IB Physics: Dynamics – Key Concepts Review | IB 物理：动力学考点精讲

📚 IB Physics: Dynamics – Key Concepts Review | IB 物理：动力学考点精讲

Dynamics is the branch of mechanics that investigates the causes of motion — forces — and how they relate to changes in velocity, momentum, and energy. In the IB Physics curriculum, dynamics forms a cornerstone of the Mechanics topic, linking Newton’s laws to circular motion, impulse, work, and conservation principles. This article unpacks the essential concepts, common pitfalls, and typical exam-style applications that every student should master.

动力学是力学中研究运动成因（即力）以及力如何与速度变化、动量和能量相关联的分支。在 IB 物理课程中，动力学是力学板块的基石，将牛顿定律与圆周运动、冲量、功和守恒原理紧密联系起来。本文梳理了核心概念、常见误区和典型考题应用，帮助同学们扎实掌握每一个考点。

1. Newton’s Laws of Motion | 牛顿运动定律

Newton’s three laws provide the foundation 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: the net force equals the rate of change of momentum, commonly expressed as F = m a for constant mass objects. The third law emphasises that forces always occur in pairs: if body A exerts a force on body B, then B exerts an equal and opposite force on A.

牛顿三定律奠定了经典动力学的基础。第一定律（惯性定律）指出，物体将保持静止或匀速直线运动，除非受到合外力作用。第二定律定量描述：合外力等于动量的变化率，对于质量恒定的物体通常写为 F = m a。第三定律强调力总是成对出现：若 A 对 B 施加一个力，则 B 同时对 A 施加大小相等、方向相反的力。

2. Free-Body Diagrams and Net Force | 受力分析与合力

A free-body diagram (FBD) isolates one object and draws all forces acting on it as vectors. Typical forces include weight (W = m g), normal contact force (N), tension (T), applied forces and friction. The vector sum of these forces gives the net force, which determines the acceleration according to Newton’s second law. Always draw FBDs with clearly labelled arrows originating from the centre of mass, and resolve forces into perpendicular components when dealing with inclined planes.

受力分析图（FBD）隔离一个物体，并将所有作用在它上面的力用矢量表示。常见力包括重力 (W = m g)、法向接触力 (N)、张力 (T)、外加力和摩擦力。这些力的矢量和即为合力，由牛顿第二定律决定物体的加速度。作图时务必从质心出发，用清晰的箭头标示每个力；涉及斜面时，将力沿垂直和平行方向分解。

3. Common Forces: Weight, Normal & Tension | 常见力：重力、法向力与张力

Weight always acts vertically downwards and is given by W = m g, where g is the gravitational field strength (approx. 9.81 N kg⁻¹ on Earth’s surface). The normal reaction force acts perpendicular to the contact surface and balances the component of weight pressing into the surface. Tension is the pulling force transmitted through a string, cable or rod; in ideal massless strings, tension is uniform throughout and pulls equally on both ends.

重力始终竖直向下，大小为 W = m g，其中 g 为引力场强度（地球表面约 9.81 N kg⁻¹）。法向反作用力垂直于接触面，用于平衡物体挤压接触面的重力分量。张力是通过细绳、缆线或杆传递的拉力；在理想轻绳中，张力处处相等，并向两端施加等大的拉力。

4. Friction: Static and Kinetic | 摩擦力：静摩擦与动摩擦

Friction opposes relative motion or attempted motion between two surfaces in contact. Static friction (f_s ≤ μ_s N) prevents sliding up to a maximum value; it is a self-adjusting force. Once motion starts, kinetic friction (f_k = μ_k N) takes over, usually with a slightly lower magnitude. The coefficients μ_s and μ_k depend on the materials and surface roughness, and friction is independent of contact area (within the classic Amontons-Coulomb model).

摩擦力阻碍接触面之间的相对运动或相对运动趋势。静摩擦力 (f_s ≤ μ_s N) 在最大静摩擦力范围内自我调节，阻止滑动；一旦开始运动，动摩擦力 (f_k = μ_k N) 起作用，通常数值略小。摩擦系数 μ_s 和 μ_k 取决于材料与表面粗糙度，且根据经典摩擦定律，摩擦力与接触面积无关。

5. Uniform Circular Motion | 匀速圆周运动

An object in uniform circular motion travels at constant speed but experiences continuous change in direction, meaning there is always an acceleration towards the centre — centripetal acceleration. The speed v, radius r and period T are linked by v = 2 π r / T. Although the speed is constant, the velocity vector is not, so a net force must act towards the centre. Common examples include a car rounding a curve, a planet orbiting a star, and a mass whirled on a string.

做匀速圆周运动的物体，速率恒定但方向时刻改变，因此始终存在指向圆心的加速度——向心加速度。速率 v、半径 r 和周期 T 满足 v = 2 π r / T。尽管速率不变，速度矢量却在变化，因此必须有指向圆心的合力。常见实例包括汽车转弯、行星绕恒星公转以及用细绳旋转的小球。

6. Centripetal Force and Acceleration | 向心力与向心加速度

Centripetal acceleration is given by a_c = v² / r or a_c = ω² r, where ω = v / r is the angular speed. According to Newton’s second law, a net centripetal force F_c = m v² / r = m ω² r must be provided by one or more real forces — tension, gravity, friction or the normal reaction. The centripetal force is not a new type of force; it is simply the net force directed towards the centre of the circular path.

向心加速度的表达式为 a_c = v² / r 或 a_c = ω² r，其中 ω = v / r 为角速度。由牛顿第二定律，所需的向心力 F_c = m v² / r = m ω² r 必须由一个或多个真实力（如张力、重力、摩擦力或法向力）提供。向心力并非新的力种，它只是指向圆心的合力。

7. Momentum and Impulse | 动量与冲量

Linear momentum is a vector quantity defined as p = m v. Impulse (J) measures the effect of a force acting over a time interval: J = F Δ t = Δ p. This impulse–momentum relationship is particularly useful when forces vary with time, as the area under a force–time graph gives the impulse and hence the change in momentum. The units of momentum are kg m s⁻¹, and impulse has the same units.

线动量是矢量，定义为 p = m v。冲量 (J) 衡量力在一段时间内产生的效果：J = F Δ t = Δ p。这一冲量-动量关系在分析变力作用时尤其有用，力-时间图线下面积即冲量，代表动量变化。动量的单位是 kg m s⁻¹，冲量单位与之相同。

8. Conservation of Momentum | 动量守恒定律

In a closed system with no external forces, the total linear momentum before an interaction equals the total momentum after. For two colliding bodies: m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂, where u denotes initial velocities and v final velocities. This vector law applies independently in each perpendicular direction, making it a powerful tool for solving collision and explosion problems in both SL and HL IB Physics.

在没有外力的封闭系统中，作用前后总线动量守恒。对于两个碰撞物体：m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂，其中 u 代表初速度，v 代表末速度。这一矢量定律在任意正交方向上独立成立，因此成为解决 IB 物理 SL 与 HL 中碰撞、爆炸问题的强有力工具。

9. Work, Energy, and Power | 功、能与功率

Work done by a constant force is W = F s cos θ, where θ is the angle between the force and displacement. Work transfers energy; kinetic energy (Eₖ = ½ m v²) is the energy due to motion, while gravitational potential energy change near Earth’s surface is ΔEₚ = m g Δh. Power is the rate of doing work: P = W / t = F v for a constant force acting in the direction of velocity. The unit of work and energy is the joule (J), and power is measured in watts (W).

恒力做功 W = F s cos θ，其中 θ 为力与位移的夹角。功是能量传递的量度；动能 (Eₖ = ½ m v²) 源自物体运动，地球表面附近的重力势能变化为 ΔEₚ = m g Δh。功率是做功的快慢：P = W / t，当力与速度同向时也可写为 P = F v。功和能量的单位是焦耳 (J)，功率单位为瓦特 (W)。

10. Conservation of Energy | 能量守恒定律

Energy cannot be created or destroyed, only converted from one form to another. For isolated systems, total mechanical energy (sum of kinetic and potential energies) remains constant if only conservative forces do work. When non-conservative forces such as friction or air resistance act, mechanical energy is dissipated as thermal energy, yet total energy including heat still obeys conservation. Energy bar charts and Sankey diagrams are useful visual tools.

能量不能被创造或消灭，只能从一种形式转化为另一种形式。对于孤立系统，若只有保守力做功，总机械能（动能与势能之和）保持不变。当摩擦力或空气阻力等非保守力作用时，机械能将耗散为热能，但包含热能在内的总能量仍然守恒。能量柱状图和桑基图是直观的视觉工具。

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

In an elastic collision, both momentum and total kinetic energy are conserved. The relative speed of separation equals the relative speed of approach (coefficient of restitution e = 1). In a perfectly inelastic collision, the objects stick together, kinetic energy is not conserved (maximum loss), but momentum is still conserved. Most real collisions lie between these extremes. IB exam questions often ask for final velocities using conservation of momentum alone, or combined with kinetic energy conservation if elastic.

弹性碰撞中，动量和总动能同时守恒，分离时相对速度大小等于接近时相对速度大小（恢复系数 e = 1）。完全非弹性碰撞中，物体粘合在一起，动能不再守恒（损失最大），但动量依然守恒。大多数真实碰撞介于两者之间。IB 考题常要求仅用动量守恒，或结合动能守恒（若注明弹性）来求解末速度。

Property	Elastic Collision	Perfectly Inelastic Collision
Momentum	Conserved	Conserved
Kinetic Energy	Conserved	Not conserved (maximum loss)
Objects after impact	Separate	Stick together
Coefficient of restitution e	e = 1	e = 0

12. Problem-Solving Strategies | 解题策略

Approach dynamics problems systematically: (1) Define the system and identify known/unknown quantities. (2) Draw a clear free-body diagram for each object. (3) Choose a convenient coordinate system and resolve forces. (4) Apply Newton’s second law (F_net = m a) or conservation laws (momentum, energy) as appropriate. (5) For collisions, determine whether kinetic energy is conserved; if not, use momentum conservation alone. (6) Check units and physical reasonableness of the final answer. Regular practice with past IB papers will build confidence and speed.

系统性地处理动力学问题：(1) 明确系统，标出已知量与未知量。(2) 为每个物体画出清晰的受力分析图。(3) 选择合适的坐标系并分解力。(4) 根据情况应用牛顿第二定律 (F_net = m a) 或守恒定律（动量、能量）。(5) 对于碰撞问题，判断动能是否守恒；若不守恒，仅用动量守恒。(6) 检查单位与最终答案的物理合理性。通过反复练习 IB 历年真题，可以有效提升信心与解题速度。

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