📚 IB & CIE Physics: Dynamics – Key Concepts and Exam Tips | IB CIE 物理：动力学考点精讲
Dynamics is a cornerstone of both IB and CIE physics syllabuses, bridging kinematics with the laws of motion and conservation principles. This guide clarifies key concepts, equations, and exam strategies to help you master motion, forces, momentum, energy, and circular motion with confidence.
动力学是 IB 与 CIE 物理大纲的核心支柱，它将运动学与运动定律、守恒原理连接起来。本文深入解析位移、牛顿定律、动量、能量及圆周运动等关键概念和应考技巧，帮助你扎实掌握力学。
1. Displacement, Velocity and Acceleration | 位移、速度和加速度
Displacement (s) is a vector quantity representing the straight-line distance and direction from the initial to the final position. Velocity (v) is the rate of change of displacement, while speed is the scalar rate of distance covered. Acceleration (a) describes how quickly velocity changes per unit time.
位移（s）是矢量，表示从起点到终点的直线距离与方向。速度（v）是位移的变化率，而速率是路程的标量速率。加速度（a）描述速度在单位时间内的变化快慢。
The average velocity is vavg = Δs/Δt, and instantaneous velocity is the limit as Δt approaches zero. For constant acceleration, acceleration is given by a = (v − u)/t, where u is initial velocity and v is final velocity.
平均速度 vavg = Δs/Δt，瞬时速度是 Δt 趋于零时的极限。在匀加速运动中，加速度 a = (v − u)/t，其中 u 为初速度，v 为末速度。
Interpreting motion graphs is critical: the gradient of a displacement–time graph gives velocity, the gradient of a velocity–time graph gives acceleration, and the area under a velocity–time graph equals displacement.
运动图线的解读至关重要：位移–时间图的斜率表示速度，速度–时间图的斜率表示加速度，而速度–时间图下的面积等于位移。
2. Equations of Motion (SUVAT) | 运动学方程 (SUVAT)
For uniform acceleration in a straight line, five standard equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). These are often called the SUVAT equations.
对于匀加速直线运动，五个标准方程将位移（s）、初速度（u）、末速度（v）、加速度（a）和时间（t）联系起来，常统称为 SUVAT 方程。
| Equation | Missing quantity |
|---|---|
| s = ½(u + v)t | a |
| v = u + a t | s |
| s = u t + ½a t² | v |
| s = v t − ½a t² | u |
| v² = u² + 2a s | t |
Choose the equation that omits the unknown you do not need. Always check that acceleration is constant and that the motion is along a single straight line before applying these formulas.
选择缺少你不需要的未知量的方程。在应用这些公式前，务必确认加速度恒定且运动沿一条直线。
For vertical motion under gravity, replace a with g (9.81 m s⁻²) and set a direction as positive. The same equations apply, but the sign of g must be consistent with your chosen orientation.
对于重力作用下的竖直运动，将 a 替换为 g（9.81 m s⁻²）并规定正方向。相同的公式适用，但 g 的符号必须与你选取的方向一致。
3. Free Fall and Projectile Motion | 自由落体与抛体运动
An object in free fall accelerates downwards at g regardless of its mass, provided air resistance is negligible. Use the SUVAT equations with a = g or −g depending on the sign convention.
只要空气阻力可忽略，自由落体的物体以 g 向下加速，与质量无关。根据符号规定，使用 a = g 或 −g 的 SUVAT 方程。
Projectile motion is analysed by splitting it into horizontal and vertical components. Horizontally, velocity remains constant (ax = 0), while vertically, the motion undergoes uniform acceleration due to gravity (ay = g downwards).
抛体运动需分解为水平和竖直两个分量。水平方向速度恒定（ax = 0），竖直方向因重力而作匀加速运动（ay = g 向下）。
Time of flight, maximum height, and horizontal range can all be found by combining the two independent motions. The launch angle of 45° gives maximum range on level ground when launch and landing heights are equal.
飞行时间、最大高度和水平射程均可通过组合这两个独立运动求得。在发射与落地等高时，45° 的发射角可获得最大水平射程。
4. Newton’s Laws of Motion | 牛顿运动定律
Newton’s first law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by a net external force. This introduces the concept of inertia.
牛顿第一定律指出，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。这引出了惯性的概念。
The second law defines the relationship Fnet = m a, where Fnet is the vector sum of all forces acting on a body. Acceleration is directly proportional to resultant force and inversely proportional to mass.
第二定律定义了 Fnet = m a，其中 Fnet 是作用在物体上所有力的矢量和。加速度与合力成正比，与质量成反比。
Newton’s third law emphasizes that forces come in pairs: if body A exerts a force on body B, then B exerts an equal and opposite force on A. These action–reaction pairs act on different bodies and never cancel each other.
牛顿第三定律强调力成对出现：若物体 A 对 B 施加一个力，则 B 同时对 A 施加一个大小相等、方向相反的力。这对作用力与反作用力作用在不同物体上，绝不相互抵消。
5. Free-Body Diagrams and Tension | 受力分析与张力
A free-body diagram isolates an object and shows all forces acting on it as vector arrows. Drawing clear diagrams is essential for setting up Fnet = m a in any dynamics problem.
受力分析图将物体隔离，以矢量箭头标出所有作用于其上的力。在求解任何动力学问题时，清晰的受力图至关重要。
Tension is the pulling force transmitted through a string, rope or cable when it is taut. In a light, inextensible string passing over a smooth pulley, the tension is the same on both sides.
张力是通过张紧的细绳、绳索或线缆传递的拉力。在一根轻质不可伸长的细绳绕过光滑滑轮时，两端的张力大小相等。
When solving connected-body problems, apply Fnet = m a to each mass individually, link accelerations using the constraint of the string, and solve the simultaneous equations.
求解连接体问题时，对每个物体分别应用 Fnet = m a，利用细绳约束条件联系加速度，然后解联立方程。
6. Friction and Normal Force | 摩擦与法向力
Friction is a contact force that opposes relative motion or attempted motion. The maximum static friction is given by fs,max = μs N, and kinetic friction by fk = μk N, where N is the normal reaction force.
摩擦力是阻碍相对运动或运动趋势的接触力。最大静摩擦力 fs,max = μs N，滑动摩擦力 fk = μk N，其中 N 为法向反作用力。
The normal force N is not always equal to mg; it adjusts according to other vertical forces and the slope of the surface. On an incline of angle θ without other vertical forces, N = mg cos θ.
法向力 N 并不总等于 mg；它会根据其他竖直力和斜面倾角进行调整。在没有其他竖直力的倾角为 θ 的斜面上，N = mg cos θ。
Always decide whether the problem involves static or kinetic friction and use the appropriate coefficient. Remember that static friction can vary from zero up to μs N, while kinetic friction is roughly constant.
务必判断问题涉及静摩擦还是动摩擦，并选用相应的系数。注意静摩擦可从零变化到 μs N，而动摩擦则基本保持恒定。
7. Momentum and Impulse | 动量与冲量
Linear momentum is defined as p = m v, a vector quantity with units kg m s⁻¹. Momentum becomes particularly useful when analysing collisions and explosions.
线动量定义为 p = m v，是矢量，单位为 kg m s⁻¹。动量在分析碰撞和爆炸时特别有用。
Impulse equals the change in momentum: F Δt = Δp = m v − m u. This impulse-momentum theorem follows directly from Newton’s second law and is especially helpful when forces vary over short intervals.
冲量等于动量的变化量：F Δt = Δp = m v − m u。该冲量–动量定理直接来源于牛顿第二定律，对于在极短时间内变化的力尤其有用。
The area under a force–time graph represents impulse, so calculating the area in a graph allows determination of momentum change even for non-constant forces.
力–时间图下的面积代表冲量，因此通过求面积可在力非恒定时确定动量的变化。
8. Conservation of Momentum | 动量守恒
In any closed system with no external resultant force, total linear momentum remains constant. For two interacting bodies, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
在任何合外力为零的封闭系统中，总线动量守恒。对于两个相互作用的物体，有 m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
Apply the conservation law separately to each perpendicular direction in two-dimensional collisions. In perfectly inelastic collisions, bodies stick together and kinetic energy is not conserved, though momentum still is.
在二维碰撞中，需对每个垂直方向分别应用守恒定律。完全非弹性碰撞中，物体粘在一起，动能不守恒，但动量仍守恒。
Explosions are simply the reverse of inelastic collisions: a single object breaks apart, and the fragments fly apart with total momentum still zero if the body was initially at rest.
爆炸可看作是碰撞的逆过程：单个物体碎裂，若其初始静止，碎片飞散的总动量仍保持为零。
9. Work, Energy and Power | 功、能量与功率
Work done by a constant force is W = F s cos θ, where θ is the angle between force and displacement. Work transfers energy and is measured in joules (J).
恒力做的功 W = F s cos θ，其中 θ 是力与位移的夹角。功传递能量，单位为焦耳 (J)。
Kinetic energy (KE) is the energy of motion, KE = ½ m v². The work–energy principle states that the net work done on an object equals its change in kinetic energy.
动能 (KE) 是运动具有的能量，KE = ½ m v²。动能定理指出，物体所受合外力做的总功等于其动能的变化量。
Power is the rate of doing work, P = W/t = F v, where v is the instantaneous velocity in the direction of the force. The unit is the watt (W), equivalent to J s⁻¹.
功率是做功的速率，P = W/t = F v，其中 v 是沿力方向的瞬时速度。单位是瓦特 (W)，等于 J s⁻¹。
10. Conservation of Energy | 能量守恒
The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In a closed system, total mechanical energy (KE + PE) is constant if only conservative forces do work.
能量守恒定律指出，能量既不能被创造也不能被消灭，只能从一种形式转化为另一种形式。若只有保守力做功，封闭系统的总机械能（动能+势能）守恒。
Gravitational potential energy near Earth’s surface is ΔPE = m g Δh. In the absence of friction and air resistance, the sum m g h + ½ m v² remains unchanged throughout a fall or swing.
地表附近的重力势能变化为 ΔPE = m g Δh。在没有摩擦和空气阻力时，m g h + ½ m v² 之和在下落或摆动过程中保持不变。
When non-conservative forces like friction act, mechanical energy is dissipated, often as heat. Use the work done against friction to account for the ‘missing’ energy in energy balance equations.
当有摩擦力等非保守力作用时，机械能会耗散，通常转变为热量。在能量平衡方程中，需用克服摩擦力做的功来解释“消失”的能量。
11. Circular Motion Dynamics | 圆周运动动力学
An object moving at constant speed in a circle experiences an acceleration directed toward the centre: centripetal acceleration ac = v²/r = ω² r, where ω is the angular speed in rad s⁻¹.
做匀速圆周运动的物体具有指向圆心的向心加速度：ac = v²/r = ω² r，其中 ω 为角速度，单位 rad s⁻¹。
By Newton’s second law, the net force toward the centre, the centripetal force, is Fc = m v²/r. This resultant force can be provided by tension, gravity, friction, or the normal reaction, depending on the context.
根据牛顿第二定律，指向圆心的合力即向心力为 Fc = m v²/r。这一合力可以由张力、重力、摩擦力或法向反作用力提供，视情境而定。
Common exam scenarios include a car rounding a banked curve, a conical pendulum, and a mass on a string in vertical circles. Always draw a free-body diagram and resolve forces toward the centre.
常见考题情景包括汽车在倾斜弯道上行驶、锥摆，以及竖直面上的绳系小球圆周运动。务必画出受力图并将力沿径向分解。
12. Common Misconceptions and Exam Tips | 常见误区与应考技巧
Misconception: ‘A constant force produces constant velocity.’ In reality, constant net force produces constant acceleration, meaning velocity changes steadily. Without net force, velocity remains constant (Newton’s first law).
误区：“恒力产生恒定速度。” 事实上，恒定的合力产生恒定加速度，速度会均匀变化。只有无净外力时，速度才保持恒定（牛顿第一定律）。
Misconception: ‘Action and reaction forces cancel out.’ They act on different objects, so they do not cancel within a single free-body diagram. Always check which object you are analysing.
误区：“作用力与反作用力相互抵消。” 它们作用在不同物体上，因此在单一受力分析图中并不抵消。务必明确你正在分析哪个物体。
In calculations, adopt a consistent sign convention (e.g., upward positive for vertical motion). When applying conservation of momentum, remember that it is a vector relation — directions matter. Write separate component equations for 2D problems.
计算时应采用一致的符号规定（例如竖直运动以上为正）。应用动量守恒时，务必记住它是矢量关系——方向至关重要。二维问题要分别写分量方程。
Finally, double-check units: convert grams to kilograms, centimetres to metres, and ensure velocities are in m s⁻¹. In energy problems, remember that ΔPE = m g Δh uses the vertical height change, not the distance along a slope unless the slope angle is used.
最后，仔细检查单位：将克转换为千克、厘米转换为米，并确保速度单位为 m s⁻¹。在能量问题中，ΔPE = m g Δh 使用的是竖直高度变化，而非沿斜面的距离，除非结合斜面倾角计算。
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