration of free fall, g. This value is constant provided air resistance is negligible. Even when an object is thrown upwards, it still accelerates downwards at g throughout its flight, which is why it slows down on the way up and speeds up on the way down.
在地球表面附近自由下落的物体会经历约 9.8 m/s² 的匀加速度，称为自由落体加速度 g。只要空气阻力可以忽略，该值恒定。即使物体被向上抛出，它在整个飞行过程中也始终以 g 向下加速，这就是为什么它上升时减慢、下降时加快。
5. Distance-Time Graphs | 距离-时间图
A distance-time graph plots distance travelled against time. The gradient of the line represents the speed of the object. A straight, sloping line indicates constant speed; a horizontal line means the object is stationary. A curved line shows changing speed — if the curve becomes steeper, the object is accelerating; if it becomes less steep, the object is decelerating.
距离-时间图绘制了行驶距离随时间变化的关系。线的斜率代表物体的速率。一条倾斜的直线表示匀速；水平线意味着物体静止。曲线表示速率在变化——如果曲线变陡，物体在加速；如果变平缓，物体在减速。
To calculate speed at a specific instant from a curved distance-time graph, draw a tangent at that point and find its gradient. The average speed is simply the total distance divided by total time, which is the gradient of the straight line connecting the start and end points. These skills are frequently tested in IGCSE exams.
要从曲线的距离-时间图上计算某一特定时刻的速率，可在该点作切线并求其斜率。平均速率就是总距离除以总时间，即连接起点和终点的直线的斜率。这些技能在 IGCSE 考试中经常考查。
6. Velocity-Time Graphs | 速度-时间图
A velocity-time graph provides even more information. The gradient gives acceleration, and the area under the graph gives the displacement. A horizontal line shows constant velocity. A straight sloping line indicates uniform acceleration; the steeper the line, the larger the acceleration. A downward sloping line toward the time axis indicates deceleration.
速度-时间图提供了更多信息。斜率代表加速度，图线下的面积代表位移。水平线表示匀速。倾斜的直线表示匀加速；线越陡，加速度越大。向时间轴方向下倾的线表示减速。
When the graph crosses the time axis, the object has momentarily zero velocity before changing direction. The area above the axis is positive displacement, and area below is negative displacement relative to the chosen direction. If you need to find the total distance travelled, add the magnitudes of the areas above and below the axis.
当图线穿过时间轴时，物体在改变方向前速度瞬时为零。轴上方面积是正位移，轴下方面积相对于所选方向是负位移。如果需要求总行程距离，就把轴上和轴下的面积大小相加。
| Graph Feature | 图线特征 | Velocity-Time Graph Meaning | 速度-时间图含义 |
|---|---|
| Gradient | 斜率 | Acceleration | 加速度 |
| Area under graph | 图下面积 | Displacement | 位移 |
| Horizontal line | 水平线 | Constant velocity | 匀速 |
| Line sloping up | 向上斜线 | Uniform positive acceleration | 正向匀加速 |
| Line sloping down | 向下斜线 | Uniform negative acceleration (deceleration) | 负向匀加速（减速） |
7. Newton’s First Law | 牛顿第一定律
Newton’s first law states that an object will remain at rest or continue to move at a constant velocity unless acted upon by a resultant external force. This property of an object to resist changes in its motion is called inertia. The greater the mass of an object, the larger its inertia, meaning a larger force is required to change its velocity.
牛顿第一定律指出，除非受到合外力的作用，物体将保持静止或匀速直线运动状态。物体抵抗运动状态变化的这种性质称为惯性。物体的质量越大，其惯性越大，意味着需要更大的力才能改变其速度。
When the resultant force on an object is zero, the forces are balanced. In such a case, a stationary object stays stationary, and a moving object continues with the same speed and direction. This explains why a passenger lurches forward when a bus brakes suddenly: the passenger’s body tends to continue moving forward due to inertia.
当物体所受的合力为零时，力达到平衡。在这种情况下，静止的物体保持静止，运动的物体保持相同的速率和方向运动。这就解释了为什么公共汽车突然刹车时乘客会向前倾：由于惯性，乘客的身体倾向于继续向前运动。
8. Newton’s Second Law (F = ma) | 牛顿第二定律
Newton’s second law tells us that the acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass. This relationship is summed up in the equation: F = m × a, where F is the resultant force in newtons (N), m is mass in kg and a is acceleration in m/s².
牛顿第二定律告诉我们，物体的加速度与作用在其上的合外力成正比，与其质量成反比。这个关系概括为方程：F = m × a，其中 F 是合力，单位为牛顿 (N)，m 是质量，单位为 kg，a 是加速度，单位为 m/s²。
This law allows you to calculate any one of these three quantities if the other two are known. For example, a resultant force of 10 N acting on a 2 kg mass produces an acceleration of 5 m/s². If multiple forces act, you must first determine the resultant force by vector addition. The direction of acceleration is always the same as the direction of the resultant force.
这个定律让你在已知其中两个量的情况下可以计算第三个。例如，10 N 的合力作用在 2 kg 的质量上产生 5 m/s² 的加速度。如果有多个力作用，你必须先通过矢量加法确定合力。加速度的方向总是与合力的方向相同。
9. Newton’s Third Law | 牛顿第三定律
Newton’s third law states that when object A exerts a force on object B, object B simultaneously exerts a force equal in magnitude and opposite in direction on object A. These two forces are called action and reaction pairs. Crucially, they act on different objects, so they do not cancel each other out when considering the motion of a single object.
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。这两个力称为作用力与反作用力对。关键的是，它们作用在不同的物体上，因此在考虑单个物体的运动时，它们不会相互抵消。
A classic example is a book resting on a table. The book exerts a downward force on the table (its weight), and the table exerts an upward normal reaction force on the book. These two forces are equal and opposite, but they are not an action-reaction pair of the third law because they act on the same object (the book). The correct action-reaction pair is the Earth pulling the book downward, and the book pulling the Earth upward.
一个经典的例子是放在桌子上的一本书。书对桌子施加一个向下的力（其重量），桌子对书施加一个向上的法向反作用力。这两个力大小相等方向相反，但它们不是牛顿第三定律中的作用力与反作用力对，因为它们作用在同一个物体（书）上。正确的作用力与反作用力对是：地球向下拉书，书向上拉地球。
10. Mass, Weight and Gravity | 质量、重量与重力
Mass is a measure of the amount of matter in an object. It is a scalar quantity, measured in kilograms (kg), and does not change with location. Weight, however, is the gravitational force acting on an object’s mass. Weight is a vector measured in newtons (N) and depends on the gravitational field strength g at that location.
质量是物体所含物质的量度。它是一个标量，以千克 (kg) 为单位，并且不随位置改变。然而，重量是作用在物体质量上的引力。重量是矢量，以牛顿 (N) 为单位，取决于该位置的重力场强度 g。
The relationship is given by W = m × g. On Earth, g is approximately 9.8 N/kg, so an object with a mass of 1 kg has a weight of about 9.8 N. On the Moon, g is only about 1.6 N/kg, so the same object would weigh much less, but its mass remains 1 kg. Always distinguish between mass and weight in exam answers.
两者关系由 W = m × g 给出。在地球上，g 大约为 9.8 N/kg，所以质量为 1 kg 的物体重量约为 9.8 N。在月球上，g 只有大约 1.6 N/kg，因此相同物体的重量会小得多，但其质量仍然是 1 kg。在考试答题时一定要区分质量与重量。
11. Free Fall and Terminal Velocity | 自由落体与终端速度
When an object falls under gravity alone with no air resistance, it experiences free fall. Its acceleration is constant at g (9.8 m/s²) regardless of its mass. However, in real situations air resistance increases with speed. Initially, the only force is weight, causing the object to accelerate downward at g.
当物体只受重力作用、没有空气阻力时，它做自由落体运动。其加速度恒定，为 g (9.8 m/s²)，与质量无关。然而，在实际情况中，空气阻力随速度增大。最初，唯一的力是重力，使物体以 g 向下加速。
As speed builds, air resistance grows until it equals the weight. At this point the resultant force becomes zero, and according to Newton’s first law, the object stops accelerating and continues at a constant speed called terminal velocity. For a skydiver, terminal velocity in a spread-eagle position is around 55 m/s; changing body shape alters air resistance and thus terminal velocity.
随着速度增加，空气阻力逐渐增大，直到与重力相等。此时合力变为零，根据牛顿第一定律，物体停止加速并保持恒定速度，这个速度称为终端速度。对于跳伞者来说，四肢展开姿势的终端速度大约为 55 m/s；改变身体形状会改变空气阻力，从而改变终端速度。
12. Momentum and Its Conservation | 动量与动量守恒
Momentum is a vector quantity defined as the product of an object’s mass and velocity: p = m × v. The unit is kg m/s. Momentum describes how difficult it is to stop a moving object — a heavy lorry has much more momentum than a bicycle even if both move at the same speed, because mass is larger.
动量是一个矢量，定义为物体质量与速度的乘积：p = m × v。单位是 kg m/s。动量描述了让运动物体停下来的难易程度——一辆重型卡车的动量远大于一辆自行车，即使两者以相同的速度运动，因为卡车的质量更大。
The principle of conservation of momentum states that in a closed system with no external forces, the total momentum before an event (such as a collision or explosion) equals the total momentum after the event. This is a direct consequence of Newton’s third law. In collisions, momentum is always conserved, but kinetic energy may not be conserved if the collision is inelastic.
动量守恒原理指出，在没有外力的封闭系统中，事件（例如碰撞或爆炸）前的总动量等于事件后的总动量。这是牛顿第三定律的直接结果。在碰撞中，动量总是守恒的，但如果碰撞是非弹性的，动能可能不守恒。
For example, consider a stationary 2 kg ball hit by a 1 kg ball moving at 3 m/s. After a perfectly inelastic collision where they stick together, the total mass is 3 kg. Using conservation: (1 kg × 3 m/s) = (3 kg × v), so v = 1 m/s. This simple calculation tool appears frequently in IGCSE structured questions.
例如，考虑一个静止的 2 kg 球被一个以 3 m/s 运动的 1 kg 球撞击。发生完全非弹性碰撞后它们粘在一起，总质量为 3 kg。利用守恒：(1 kg × 3 m/s) = (3 kg × v)，所以 v = 1 m/s。这个简单的计算工具经常出现在 IGCSE 结构化问题中。
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