📚 A-Level WJEC Physics: Dynamics Essentials | A-Level WJEC 物理：动力学 考点精讲
Dynamics is the branch of mechanics that explains how and why objects move. In the WJEC A-Level specification, you are expected to master motion in one and two dimensions, Newton’s laws, momentum and impulse, collisions, and the application of these principles to solve real‑world problems. This guide brings together all the key concepts, equations and graphical techniques you need, with clear worked examples.
动力学是力学中解释物体如何以及为何运动的分支。在 WJEC A-Level 课程大纲中，你需要掌握一维和二维运动、牛顿定律、动量和冲量、碰撞，以及运用这些原理解决实际问题。本指南汇总了所有关键概念、方程式和图像技巧，并配有清晰的例题解析。
1. Equations of Motion (SUVAT) | 运动学方程 (SUVAT)
For an object moving with constant acceleration along a straight line, five quantities are linked: displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). Remember that these equations only apply when acceleration is uniform.
对于沿直线做匀加速运动的物体，五个物理量相互关联：位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t)。请记住这些方程仅在加速度恒定时适用。
The four standard SUVAT equations are:
四个标准的 SUVAT 方程为：
v = u + a t
s = ½ (u + v) t
s = u t + ½ a t²
v² = u² + 2 a s
You must be able to identify which three quantities are known and choose the equation that contains the unknown you need. Always define your positive direction before substituting values – this helps avoid sign errors when dealing with deceleration or downward motion under gravity.
你必须能够识别哪三个量已知，并选择包含所求未知量的方程。代入数值前务必定义正方向——这有助于处理减速或重力作用下的向下运动时避免符号错误。
2. Motion Graphs | 运动图像
Displacement–time (s–t), velocity–time (v–t) and acceleration–time (a–t) graphs are powerful tools for analysing motion. The gradient of an s–t graph gives velocity; the gradient of a v–t graph gives acceleration. The area under a v–t graph represents the change in displacement.
位移—时间 (s–t)、速度—时间 (v–t) 和加速度—时间 (a–t) 图像是分析运动的有力工具。s–t 图的斜率表示速度；v–t 图的斜率表示加速度。v–t 图下的面积代表位移的变化。
For WJEC exams, you may be asked to sketch graphs for bouncing balls, cars overtaking, or parachutists. Key features include constant slopes for uniform velocity/acceleration and curved lines for changing acceleration. Always label axes clearly and mark important values.
在 WJEC 考试中，你可能会被要求画出弹跳球、超车或跳伞者的运动图像。关键特征包括匀速/匀加速对应的恒定斜率，以及加速度变化对应的曲线。务必清晰标注坐标轴并标记重要数值。
3. Free Fall and Projectile Motion | 自由落体与抛体运动
Objects moving under gravity alone experience constant downward acceleration g (approximately 9.81 m s⁻²). In free fall, you can apply SUVAT equations with a = g or a = −g depending on your sign convention.
仅在重力作用下运动的物体经历恒定的向下加速度 g（约 9.81 m s⁻²）。在自由落体中，你可以将 a = g 或 a = −g 代入 SUVAT 方程，具体取决于你选取的正方向。
For projectiles, horizontal and vertical motions are independent. Horizontally, velocity is constant (assuming no air resistance), so sₓ = uₓ t. Vertically, the motion is governed by g, using u_y and SUVAT. The trajectory is parabolic. Time of flight is determined entirely by the vertical component.
对于抛体，水平和竖直运动是独立的。水平方向速度恒定（假设无空气阻力），因此 sₓ = uₓ t。竖直方向受 g 控制，使用 u_y 和 SUVAT 方程。轨迹为抛物线。飞行时间完全由竖直分量决定。
4. Newton’s Three Laws of Motion | 牛顿运动三定律
Newton’s First Law states that an object remains at rest or in uniform motion unless acted upon by a resultant force. It introduces the concept of inertia.
牛顿第一定律指出，除非受到合外力作用，否则物体将保持静止或匀速直线运动。这引入了惯性的概念。
Newton’s Second Law is the cornerstone of dynamics: F = m a, where F is the resultant force in newtons, m the mass in kilograms and a the acceleration in m s⁻². In WJEC, you must use net force when applying this law, often after resolving components.
牛顿第二定律是动力学的基石：F = m a，其中 F 是合外力（牛顿），m 是质量（千克），a 是加速度（m s⁻²）。在 WJEC 考试中，应用该定律时必须使用净力，通常需要在分解力之后。
Newton’s Third Law reminds us that forces come in pairs: if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. These action–reaction pairs act on different bodies and never cancel out in the motion of a single object.
牛顿第三定律提醒我们力成对出现：如果物体 A 对物体 B 施加一个力，那么物体 B 同时对 A 施加一个等大反向的力。这一对作用力和反作用力作用在不同物体上，绝不能在单个物体的运动中互相抵消。
5. Linear Momentum and Impulse | 线动量与冲量
Momentum p is the product of mass and velocity: p = m v. It is a vector quantity and is conserved in isolated systems. The unit of momentum is kg m s⁻¹ or equivalently N s.
动量 p 是质量与速度的乘积：p = m v。它是矢量，在孤立系统中守恒。动量的单位是 kg m s⁻¹，等同于 N s。
Impulse is defined as the change in momentum of an object when a force acts over a time interval: Impulse = F Δt = Δ(m v). A large force applied for a short time (e.g. in a collision) can produce the same impulse as a smaller force applied for a longer time.
冲量定义为力在一段时间间隔内作用时物体的动量变化：冲量 = F Δt = Δ(m v)。短时间内施加的大力度（例如碰撞中）可以产生与较长时间内较小力度相同的冲量。
Rearranging gives the force–momentum relationship: F = Δp / Δt. This is especially useful when the mass changes (e.g. rocket thrust) or when the force varies with time.
整理可得力与动量的关系：F = Δp / Δt。当质量变化（例如火箭推力）或力随时间变化时，此式特别有用。
6. Conservation of Momentum | 动量守恒
In any interaction where no external resultant force acts, the total momentum of a system remains constant. For a two‑body collision or explosion, this is expressed as:
在没有任何外部合外力作用的情况下，系统的总动量保持不变。对于两体碰撞或爆炸，可表示为：
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
This principle underpins collision analysis, recoil problems and jet propulsion. Remember that momentum is a vector, so you must assign positive and negative directions consistently, especially in one‑dimensional problems where objects move in opposite directions.
这一原理是碰撞分析、反冲问题和喷气推进的基础。切记动量是矢量，因此必须始终如一地设定正负方向，尤其在一维问题中物体反向运动时。
7. Elastic and Inelastic Collisions | 弹性与非弹性碰撞
In an elastic collision, both momentum and kinetic energy are conserved. This idealised case rarely occurs in macroscopic collisions but is common for gas molecules. The relative speed of approach equals the relative speed of separation: u₁ – u₂ = v₂ – v₁ (for head‑on collisions).
在弹性碰撞中，动量和动能都守恒。这种理想化情况在宏观碰撞中极少发生，但对于气体分子却很常见。相对接近速度等于相对分离速度：u₁ – u₂ = v₂ – v₁（用于正面碰撞）。
In an inelastic collision, momentum is conserved but kinetic energy is not – some energy is transferred to heat, sound or permanent deformation. A perfectly inelastic collision is one where the bodies stick together after impact, moving with a common velocity.
在非弹性碰撞中，动量守恒但动能不守恒——一部分能量转化为热能、声能或永久形变。完全非弹性碰撞指物体碰撞后粘在一起，以共同速度运动。
8. Force–Time Graphs and Impulse | 力-时间图与冲量
The area under a force–time graph (including the direction sign) equals the impulse delivered, and hence the change in momentum. WJEC questions often involve a graph with a peak force and a base time, from which you calculate the impulse and then determine final velocity or average force.
力-时间图下的面积（包括方向符号）等于所施加的冲量，也就是动量的变化。WJEC 考题常给出带有峰值力和作用时间的图像，要求计算冲量，然后求出末速度或平均力。
The average force can be found using F_avg = Δp / Δt. If the force is not constant, you may need to estimate the area under the curve by counting squares or using geometric formulas for triangles and rectangles.
平均力可用 F_avg = Δp / Δt 求得。若力不恒定，你可能需要通过数格或运用三角形和矩形的几何公式来估算曲线下面积。
9. Connected Particles and Tension | 连接体与张力
When two or more bodies are connected by a light inextensible string over a pulley, or by a rod, the key assumption is that the string has the same tension throughout (if masless and smooth pulley) and the acceleration of the connected masses has the same magnitude.
当两个或多个物体通过轻质不可伸长的绳子跨过滑轮连接，或通过杆连接时，关键假设是绳中各点张力相等（若无摩擦且不计绳质量），且连接体的加速度大小相同。
To solve such problems, draw free‑body diagrams for each particle, apply F = m a separately, and link the equations via the common acceleration and tension. Typical examples include lifts, Atwood machines, and blocks on slopes with one mass hanging vertically.
解决此类问题时，为每个质点画出隔离体图，分别应用 F = m a，并通过共同的加速度和张力将方程联系起来。典型例子包括电梯、阿特伍德机，以及斜面上一个物块连接竖直悬挂质量的系统。
10. Friction and Resistive Forces | 摩擦力与阻力
Frictional force acts parallel to the surfaces in contact and opposes relative motion. The maximum static friction is F_f ≤ μ_s R, and kinetic friction is usually given by F_f = μ_k R, where R is the normal reaction force. In WJEC, you may be expected to resolve forces on inclined planes to find R and then the frictional force.
摩擦力沿接触面平行方向作用，阻碍相对运动。最大静摩擦力为 F_f ≤ μ_s R，动摩擦力通常表示为 F_f = μ_k R，其中 R 是法向反作用力。在 WJEC 中，你可能需要分解斜面上的力以求出 R，再算出摩擦力。
Air resistance or drag increases with speed and often depends on v or v². When drag equals the driving force, terminal velocity is reached. Skydivers and falling objects in fluids are common WJEC contexts for applying Newton’s laws with variable forces.
空气阻力或拖拽力随速度增大而增大，通常与 v 或 v² 有关。当拖拽力等于驱动力时，物体达到终极速度。跳伞者和流体中下落的物体是 WJEC 常见的应用牛顿定律处理变力的情境。
11. Moments and Equilibrium (Extended Dynamics) | 力矩与平衡（拓展动力学）
Although often treated in statics, the principle of moments is vital for dynamic situations where a system has rotational equilibrium or angular acceleration. A moment is defined as the product of the force and the perpendicular distance from the pivot: Moment = F × d.
虽然力矩通常在静力学中处理，但在系统具有转动平衡或有角加速度的动力学情境中，力矩原理至关重要。力矩定义为力与从转轴到力作用线的垂直距离的乘积：力矩 = F × d。
For a rigid body in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about any point. This concept appears in WJEC problems involving beams, levers, and even rolling objects where torque leads to angular acceleration governed by τ = I α (if extended to rotational dynamics).
对于处于转动平衡的刚体，绕任意点的顺时针力矩之和等于逆时针力矩之和。这一概念出现在 WJEC 涉及横梁、杠杆乃至滚动物体的问题中，此时转矩导致角加速度，由 τ = I α 控制（若扩展到转动动力学）。
12. Problem‑Solving Strategy for Dynamics | 动力学的解题策略
Step 1: Draw a clear diagram showing all forces and known values. Define a positive direction. Step 2: Resolve forces into components if motion is on an incline or in two dimensions. Step 3: Write down relevant equations – SUVAT for kinematics, F = m a for dynamics, and conservation laws if applicable. Step 4: Solve algebraically and check units.
第一步：画出示力图，标明所有力和已知量。定义正方向。第二步：若运动在斜面上或涉及二维，分解力为分量。第三步：写出相关方程式——运动学用 SUVAT，动力学用 F = m a，若适用则用守恒定律。第四步：代数求解并检查单位。
WJEC examiners reward structured working. Label steps clearly, avoid jumping straight to numeric answers, and always state assumptions (e.g., ‘no air resistance’, ‘smooth pulley’, ‘light string’). If a question involves impacts or explosions, identify whether momentum is conserved and verify that no external force acts along the line of collision.
WJEC 考官青睐结构清晰的答题。清晰标注步骤，避免直接跳到数值答案，并始终陈述假设（例如，“无空气阻力”、“光滑滑轮”、“轻绳”）。若题目涉及碰撞或爆炸，确定动量是否守恒，并验证碰撞方向上无外力作用。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导