Dynamics: Key Concepts and Exam Tips | 动力学：核心概念与考点精讲

📚 Dynamics: Key Concepts and Exam Tips | 动力学：核心概念与考点精讲

Dynamics is the branch of mechanics that explains why objects move by relating forces to motion. For IB and Edexcel Physics, mastering dynamics means going beyond memorising formulas – you need to apply Newton’s laws, momentum principles, and energy methods confidently in a variety of problem-solving contexts. This article walks you through the essential topics, common pitfalls, and exam-ready strategies.

动力学是力学中通过力与运动的联系来解释物体为何运动的分支。对于 IB 和 Edexcel 物理考试，掌握动力学远不止是记住公式——你需要能够熟练地运用牛顿定律、动量原理和能量方法解决各类问题。本文将带你梳理核心知识点、常见易错点以及实用的应试策略。

1. Newton’s Laws of Motion | 牛顿运动定律

Newton’s three laws form the backbone of classical dynamics. The First Law (inertia) states that an object remains at rest or in uniform motion unless acted upon by a net external force. The Second Law quantifies this as F = ma, where the net force is proportional to acceleration and inversely proportional to mass. The Third Law asserts that forces come in pairs: if body A exerts a force on body B, B exerts an equal and opposite force on A.

牛顿三定律是经典动力学的基石。第一定律（惯性定律）指出，除非受到净外力作用，物体将保持静止或匀速直线运动状态。第二定律将其量化为 F = ma，即净外力与加速度成正比，与质量成反比。第三定律强调力成对出现：若物体 A 对物体 B 施加一个力，则 B 对 A 施加等大反向的力。

In exams, always identify the net force before applying F = ma. Confusing individual forces with net force is a common mistake. Also remember that the Third Law pair acts on different objects, so they do not cancel each other in a single free-body diagram.

考试中，在应用 F = ma 之前务必先确定净外力。将单个力与净外力混淆是常见错误。同时要牢记，第三定律中的力对作用在不同物体上，因此它们不会在单个受力分析图中互相抵消。

2. Free-Body Diagrams | 受力分析图

Drawing a clear free-body diagram (FBD) is the most reliable way to start any dynamics problem. Isolate the object of interest and draw arrows representing all forces acting on it: weight (mg), normal reaction, tension, friction, applied forces, etc. Do not include forces exerted by the object.

绘制清晰的受力分析图是解决任何动力学问题最可靠的第一步。把研究对象隔离出来，画出作用在其上的所有力：重力 (mg)、法向反作用力、张力、摩擦力、施加的外力等。不要把物体施加给外界的力画进去。

For inclined plane problems, it is often helpful to resolve weight into components parallel and perpendicular to the slope. Use mg sin θ down the plane and mg cos θ into the plane. Always state the chosen direction of positive acceleration before writing the equation of motion.

对于斜面问题，将重力分解为平行和垂直于斜面的分量往往更有帮助。沿斜面向下的分量为 mg sin θ，垂直压向斜面的分量为 mg cos θ。在列出运动方程之前，务必先声明所选的正加速度方向。

3. Linear Momentum and Impulse | 线动量与冲量

Linear momentum p is defined as the product of mass and velocity: p = mv. It is a vector quantity with the same direction as velocity. Impulse J is the change in momentum caused by a force acting over a time interval: J = FΔt = Δp = mv − mu. The unit of both momentum and impulse is kg m s⁻¹ or N s.

线动量 p 定义为质量与速度的乘积：p = mv。它是一个矢量，方向与速度相同。冲量 J 是由力在一段时间间隔内作用引起的动量变化：J = FΔt = Δp = mv − mu。动量和冲量的单位均为 kg m s⁻¹ 或 N s。

The area under a force–time graph gives the impulse. This is particularly useful when the force is not constant, such as during a collision or a kick. In an exam, sketch the graph carefully and use geometry to find the area.

力—时间图线下的面积代表冲量。这在力不恒定的情况下（例如碰撞或踢击时）特别有用。考试时，认真绘制草图，利用几何方法求出面积。

4. Conservation of Momentum | 动量守恒

When no external resultant force acts on a system, total momentum is conserved. Mathematically: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. This principle is especially powerful for analysing collisions and explosions, where internal forces are much larger than any external influence during the brief interaction.

当系统不受净外力作用时，总动量守恒。数学表达式为：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。这一原理在分析碰撞和爆炸时格外有效，因为在这短暂的相互作用过程中，内力远大于任何外部影响。

Remember to assign a positive direction and treat velocities accordingly as positive or negative. Many marks are lost through sign errors. For two-dimensional collisions, resolve momentum into perpendicular components (e.g., x and y axes) and apply conservation independently to each direction.

记住要设定正方向，并相应地将速度取正负值。很多失分都是因为符号错误造成的。对于二维碰撞，将动量分解到两个相互垂直的方向（如 x 轴和 y 轴），并分别对每个方向应用动量守恒。

5. Elastic and Inelastic Collisions | 弹性碰撞与非弹性碰撞

In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not – some energy is transformed into heat, sound or deformation. A perfectly inelastic collision is one where the objects stick together and move with a common velocity after impact.

在弹性碰撞中，动量和动能均守恒。在非弹性碰撞中，动量守恒但动能不守恒——部分能量转化为热量、声音或形变能。完全非弹性碰撞是指碰撞后物体粘在一起并以共同速度运动的碰撞。

To check whether a collision is elastic, compare total kinetic energy before and after. If ½ m₁u₁² + ½ m₂u₂² > ½ m₁v₁² + ½ m₂v₂², the collision is inelastic. In IB and Edexcel problems, you may be asked to calculate the loss in kinetic energy. Write the expression clearly and substitute values carefully.

要判断碰撞是否为弹性，比较碰撞前后的总动能。如果 ½ m₁u₁² + ½ m₂u₂² > ½ m₁v₁² + ½ m₂v₂²，碰撞是非弹性的。在 IB 和 Edexcel 考题中，你可能需要计算动能损失。清晰地写出表达式，并仔细代入数值。

6. Friction and Drag Forces | 摩擦力与阻力

Friction between solid surfaces is modelled by F_f ≤ μ R, where R is the normal reaction and μ is the coefficient of friction. The maximum static friction is μ_sR, while kinetic friction is constant at μ_kR once motion begins. Drag force (air resistance) increases with speed and often depends on v or v².

固体表面之间的摩擦用 F_f ≤ μ R 来建模，其中 R 是法向反作用力，μ 是摩擦系数。最大静摩擦力为 μ_sR，而一旦运动开始，动摩擦力恒定为 μ_kR。阻力（空气阻力）随速度增大而增大，通常与 v 或 v² 有关。

When an object reaches terminal velocity, the net force is zero: weight = drag force. In exam questions, draw FBDs showing all forces and always check whether the object is accelerating or moving at constant speed – this determines if you can set F_net = 0 or F_net = ma.

当物体达到终极速度时，净力为零：重力等于阻力。在考试题目中，画出受力分析图显示所有力，并始终检查物体是正在加速还是匀速运动——这决定了你是设 F_net = 0 还是 F_net = ma。

7. Connected Particles and Pulleys | 连接体与滑轮系统

For systems of connected particles (e.g., masses linked by a light inextensible string over a smooth pulley), treat each particle separately with its own equation of motion, or consider the whole system for the common acceleration. The tension in a light string is uniform throughout its length.

对于连接体系统（例如通过绕过光滑滑轮的轻质不可伸长细绳相连的质量块），可以分别对每个质点列出运动方程，也可以将整个系统视为整体求共同加速度。轻绳中的张力在其长度上处处相等。

Write equations like T − mg = ma or mg − T = ma depending on direction of motion. Then solve simultaneously. In Edexcel M1 or IB Mechanics, these appear frequently and often combine with friction on a horizontal surface or an incline.

根据运动方向列出例如 T − mg = ma 或 mg − T = ma 这样的方程，然后联立求解。在 Edexcel M1 或 IB 力学中，这类问题频繁出现，并常常与水平面或斜面上的摩擦结合起来考查。

8. Work, Energy and Power in a Dynamics Context | 动力学中的功、能与功率

Work done by a force is W = F s cos θ, where θ is the angle between the force and displacement. The work–energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½ mv² − ½ mu².

力做的功为 W = F s cos θ，其中 θ 是力与位移之间的夹角。功能原理指出，作用在物体上的净功等于其动能变化量：W_net = ΔKE = ½ mv² − ½ mu²。

Gravitational potential energy change near Earth’s surface is ΔGPE = mgΔh. Power, the rate of doing work, is P = W/t or for uniform motion against a force, P = Fv. These concepts often provide an energy-based shortcut to solving dynamics problems without needing acceleration.

地表附近的重力势能变化为 ΔGPE = mgΔh。功率，即做功的速率，为 P = W/t，对于克服某个力做匀速运动的情况，P = Fv。这些概念常常提供一种基于能量的捷径，无需使用加速度即可解决动力学问题。

9. Circular Motion Dynamics | 圆周运动动力学

For an object moving in a circle with constant speed, there is always a net force directed towards the centre – the centripetal force. Its magnitude is F = mv²/r or mω²r, where ω is angular speed. The centripetal force is not a new type of force; it is provided by tension, gravity, friction, or the normal reaction.

对于匀速圆周运动的物体，总存在一个指向圆心的净力——向心力。其大小为 F = mv²/r 或 mω²r，其中 ω 是角速度。向心力并不是一种新的力，它是由张力、重力、摩擦力或法向反作用力提供的。

Do not add a separate “centripetal force” arrow on your FBD. Instead, identify the physical force(s) pointing towards the centre and set their total equal to mv²/r. Very common scenarios include a car rounding a banked curve, a conical pendulum, or a mass on a string in a vertical circle.

不要在受力分析图上额外画一个“向心力”箭头。相反，应找出指向圆心的实际力，并令它们的总和等于 mv²/r。极为常见的场景包括汽车在倾斜弯道上转弯、锥摆，或小球系在绳端在竖直面内做圆周运动。

10. Key Equations and Exam Strategy | 核心公式与应试策略

Keep a concise equation bank: F = ma, p = mv, J = FΔt = Δp, conservation of momentum, W = F s cos θ, KE = ½ mv², GPE = mgΔh, P = Fv, and centripetal force = mv²/r. Translate wordy problems into labelled diagrams and variables first.

准备一个简明的公式库：F = ma, p = mv, J = FΔt = Δp, 动量守恒, W = F s cos θ, KE = ½ mv², GPE = mgΔh, P = Fv, 以及向心力 = mv²/r。遇到文字冗长的题目，先将其转化为标注清晰的示意图和变量符号。

Always check units (SI: kg, m, s, N, J, W) and convert grams, centimetres, or km h⁻¹ when necessary. State assumptions explicitly, such as “smooth surface” (no friction) or “light string” (negligible mass). In multi-step problems, show full working – marks are awarded for equations, substitution, and final answers with units.

始终检查单位（国际单位制：kg, m, s, N, J, W），必要时换算克、厘米或 km h⁻¹。明确写出假设，例如“光滑表面”（无摩擦）或“轻绳”（质量忽略不计）。在多步计算题中，展示完整的解题过程——评分点包括方程、代入过程以及带单位的最终答案。

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