📚 IB & CCEA Physics: Dynamics – Key Concepts & Exam Tips | IB与CCEA物理：动力学考点精讲
Dynamics is the study of forces and their effect on motion, forming the core of classical mechanics. In IB and CCEA physics, this topic covers Newton’s laws, momentum, energy, collisions, and circular motion. Mastering these concepts is essential for tackling both conceptual and calculation problems in the exam.
动力学研究力及其对运动的影响，是经典力学的核心。在IB和CCEA物理中，该主题涵盖牛顿定律、动量、能量、碰撞和圆周运动。掌握这些概念对于解决考试中的概念题和计算题至关重要。
1. Newton’s Laws of Motion | 牛顿运动定律
Newton’s First Law states that an object remains at rest or in uniform motion in a straight line unless acted upon by a net external force. This property is called inertia.
牛顿第一定律指出，物体将保持静止或匀速直线运动状态，除非受到净外力的作用。这种性质称为惯性。
Newton’s Second Law relates the net force to the rate of change of momentum, commonly expressed as F = m a. The direction of acceleration is the same as the net force.
牛顿第二定律将净力与动量的变化率联系起来，通常表示为 F = m a。加速度的方向与净力方向相同。
Newton’s Third Law states that if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. These forces act on different objects and never cancel out.
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。这两个力作用在不同物体上，永远不会相互抵消。
The unit of force is the newton (N), where 1 N = 1 kg m s⁻². Understanding these laws is the foundation for solving any dynamics problem.
力的单位是牛顿（N），1 N = 1 kg m s⁻²。理解这些定律是解决任何动力学问题的基础。
2. Force Diagrams and Free-body Analysis | 受力图与自由体分析
A free-body diagram shows all the forces acting on a single object, drawn as vectors from the centre of mass. Common forces include weight (mg), normal reaction (N), tension (T), friction (f), and applied forces.
自由体图显示作用在单个物体上的所有力，以质心为起点用矢量画出。常见的力包括重力（mg）、法向反作用力（N）、张力（T）、摩擦力（f）和外加力。
When resolving forces on an inclined plane, the weight is split into components parallel and perpendicular to the slope: mg sin θ down the slope and mg cos θ into the slope. The normal force equals mg cos θ if there is no acceleration perpendicular to the plane.
在斜面上分解力时，重力被分解为平行于斜面的分量 mg sin θ（沿斜面向下）和垂直于斜面的分量 mg cos θ。若垂直于斜面方向没有加速度，则法向力等于 mg cos θ。
Friction opposes motion or attempted motion. Static friction adjusts up to a maximum value fₛ ≤ μₛ N, while kinetic friction is fₙ = μₙ N. Always draw friction parallel to the contact surface.
摩擦力阻碍运动或运动趋势。静摩擦力可自动调整，最大值为 fₛ ≤ μₛ N，而动摩擦力为 fₙ = μₙ N。始终将摩擦力画得与接触面平行。
Good free-body diagrams help avoid sign errors. Label all forces and choose a consistent coordinate system before applying ΣF = m a.
清晰的自由体图有助于避免符号错误。在应用 ΣF = m a 之前，标记所有力并选择一致的坐标系。
3. Linear Momentum and Impulse | 线性动量与冲量
Linear momentum is defined as p = m v. It is a vector quantity, measured in kg m s⁻¹.
线性动量定义为 p = m v。它是一个矢量，单位为 kg m s⁻¹。
Impulse is the product of force and the time interval over which it acts: J = F Δt. Impulse equals the change in momentum: J = Δp = m v − m u. This is the impulse–momentum theorem.
冲量是力与其作用时间间隔的乘积：J = F Δt。冲量等于动量的变化量：J = Δp = m v − m u。这就是冲量–动量定理。
In force–time graphs, the impulse is the area under the curve. This is particularly useful when the force varies with time.
在力–时间图中，冲量是曲线下的面积。当力随时间变化时，这一方法尤为有用。
For IB and CCEA exams, you must be able to calculate impulse from a graph and apply the vector nature of momentum in collisions and explosions.
在IB和CCEA考试中，你必须能够根据图形计算冲量，并在碰撞和爆炸问题中应用动量的矢量特性。
4. Conservation of Momentum | 动量守恒
The total momentum of an isolated system remains constant, provided no external forces act. This principle is used in all collision and explosion problems.
在没有外力作用的孤立系统中，总动量保持不变。该原理用于所有碰撞和爆炸问题。
For two objects colliding, momentum conservation gives: m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂, where u represents initial velocities and v final velocities.
对于两个碰撞物体，动量守恒给出：m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂，其中 u 表示初速度，v 表示末速度。
Explosions also obey momentum conservation. Initially the total momentum is zero, so the fragments move apart with equal and opposite total momentum.
爆炸也遵循动量守恒。初始总动量为零，因此碎片以大小相等、方向相反的总动量分开。
Always assign a positive direction and treat velocities as positive or negative accordingly. This is a common source of error in two-dimensional collision problems.
始终指定正方向，并相应地将速度视为正值或负值。这是二维碰撞问题中常见的错误来源。
5. Work and Energy | 功与能
Work is done when a force moves its point of application in the direction of the force. It is calculated as W = F d cos θ, where d is the displacement and θ the angle between force and displacement.
当力使其作用点沿力的方向发生位移时，就说力做了功。功的计算公式为 W = F d cos θ，其中 d 为位移，θ 为力与位移之间的夹角。
If the force is perpendicular to displacement, no work is done. For example, the normal force does no work when an object slides along a horizontal surface.
如果力与位移垂直，则不做功。例如，物体沿水平面滑动时，法向力不做功。
The area under a force–displacement graph gives the work done. Energy is the capacity to do work and is measured in joules (J).
力–位移图下方的面积表示做功的多少。能量是做功的能力，单位为焦耳（J）。
The work–energy principle states that the net work done on an object equals its change in kinetic energy: Wₙₑₜ = Δ KE. This principle allows solving problems without considering acceleration or time.
功能原理指出，对物体做的净功等于其动能的变化量：Wₙₑₜ = Δ KE。利用该原理解题时无需考虑加速度或时间。
6. Gravitational Potential and Kinetic Energy | 重力势能与动能
Kinetic energy (KE) is the energy due to motion: KE = ½ m v². It is a scalar quantity and always non-negative.
动能（KE）是因运动而具有的能量：KE = ½ m v²。它是一个标量，且总是非负的。
Gravitational potential energy (GPE) near the Earth’s surface is given by GPE = m g h, where h is the height above a chosen reference level. The choice of reference does not affect changes in GPE.
地表附近的重力势能（GPE）由 GPE = m g h 给出，其中 h 是相对于选定参考面的高度。参考面的选择不影响重力势能的变化。
In the absence of non-conservative forces such as friction, total mechanical energy is conserved: KE₁ + GPE₁ = KE₂ + GPE₂. This is a very common problem-solving approach in IB and CCEA physics.
在没有摩擦力等非保守力的情况下，总机械能守恒：KE₁ + GPE₁ = KE₂ + GPE₂。这是IB和CCEA物理中非常常见的一种解题方法。
When friction is present, the work done against friction reduces the total mechanical energy, usually appearing as thermal energy.
当存在摩擦力时，克服摩擦力做功会使总机械能减少，通常以内能的形式体现。
7. Power and Efficiency | 功率与效率
Power is the rate of doing work or transferring energy: P = W / t = ΔE / t. It is measured in watts (W), where 1 W = 1 J s⁻¹.
功率是做功或传递能量的速率：P = W / t = ΔE / t。单位为瓦特（W），1 W = 1 J s⁻¹。
For a constant force moving at velocity v, the power output can also be written as P = F v, provided the force and velocity are parallel.
对于以速度 v 运动的恒定力，若力与速度平行，功率也可表示为 P = F v。
Efficiency is the ratio of useful output power (or energy) to total input power: η = (useful output / total input) × 100%. No real machine is 100% efficient due to energy losses like friction and heat.
效率是有用输出功率（或能量）与总输入功率之比：η = (有用输出 / 总输入) × 100%。由于摩擦和热量等能量损失，任何真实机器的效率都不可能达到100%。
Exam questions often ask you to calculate the efficiency of a motor lifting a load or the power needed to maintain constant speed against resistive forces.
考题常常要求计算电动机提升重物时的效率，或为克服阻力保持匀速所需的功率。
8. Elastic and Inelastic Collisions | 弹性与非弹性碰撞
In an elastic collision, both momentum and kinetic energy are conserved. The colliding objects bounce apart without permanent deformation or heat generation.
在弹性碰撞中，动量和动能均守恒。碰撞物体弹开后不发生永久形变或产生热量。
For a perfectly elastic head-on collision between two masses, the relative speed of approach equals the relative speed of separation: |v₁ − v₂| = |u₂ − u₁|. Combined with momentum conservation, this allows finding final velocities.
对于两个质量的正碰完全弹性碰撞，接近时的相对速度大小等于分离时的相对速度大小：|v₁ − v₂| = |u₂ − u₁|。结合动量守恒即可求出末速度。
In an inelastic collision, momentum is conserved but kinetic energy is not. The ‘lost’ energy is converted into other forms such as heat or sound. A completely inelastic collision is one where the objects stick together, moving with a common velocity.
在非弹性碰撞中，动量守恒但动能不守恒。“损失”的能量转化为热能或声能等其他形式。完全非弹性碰撞是指碰撞后物体粘在一起，以共同速度运动。
IB and CCEA papers frequently include questions requiring identification of collision type from given data or calculating energy lost in an inelastic collision.
IB和CCEA试卷中经常要求根据给定数据判断碰撞类型，或计算非弹性碰撞中损失的能量。
9. Centripetal Force and Circular Motion | 向心力与圆周运动
An object moving in a circle at constant speed is accelerating because its direction changes continuously. This centripetal acceleration is directed towards the centre and has magnitude a = v² / r = ω² r.
做匀速圆周运动的物体由于方向不断改变而具有加速度。该向心加速度指向圆心，大小由 a = v² / r = ω² r 给出。
The net force required to produce this acceleration is the centripetal force: F = m v² / r = m ω² r. It is not a new type of force but the resultant of forces such as tension, gravity, or friction, acting radially inward.
产生这一加速度所需的净力即为向心力：F = m v² / r = m ω² r。它并不是一种新的力，而是张力、重力或摩擦力等沿半径方向指向圆心的合力。
Common exam contexts include a car rounding a banked curve, a mass on a string, or a satellite in orbit. Always identify the force(s) providing the centripetal component.
常见的考试情景包括汽车在倾斜弯道上转弯、绳端小球，以及轨道上的卫星。务必分辨出提供向心力分量的力。
Note that the centrifugal ‘force’ is a fictitious force observed in a rotating reference frame and is not included in free-body diagrams in inertial frames.
注意，“离心力”是在旋转参考系中观察到的虚拟力，在惯性系的受力图中不应画出。
10. Key Equations and Common Pitfalls | 核心公式与常见误区
The table below summarises the essential dynamics equations you must be able to recall and apply. Familiarity with these will save time during the exam.
下表总结了必须熟记并应用的核心动力学公式。熟悉这些公式将有助于在考试中节省时间。
| Quantity 物理量 | Equation 公式 | Notes 备注 |
|---|---|---|
| Newton’s 2nd Law | ΣF = m a | Net force causes acceleration |
| Momentum | p = m v | Vector; unit kg m s⁻¹ |
| Impulse | J = F Δt = Δp | Area under F–t graph |
| Work | W = F d cos θ | θ between F and d |
| Kinetic Energy | KE = ½ m v² | Always non‑negative |
| Gravitational PE | GPE = m g h | Near Earth’s surface |
| Power | P = W / t = F v | v constant, F parallel to v |
| Centripetal Force | F = m v² / r = m ω² r | Net radial force |
Common pitfalls include forgetting to treat momentum as a vector, misidentifying the angle in the work formula, and using ‘total energy conservation’ when non-conservative forces are present. Also, many students incorrectly include centripetal force as an extra force on a free-body diagram rather than as the resultant force.
常见的误区包括忘记将动量作为矢量处理、在功公式中用错角度，以及在存在非保守力时错误地使用“总能量守恒”。此外，许多学生错误地将向心力作为自由体图中的额外力，而不是合力。
Practice past paper questions regularly, and always check your signs and units. Dynamics becomes intuitive once the links between force, motion, and energy are firmly established.
定期练习历年真题，并始终检查符号和单位。一旦牢固建立起力、运动和能量之间的联系，动力学就会变得直观起来。
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