📚 Dynamics: Key Exam Points for IB & OCR Physics | IB OCR 物理：动力学 考点精讲
Mastering dynamics is the key to unlocking high scores in both IB and OCR Physics. This article consolidates the core concepts of forces, momentum, and circular motion, and illustrates how examiners test your understanding through typical problem scenarios. Read on for a bilingual breakdown that pairs every essential idea in English and Chinese, helping you recall the details precisely under time pressure.
掌握动力学是在IB和OCR物理中取得高分的关键。本文整合了力、动量与圆周运动的核心概念，并以典型问题情境说明考官如何考察你的理解。请仔细阅读以下双语精讲，每个要点均以英语和中文配对呈现，帮助你在限时考试中准确回忆细节。
1. Newton’s Laws of Motion | 牛顿运动定律
Newton’s first law states that an object remains at rest or continues with uniform velocity in a straight line unless acted upon by a net external force. This is the principle of inertia.
牛顿第一定律指出，物体保持静止或沿直线匀速运动，除非受到净外力的作用。这就是惯性原理。
The second law provides the quantitative link: the net force acting on an object equals the product of its mass and acceleration. For a constant-mass system, acceleration is directly proportional to the net force.
第二定律给出了定量关系：作用在物体上的净力等于质量与加速度的乘积。在质量不变的系统中，加速度与净力成正比。
ΣF = m a
Newton’s third law reminds us that forces always come in pairs: if body A exerts a force on body B, then B exerts an equal and opposite force on A. The two forces act on different objects and never cancel within a single free-body diagram.
牛顿第三定律提醒我们，力总是成对出现：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。这两个力作用在不同物体上，在单个受力图中永远不会相互抵消。
2. Free-Body Diagrams and Resolution of Forces | 受力图与力的分解
A clear free-body diagram is the first step in solving any dynamics problem. Draw all forces acting on the chosen body, label them, and define a convenient coordinate system before writing equations.
清晰的受力图是求解任何动力学问题的第一步。画出作用在所选物体上的所有力、标明符号，并在写方程之前定义方便的坐标系。
Forces can be resolved into perpendicular components, typically horizontal and vertical, or parallel and perpendicular to an inclined plane. Use trigonometric ratios to find components.
力可以分解为互相垂直的分量，通常沿水平与竖直方向，或沿斜面的平行与垂直方向。使用三角函数关系求出各分量。
If a system is in translational equilibrium, the net force in each perpendicular direction must be zero, which gives two independent equations for static or constant-velocity situations.
若系统处于平动平衡，每个垂直方向上的净力必须为零，这为静止或匀速直线运动情境提供了两个独立的方程。
ΣFₕ = 0 , ΣFᵥ = 0
3. Friction, Drag and Terminal Velocity | 摩擦、阻力与终极速度
Static friction prevents relative motion and can vary up to a maximum value. Kinetic friction acts when surfaces slide and has a constant magnitude for given surfaces and normal force.
静摩擦力阻止相对运动，其大小可在零至最大值之间变化。动摩擦力在表面滑动时起作用，对于给定的接触表面和法向力，其大小恒定。
The magnitudes are described by coefficients of friction μₛ (static) and μₖ (kinetic), and both are proportional to the normal reaction N.
摩擦力的大小由静摩擦系数μₛ和动摩擦系数μₖ描述，两者均与法向反作用力N成正比。
fₘₐₓ = μₛ N , fₖ = μₖ N
When an object moves through a fluid, drag force increases with speed. For a falling object, drag eventually balances weight, resulting in zero net force and a constant terminal velocity. IB and OCR frequently test this via velocity-time graphs.
当物体在流体中运动时，阻力随速度增大。对于下落的物体，阻力最终与重力平衡，净力为零，达到恒定的终极速度。IB和OCR常通过速度-时间图来考查此知识点。
4. Momentum and Impulse | 动量与冲量
Linear momentum is a vector quantity defined as the product of mass and velocity. It points in the same direction as the velocity.
动量是矢量，定义为质量与速度的乘积，其方向与速度方向相同。
p = m v
Impulse measures the effect of a force acting over a time interval. It equals the change in momentum of the object on which the force acts, which is the impulse-momentum theorem.
冲量衡量力在一段时间间隔内的作用效果，等于受力物体的动量变化量，这就是冲量-动量定理。
J = F Δt = Δp
In collisions and explosions, the individual momenta change, but as long as the system is isolated, the total vector momentum remains constant. This is the principle of conservation of momentum.
在碰撞和爆炸中，个别物体的动量会变化，但只要系统不受外力的净冲量，总矢量和动量保持不变。这就是动量守恒原理。
5. Conservation of Momentum | 动量守恒
In any closed system, the total initial momentum vector equals the total final momentum vector. This allows us to relate the velocities before and after an interaction without needing to know the detailed forces.
在任何封闭系统中，总初动量矢量等于总末动量矢量。这使我们无需了解具体受力细节，就可以关联相互作用前后的速度。
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
Momentum conservation is a vector law. In two-dimensional problems, you must resolve components along perpendicular axes and apply conservation independently to each axis, a skill examined in both IB HL and OCR A-level.
动量守恒是矢量定律。在二维问题中，你必须沿垂直坐标轴分解动量，并对每个轴独立应用守恒定律，这是IB HL和OCR A-level都考察的技能。
Typical exam questions involve recoil of a gun, explosions splitting a stationary object into fragments, or two particles colliding at an angle. Always define a sign convention for directions.
典型的考题包括枪的后坐力、静止物体爆炸分裂成碎片、两个粒子以一定角度碰撞。务必先规定正方向。
6. Elastic and Inelastic Collisions | 弹性碰撞与非弹性碰撞
Collisions are classified by what happens to kinetic energy. In an elastic collision, both momentum and total kinetic energy are conserved. In an inelastic collision, momentum is conserved but some kinetic energy is transformed into other forms.
碰撞根据动能的变化来分类。在弹性碰撞中，动量和总动能都守恒。在非弹性碰撞中，动量守恒，但部分动能转化为其他形式的能量。
| Property | Elastic | Inelastic |
|---|---|---|
| Momentum | Conserved | Conserved |
| Total KE | Conserved | Not conserved |
| Objects | Bounce apart perfectly | May stick together (perfectly inelastic) or separate with less KE |
The table above summarizes the key differences. A perfectly inelastic collision is a common special case where the colliding bodies stick together and move with a common final velocity, yielding the maximum kinetic energy loss.
上表总结了关键区别。完全非弹性碰撞是一个常见的特殊情况，碰撞物体粘在一起并以共同速度运动，导致动能损失最大。
In IB internal assessments or OCR practical questions, you may be asked to use air tracks or light gates to verify momentum conservation and classify a collision by comparing initial and final kinetic energies.
在IB内部评估或OCR实验题中，你可能需要用气垫导轨或光电门验证动量守恒，并通过比较初末动能来分类碰撞类型。
7. Impulse from Force-Time Graphs | 由力-时间图求冲量
The impulse delivered by a varying force is equal to the area under the force-time graph. This is a direct consequence of the definition of impulse as the integral of force over time.
变力提供的冲量等于力-时间曲线下的面积。这是冲量定义为力对时间积分的直接结果。
J = Area under F–t graph
Examiners often give a graph of a non-constant force, such as a kick or a crash, and ask for the impulse, the average force, or the change in velocity. Count squares or use area formulas for triangles and rectangles to find the impulse.
考官常给出一个非恒力的图像，例如踢球或碰撞，要求求出冲量、平均力或速度变化。可以用计数格子的方法或使用三角形、矩形的面积公式来求冲量。
Once the impulse is obtained, combine it with the impulse-momentum theorem to determine the resulting speed, provided the initial momentum is known. This is a reliable technique across all major exam boards.
一旦求得冲量，结合冲量-动量定理，在已知初动量的情况下即可确定末速度。这是各大考试局通用的可靠技巧。
8. Uniform Circular Motion | 匀速圆周运动
An object moving in a circle at constant speed is accelerating because the direction of its velocity is continuously changing. The acceleration points towards the centre of the circle and has constant magnitude.
物体做匀速圆周运动时仍存在加速度，因为其速度方向不断改变。加速度指向圆心，大小恒定。
aᵣ = v² / r = ω² r
The angular speed ω is the rate of change of angular displacement, related to the period T and frequency f. These relationships are essential for linking rotational and linear quantities.
角速度ω是角位移的变化率，与周期T和频率f相关。这些关系式对于联系转动量与线量至关重要。
ω = 2π / T = 2π f , v = ω r
In both IB and OCR, you must be comfortable switching between these expressions, especially when analyzing the forces causing the centripetal acceleration.
在IB和OCR中，你必须熟练切换这些表达式，尤其是在分析产生向心加速度的力时。
9. Centripetal Force and Applications | 向心力及其应用
A net force directed towards the centre of the circular path is required for circular motion. This centripetal force is not a new type of force but is provided by tension, gravity, friction, or a normal reaction.
圆周运动需要一个指向圆心的净力。这个向心力不是新型的力，而是由张力、重力、摩擦力或法向反作用力提供。
Fᵣ = m v² / r = m ω² r
Common applications include a car rounding a bend (friction provides the centripetal force), a satellite orbiting a planet (gravity provides it), and a stone whirled on a string (tension). Banking of road curves uses a component of the normal reaction to assist, reducing reliance on friction.
常见的应用包括汽车转弯（摩擦力提供向心力）、卫星绕行星运行（万有引力提供）、以及用绳子旋转石块（张力提供）。弯道倾斜设计利用法向反作用力的分量来辅助，降低对摩擦力的依赖。
When analyzing vertical circular motion, such as a bucket of water swung overhead, the speed must be high enough at the top so that the sum of forces gives the required cent
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