A-Level Physics: Dynamics Key Points | A-Level物理：动力学考点精讲

📚 A-Level Physics: Dynamics Key Points | A-Level物理：动力学考点精讲

Welcome to the Dynamics revision guide for A-Level Physics. This module explores the relationship between motion and the forces that cause it, bridging kinematics (the description of motion) with Newton’s laws and momentum. Understanding these core principles is essential for solving problems ranging from projectile motion to collisions, and it lays the groundwork for more advanced topics like circular motion and oscillations.

欢迎来到A-Level物理动力学复习指南。本模块探讨运动与引起运动的力之间的关系，将运动学（对运动的描述）与牛顿定律和动量联系起来。理解这些核心原理对于解决从抛体运动到碰撞的各种问题至关重要，并为圆周运动和振动等更高级的主题奠定了基础。

1. Scalars and Vectors | 标量与矢量

Scalars are physical quantities that have only magnitude, such as distance, speed, mass, and time. Vectors, however, possess both magnitude and direction, including displacement, velocity, acceleration, and force. In dynamics, distinguishing between these two is crucial because vector addition follows specific rules, and direction often determines the sign of a quantity.

标量是只有大小的物理量，例如路程、速率、质量和时间。而矢量既有大小又有方向，包括位移、速度、加速度和力。在动力学中，区分两者至关重要，因为矢量加法遵循特定规则，方向常常决定了一个量的正负号。

When adding vectors, you can use the tip-to-tail method or resolve them into perpendicular components. Resolving a vector into horizontal and vertical components using trigonometry (e.g. F_x = F cos θ, F_y = F sin θ) simplifies two-dimensional motion analysis. Always define a positive direction before beginning calculations.

进行矢量相加时，可以使用三角形法则（头尾相接法）或将矢量分解为相互垂直的分量。利用三角函数将矢量分解为水平与竖直分量（例如 F_x = F cos θ，F_y = F sin θ）可以简化二维运动分析。在开始计算之前，请务必规定一个正方向。

2. Displacement, Velocity and Acceleration | 位移、速度和加速度

Displacement is the vector quantity that measures the straight-line distance from the initial position to the final position in a specified direction. It differs from distance, which is a scalar path length. Velocity is the rate of change of displacement, while speed is the rate of change of distance.

位移是矢量，测量从初位置到末位置在指定方向上的直线距离。它不同于路程，路程是标量路径长度。速度是位移的变化率，而速率是路程的变化率。

Acceleration is the rate of change of velocity. An object accelerates if its speed changes or if its direction changes. The definition is a = Δv / Δt, and the unit is m s⁻². In the context of constant acceleration, the five kinematic quantities — initial velocity u, final velocity v, acceleration a, displacement s, and time t — are linked by a set of equations.

加速度是速度的变化率。如果一个物体的速度大小改变或方向改变，它就具有加速度。其定义为 a = Δv / Δt，单位是 m s⁻²。在匀加速直线运动中，五个运动学量——初速度 u、末速度 v、加速度 a、位移 s 和时间 t——通过一组方程联系起来。

3. Kinematic Equations for Constant Acceleration | 匀加速运动学方程

For motion in a straight line with uniform acceleration, the following SUVAT equations apply. These are derived from the definitions of velocity and acceleration assuming a is constant. You must be able to select the correct equation based on which quantities are known and which are required.

对于匀加速直线运动，以下 SUVAT 方程成立。它们是根据速度和加速度的定义在 a 恒定的假设下推导出来的。你必须能够根据已知量和待求量选择正确的方程。

v = u + at

s = ut + ½at²

v² = u² + 2as

s = ½(u + v)t

Remember that s is the displacement, not the total distance travelled. If an object returns to its starting point, s = 0. For problems involving vertical motion under gravity, simply replace a with g (9.81 m s⁻²) and define upward or downward as positive consistently.

请记住，s 是位移，而不是通过的总路程。如果物体回到出发点，则 s = 0。对于涉及重力作用下的竖直运动问题，只需用 g（9.81 m s⁻²）代替 a，并始终如一地规定向上或向下为正方向。

4. Free Fall and Projectile Motion | 自由落体与抛体运动

Free fall is a special case of uniformly accelerated motion where the only force acting is gravity. The acceleration a becomes g, directed downward. When air resistance is negligible, all objects fall with the same acceleration regardless of mass.

自由落体是一种特殊的匀加速运动，其中唯一作用的力是重力。加速度 a 变为 g，方向向下。当空气阻力可以忽略时，所有物体无论质量大小都以相同的加速度下落。

Projectile motion is analysed by separating the horizontal and vertical components. Horizontally, velocity remains constant (if air resistance is ignored). Vertically, the motion is governed by constant acceleration g. The time of flight is determined by the vertical motion, while the range is found from the horizontal velocity and time.

抛体运动通过分解水平与竖直分量来分析。水平方向的速度保持不变（若忽略空气阻力）。竖直方向的运动由恒定加速度 g 控制。飞行时间由竖直运动决定，而射程则由水平速度和时间求出。

Use these equations for projectile motion: horizontal displacement x = u_x t, vertical displacement y = u_y t − ½gt², where u_x = u cos θ and u_y = u sin θ. Maximum height occurs when vertical velocity becomes zero, and the trajectory is parabolic in the absence of air resistance.

抛体运动使用以下方程：水平位移 x = u_x t，竖直位移 y = u_y t − ½gt²，其中 u_x = u cos θ，u_y = u sin θ。最大高度出现在竖直速度为零时，在没有空气阻力的情况下轨迹为抛物线。

5. Motion Graphs | 运动图像

Graphs of displacement-time, velocity-time, and acceleration-time provide powerful visual tools for interpreting motion. The gradient of a displacement-time graph gives the velocity; the gradient of a velocity-time graph gives the acceleration; the area under a velocity-time graph gives the displacement.

位移-时间、速度-时间和加速度-时间图像为解释运动提供了强有力的可视化工具。位移-时间图像的斜率表示速度；速度-时间图像的斜率表示加速度；速度-时间图像下方的面积表示位移。

In a displacement-time graph, a straight line indicates constant velocity. A curved line indicates changing velocity (acceleration). On a velocity-time graph, a horizontal line shows constant velocity, a sloping straight line shows constant acceleration, and the area can be calculated using geometry or integration for uniform acceleration.

在位移-时间图像中，直线表示速度恒定，曲线表示速度在变化（有加速度）。在速度-时间图像中，水平直线表示匀速，倾斜直线表示匀加速，面积可以通过几何方法或匀加速运动的积分来计算。

Gradient of s-t graph = velocity	s-t 图像斜率 = 速度
Gradient of v-t graph = acceleration	v-t 图像斜率 = 加速度
Area under v-t graph = displacement	v-t 图像下方面积 = 位移
Area under a-t graph = change in velocity	a-t 图像下方面积 = 速度变化量

6. Newton’s Laws of Motion | 牛顿运动定律

Newton’s First Law states that an object will remain at rest or move with constant velocity unless acted upon by a resultant external force. This is the principle of inertia, and it explains why observation of uniform motion implies zero net force.

牛顿第一定律指出，除非受到合外力的作用，否则物体将保持静止或匀速直线运动状态。这就是惯性原理，它解释了为什么观察到匀速运动意味着合外力为零。

Newton’s Second Law quantifies the relationship: resultant force F = m a, where m is the mass and a is the acceleration in the direction of the net force. This vector equation is fundamental in dynamics problems, linking kinematics with forces.

牛顿第二定律给出了定量关系：合外力 F = m a，其中 m 是质量，a 是沿合外力方向的加速度。这个矢量方程是动力学问题的核心，将运动学与力联系起来。

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 action-reaction pairs act on different objects and never cancel each other out in a free-body diagram of a single object.

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 会同时对物体 A 施加一个大小相等、方向相反的力。这些作用力与反作用力分别作用在不同物体上，绝不能在单个物体的受力图中相互抵消。

7. Force, Mass and Acceleration | 力、质量和加速度

Mass is the measure of an object’s inertia — its resistance to change in motion. It is a scalar quantity measured in kilograms. Weight, on the other hand, is the gravitational force on an object, W = m g, and is a vector directed toward the centre of the Earth. Do not confuse mass and weight in force equations.

质量是物体惯性——即其抵抗运动状态变化的能力——的量度。它是一个标量，单位是千克。而重量是作用在物体上的重力，W = m g，是一个方向指向地心的矢量。在力方程中切勿混淆质量与重量。

When solving problems, draw a clear free-body diagram showing all forces acting on the object. Resolve forces into components parallel and perpendicular to the direction of motion. Apply F = m a in the net force direction. Typical exam questions involve objects on slopes, pulleys, and connected particles.

解题时，应画出清晰的受力图，标明作用在物体上的所有力。将力沿运动方向和垂直于运动方向分解，在合外力方向上应用 F = m a。常见考题涉及斜面上的物体、滑轮系统和连接体问题。

Weight always acts vertically downward. / 重力总是竖直向下作用。
Normal reaction is perpendicular to the surface. / 法向支持力垂直于接触面。
Friction opposes relative motion and is μR where R is the normal reaction. / 摩擦力阻碍相对运动，大小为 μR，R 为法向支持力。

8. Momentum and Impulse | 动量和冲量

Linear momentum p is defined as the product of mass and velocity: p = m v. It is a vector quantity with the same direction as velocity. The rate of change of momentum is equal to the resultant force — in fact, Newton’s second law can be expressed as F = Δp / Δt.

线动量 p 定义为质量与速度的乘积：p = m v。它是矢量，方向与速度相同。动量的变化率等于合外力——事实上，牛顿第二定律可以表示为 F = Δp / Δt。

Impulse is the change in momentum caused by a force acting over time. It is given by Impulse = F Δt = Δp. This concept is particularly useful when a force varies over time, such as during collisions. The area under a force-time graph represents the impulse.

冲量是由力在一段时间内作用而引起的动量变化。冲量 = F Δt = Δp。当力随时间变化（例如碰撞过程中）时，这一概念特别有用。力-时间图像下方的面积表示冲量。

9. Conservation of Momentum | 动量守恒

In a closed system with no external resultant force, total linear momentum is conserved. This means the vector sum of momenta before an interaction (collision or explosion) equals the vector sum after. This principle is essential for solving problems involving collisions and recoil.

在一个没有合外力的封闭系统中，总线动量守恒。这意味着相互作用（碰撞或爆炸）前动量的矢量和等于相互作用后的矢量和。这一原理对于解决涉及碰撞和反冲的问题至关重要。

For a two-body collision: m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂, where u denotes velocities before and v after. Remember to assign positive and negative signs according to direction. Momentum conservation can be applied even if kinetic energy is not conserved, as in inelastic collisions.

对于两体碰撞：m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂，其中 u 表示碰撞前的速度，v 表示碰撞后的速度。请记住根据方向赋予正负号。即使在非弹性碰撞中动能不守恒，动量守恒仍然适用。

Distinguish between elastic collisions (KE conserved) and inelastic collisions (KE not conserved). In perfectly inelastic collisions, the bodies stick together and move with a common velocity after the impact.

要区分弹性碰撞（动能守恒）和非弹性碰撞（动能不守恒）。在完全非弹性碰撞中，物体粘在一起，碰撞后以共同速度运动。

10. Problem-Solving Strategies for Dynamics | 动力学解题策略

Begin by identifying known quantities and converting units to SI (metres, seconds, kilograms, Newtons). Sketch a diagram showing all forces and velocities, including their directions. For constant-acceleration kinematics, write down the five SUVAT variables and circle those you know and the one you seek; then pick the equation that links them.

首先确定已知量并将单位转换为国际单位制（米、秒、千克、牛顿）。绘制示意图，标出所有力和速度，包括它们的方向。对于匀加速运动学，列出五个 SUVAT 变量，圈出已知量和待求量；然后选择能够将它们联系起来的方程。

For dynamics problems involving forces, always draw a free-body diagram and apply Newton’s second law in two perpendicular directions if necessary. Check whether the system is in equilibrium (a = 0) or accelerating. In connected-particle systems, treat the whole system to find acceleration, then analyse individual parts to find internal forces such as tension.

对于涉及力的动力学问题，务必绘制受力图，如有必要则在两个垂直方向上应用牛顿第二定律。检查系统是处于平衡状态（a = 0）还是在加速。在连接体系统中，可将整个系统作为研究对象求出加速度，然后分析各个部分以求出内力，如张力。

Conservation of momentum is most effective when dealing with collisions or explosions with no external horizontal force. Always define a clear positive direction before writing momentum equations, and treat velocities as signed quantities.

在处理没有水平外力的碰撞或爆炸时，动量守恒最为有效。在写出动量方程之前，务必明确规定一个正方向，并将速度视为带符号的量。

Revise by practising past-paper questions under timed conditions, and pay attention to command words such as ‘state’, ‘explain’, and ‘calculate’. Clear working and unit handling are essential to secure full marks.

通过限时练习历年真题进行复习，并注意诸如“陈述”、“解释”和“计算”等指令词。清晰的解题步骤和单位处理对于拿到满分至关重要。

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A-Level Physics: Dynamics Key Points | A-Level物理：动力学考点精讲