📚 IB WJEC Physics: Dynamics Key Concepts | IB WJEC 物理：动力学考点精讲
Dynamics is the branch of physics that studies the causes of motion, focusing on forces, momentum, and energy. In both IB and WJEC specifications, dynamics forms a cornerstone, linking kinematics with real-world applications. Mastering Newton’s laws, free-body diagrams, and conservation principles is essential for solving problems involving moving objects.
动力学是物理学中研究运动原因的分支，关注力、动量和能量。在 IB 和 WJEC 考纲中，动力学是核心基石，将运动学与现实应用相连。掌握牛顿定律、受力分析图和守恒原理对于解决物体运动问题至关重要。
1. Newton’s First Law (Inertia) | 牛顿第一定律（惯性）
Newton’s first law 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 property of matter is called inertia. In everyday situations, a book lying on a table stays at rest because the vertical forces cancel, and a puck sliding on frictionless ice would continue indefinitely.
牛顿第一定律指出，除非受到净外力，否则物体将保持静止或沿直线匀速运动。这种物质属性称为惯性。在日常生活中，桌上一本书静止是因为垂直方向力平衡，而冰面上无摩擦的冰球会一直滑行下去。
When the net force is zero, the object is in equilibrium. The first law also implies that force is not required to sustain motion, but to change it. This corrects the ancient misconception that continual force is needed for motion.
当合外力为零时，物体处于平衡态。第一定律还表明，力不是维持运动的原因，而是改变运动的原因。这纠正了古代认为运动需要不断加力的错误观念。
2. Newton’s Second Law (F=ma) | 牛顿第二定律 (F=ma)
Newton’s second law quantifies the relationship between force, mass and acceleration. The net force acting on an object equals the product of its mass and acceleration: ΣF = m a. This is a vector equation: acceleration is always in the direction of the net force. The unit of force, the newton (N), is equivalent to kg m s-2.
牛顿第二定律定量描述了力、质量和加速度的关系。作用在物体上的净力等于其质量与加速度的乘积：ΣF = m a。这是一个矢量方程：加速度方向始终与合外力方向一致。力的单位牛顿 (N) 等于 kg·m·s⁻²。
If multiple forces act, you must first find the vector sum. For translational motion, we resolve forces into components. This law allows us to predict motion if forces are known, or to determine unknown forces from observed acceleration.
如果多个力作用，必须先求矢量和。对于平动，我们需要将力分解为分量。该定律使我们能在已知力时预测运动，或从观测到的加速度来确定未知力。
3. Newton’s Third Law (Action-Reaction) | 牛顿第三定律（作用力与反作用力）
Newton’s third law states: if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. These action-reaction pairs are of the same type (e.g. both gravitational, both normal) and act on different objects. They never cancel each other out because they act on different bodies.
牛顿第三定律指出：若物体 A 对物体 B 施加一个力，则物体 B 同时对物体 A 施加一个大小相等、方向相反的力。这一对作用力与反作用力性质相同（例如都是引力或都是法向力），且作用在不同物体上。它们不会相互抵消，因为受力对象不同。
Common confusions arise when people think that the normal force of a table on a book is the reaction to the book’s weight. In fact, the weight is the Earth pulling on the book; its reaction is the book pulling upward on Earth. The normal force and the book’s downward contact force on the table form another pair.
常见误解是认为桌子对书本的法向力是书本重力的反作用力。实际上，书本重力是地球对书本的引力，其反作用力是书本对地球的向上引力。法向力与书本对桌面的向下压力构成一对作用与反作用力。
4. Free-Body Diagrams | 受力分析图
A free-body diagram (FBD) isolates an object and shows all external forces acting on it. Each force is drawn as an arrow starting on the object, labelled with its type (weight W = mg, normal N, friction f, tension T). Choose a coordinate system to resolve forces.
受力分析图将物体隔离，显示其受到的所有外力。每个力用箭头表示，起点在物体上，标出力的类型（重力 W=mg，法向力 N，摩擦力 f，张力 T）。选定坐标系以分解力。
Drawing an accurate FBD is the first and most crucial step in solving dynamics problems. It prevents sign errors and ensures that Newton’s second law is applied correctly in each direction, e.g. ΣFx = m ax and ΣFy = m ay.
画出准确的受力分析图是解决动力学问题的首要且最关键步骤。它能避免符号错误，并确保在每个方向上正确应用牛顿第二定律，例如 ΣFx = m ax 和 ΣFy = m ay。
5. Linear Momentum and Impulse | 线性动量与冲量
Linear momentum is defined as the product of mass and velocity: p = m v. It is a vector quantity with units kg m s-1. Impulse J is the effect of a force over time: J = F Δt. For a variable force, impulse equals the area under a force-time graph.
线性动量定义为质量与速度的乘积：p = m v，是一个矢量，单位为 kg·m·s⁻¹。冲量 J 是力在一段时间内的积累效应：J = F Δt。对于变力，冲量等于力-时间图线下的面积。
The impulse-momentum theorem states that the net impulse equals the change in momentum: J = Δp = m v – m u. This is especially useful when forces act over short collision times, because the precise force variation is often unknown.
冲量-动量定理指出，合冲量等于动量的变化量：J = Δp = m v – m u。当力在极短碰撞时间内作用时，这特别有用，因为精确的力变化往往未知。
6. Conservation of Momentum | 动量守恒
In a closed system where no external forces act, the total linear momentum is conserved. Mathematically, for two objects: m1 u1 + m2 u2 = m1 v1 + m2 v2. This is a vector law; for two-dimensional problems we resolve into components.
在没有外力作用的封闭系统中，总线动量守恒。对有相互作用的两个物体：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。这是一个矢量定律；对于二维问题，我们需分解为分量。
Conservation of momentum applies to all interactions: collisions, explosions, and recoil. Even when external forces exist, if they are negligible during the interaction (as in a collision), momentum conservation can still be used approximately.
动量守恒适用于所有相互作用：碰撞、爆炸和反冲。即使存在外力，若在相互作用过程中外力可忽略（如碰撞），动量守恒仍可近似使用。
7. Types of Forces: Friction, Tension, Normal | 力的类型：摩擦力、张力、法向力
Understanding common forces is essential for dynamics. Below is a summary of key contact and non-contact forces:
理解常见力对于动力学至关重要。以下是关键接触力和非接触力的总结：
| Force (Symbol) | Description | Notes |
|---|---|---|
| Weight (W) | Gravitational force from Earth; W = mg | Acts toward Earth’s centre; does not change with contact |
| Normal (N) | Contact force perpendicular to surfaces | Adjusts to prevent interpenetration; not always equal to mg |
| Tension (T) | Force transmitted through a string, rope or cable | Directed along the string; same magnitude throughout if massless and smooth |
| Static Friction (fs) | Opposes start of motion; fs ≤ μs N | Takes the value needed up to maximum |
| Kinetic Friction (fk) | Opposes sliding motion; fk = μk N | Usually less than maximum static friction |
Friction always acts parallel to the contact surface and opposes relative motion or tendency. Tension is considered constant in light inextensible strings passing over smooth pulleys. Normal force arises from electromagnetic repulsion between atoms at surfaces.
摩擦力总是平行接触面，并阻碍相对运动或运动趋势。对于轻质不可伸长且绕过光滑滑轮的绳子，张力视为处处相等。法向力源于接触面原子间的电磁排斥。
8. Connected Bodies and Pulleys | 连接体与滑轮
When two or more bodies are connected by a string or are in contact, they often share the same acceleration magnitude. We can solve such problems using two strategies: treating the whole system as one object (system approach) or drawing free-body diagrams for each object (component approach).
当两个或多个物体通过绳子相连或接触时，它们通常具有相同的加速度大小。我们可以用两种策略解题：将整个系统视为一个物体（整体法）或分别画每个物体的受力分析图（隔离法）。
The system approach quickly finds acceleration by applying Newton’s second law to the total mass using the net driving force, ignoring internal tensions. Then the component approach is used to find the tension by isolating one object.
整体法通过将牛顿第二定律用于总质量，使用净驱动力快速求出加速度，忽略内部张力。然后隔离一个物体，使用隔离法求出张力。
For a pulley with one mass on a table and one hanging, the hanging weight provides the accelerating force for the whole system: a = (m2g) / (m1 + m2). Tension can be found as T = m1 a (if the table is smooth). Always check that the pulley is smooth and string massless, so tension is uniform.
对于桌面连接滑轮问题，悬挂重物提供整个系统的加速力：a = (m₂g)/(m₁ + m₂)。若桌面光滑，张力 T = m₁ a。务必检查滑轮光滑、绳轻质，从而张力处处均匀。
9. Work-Energy Principle and Power | 功能原理与功率
Although often treated separately, work and energy are tightly linked to dynamics. Work done by a force is W = F d cos θ, where θ is the angle between force and displacement. The net work done on an object equals its change in kinetic energy: Wnet = ΔKE = ½ mv2 – ½ mu2.
尽管常分开讲解，功和能与动力学紧密相连。力所做的功为 W = F d cos θ，其中 θ 是力与位移的夹角。对物体做的合功等于其动能变化量：W_net = ΔKE = ½ mv² – ½ mu²。
Power is the rate of doing work: P = W / t = F v, where v is instantaneous speed if force is parallel to velocity. In dynamics problems, the work-energy theorem can often replace acceleration calculations when only speed changes are needed.
功率是做功的快慢：P = W/t = F v，当力与速度平行时 v 为瞬时速率。在动力学问题中，若仅需速率变化，功能定理常可替代加速度计算。
10. Collisions: Elastic and Inelastic | 碰撞：弹性与非弹性
Collisions are analysed using momentum conservation. In an elastic collision, both momentum and kinetic energy are conserved. For two bodies: m1 u1 + m2 u2 = m1 v1 + m2 v2 and ½ m1 u12 + ½ m2 u22 = ½ m1 v12 + ½ m2 v22.
碰撞利用动量守恒进行分析。在弹性碰撞中，动量和动能均守恒。对两个物体：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ 且 ½ m₁u₁² + ½ m₂u₂² = ½ m₁v₁² + ½ m₂v₂²。
In a perfectly inelastic collision, the objects stick together after impact, moving with a common velocity. Momentum is conserved but kinetic energy is not: v = (m1 u1 + m2 u2) / (m1 + m2). The ‘lost’ kinetic energy is converted to heat, sound, or deformation.
在完全非弹性碰撞中，物体碰撞后粘在一起，以共同速度运动。动量守恒，但动能不守恒：v = (m₁u₁ + m₂u₂)/(m₁ + m₂)。“损失”的动能转化为热、声或形变能。
11. Circular Motion Dynamics (Centripetal Force) | 圆周运动动力学（向心力）
An object moving in a circular path at constant speed experiences a centripetal acceleration directed toward the centre: ac = v2 / r = ω2 r. According to Newton’s second law, there must be a net inward force: Fc = m v2 / r = m ω2 r.
物体以恒定速率做圆周运动时，受到指向圆心的向心加速度：a_c = v² / r = ω² r。由牛顿第二定律，必须存在指向圆心的净力：F_c = m v² / r = m ω² r。
Centripetal force is not a new type of force; it is the name given to the net force pointing toward the centre, provided by tension, gravity, friction, or a combination. For example, in a car rounding a bend, static friction supplies the centripetal force. In a vertical circle, the tension and a component of weight together provide Fc.
向心力不是一种新的力；它是指向圆心的合外力的名称，可由张力、重力、摩擦力或它们的组合提供。例如，汽车转弯时静摩擦力提供向心力；在竖直圆周运动中，张力和重力的分力共同提供 F_c。
12. Common Mistakes and Exam Tips | 常见错误与应试技巧
Many students confuse mass and weight: mass is in kg, weight is a force (N) and equals mg. Always use W = mg for weight in free-body diagrams, not just ‘gravity’.
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