📚 AS Physics: Kinematics & Dynamics Essentials | AS 物理：运动学与动力学考点精讲
Motion is at the heart of physics. From a falling apple to a rocket launch, the principles of kinematics and dynamics allow us to describe and predict how objects move. This AS-level revision guide covers all essential concepts—scalars, vectors, SUVAT equations, Newton’s laws, momentum, and more—with clear explanations and worked examples to help you master the topic.
运动是物理学的核心。从落下的苹果到火箭发射，运动学与动力学的原理帮助我们描述并预测物体的运动方式。这份AS阶段复习指南涵盖所有重要概念——标量与矢量、SUVAT方程、牛顿定律、动量等，配有清晰的讲解和例题分析，助你彻底掌握该主题。
1. Scalars and Vectors | 标量与矢量
Scalars are physical quantities that have magnitude only, such as distance, speed, mass, and time. Vectors have both magnitude and direction, including displacement, velocity, acceleration, and force. When adding vectors, you must consider direction, often using tip-to-tail diagrams or resolving into perpendicular components.
标量是只有大小的物理量，如距离、速率、质量和时间。矢量既有大小又有方向，包括位移、速度、加速度和力。矢量相加时必须考虑方向，通常使用首尾相接图或分解为相互垂直的分量。
- Scalar examples: speed (5 m/s), distance (100 m), energy (50 J).
- 标量示例：速率(5 m/s)、距离(100 m)、能量(50 J)。
- Vector examples: velocity (5 m/s north), displacement (100 m east), force (10 N downward).
- 矢量示例：速度(5 m/s 向北)、位移(100 m 向东)、力(10 N 向下)。
Resolving a vector into horizontal and vertical components uses trigonometry: Vx = V cos θ, Vy = V sin θ, where θ is the angle from the horizontal axis.
将矢量分解为水平和竖直分量需用到三角函数：Vx = V cos θ, Vy = V sin θ，其中θ是与水平轴的夹角。
2. Displacement, Velocity and Acceleration | 位移、速度与加速度
Displacement is the straight-line distance in a given direction from the initial to the final position. Velocity is the rate of change of displacement: v = Δs / Δt. Acceleration is the rate of change of velocity: a = Δv / Δt. These quantities are vectorial; uniform acceleration is a cornerstone of kinematics.
位移是从初始位置到最终位置的直线有向距离。速度是位移的变化率：v = Δs / Δt。加速度是速度的变化率：a = Δv / Δt。这些量均是矢量；匀加速是运动学的基础。
On a displacement–time graph, the gradient gives velocity. On a velocity–time graph, the gradient gives acceleration, and the area under the graph gives displacement.
在位移–时间图上，斜率表示速度。在速度–时间图上，斜率表示加速度，图线下面积表示位移。
3. Equations of Motion (SUVAT) | 运动学公式 (SUVAT)
For constant acceleration in a straight line, the SUVAT equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). They are fundamental problem-solving tools. The five equations are:
对于直线上的匀加速运动，SUVAT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。它们是解题的基本工具。五个方程为：
v = u + at
s = ut + ½at²
s = vt − ½at²
v² = u² + 2as
s = (u + v)t / 2
Always choose the equation that uses known variables and the one unknown you need. Remember to use consistent signs for direction (e.g., upward positive).
始终选择含有已知量和待求未知量的方程。注意使用一致的方向符号（例如，取向上为正）。
4. Free Fall and Projectile Motion | 自由落体与抛体运动
In the absence of air resistance, all objects fall with the same acceleration due to gravity, g = 9.81 m/s² near the Earth’s surface. Free fall problems apply SUVAT equations with a = g (or -g depending on sign convention).
在没有空气阻力的情况下，所有物体均以相同的重力加速度下落，地球表面附近 g = 9.81 m/s²。自由落体问题应用SUVAT方程，a = g（或 -g，取决于符号约定）。
Projectile motion is analysed by resolving initial velocity into horizontal (ux = u cos θ) and vertical (uy = u sin θ) components. Horizontal motion has constant velocity (a = 0); vertical motion has uniform acceleration a = -g. Treat the two independently, and combine results to find height, range, and time of flight.
抛体运动通过将初速度分解为水平分量(ux = u cos θ)和竖直分量(uy = u sin θ)来分析。水平方向为匀速运动(a = 0)；竖直方向为匀加速运动 a = -g。独立处理两个方向，然后合并结果求高度、射程和飞行时间。
5. Newton’s Laws of Motion | 牛顿运动定律
Newton’s First Law states that an object remains at rest or in uniform motion unless acted upon by a resultant external force. Newton’s Second Law: F = ma, where F is the resultant force. Newton’s Third Law: for every action, there is an equal and opposite reaction. These laws govern the dynamics of all systems.
牛顿第一定律指出，除非受到合外力作用，物体会保持静止或匀速直线运动状态。牛顿第二定律：F = ma，其中 F 是合外力。牛顿第三定律：每一个作用力总有一个大小相等、方向相反的反作用力。这些定律支配着所有系统的动力学行为。
Force is a vector, measured in newtons (N). 1 N is the force required to accelerate 1 kg by 1 m/s². Always identify all forces acting on a body and compute resultant force along each axis.
力是矢量，单位为牛顿(N)。1 N 是使 1 kg 的物体产生 1 m/s² 加速度所需的力。一定要找出作用在物体上的所有力，并计算每个轴上的合力。
6. Force, Mass and Acceleration | 力、质量与加速度
Inertial mass is defined as the ratio of net force to acceleration: m = F / a. It indicates how difficult it is to change an object’s velocity. In multi-body systems (e.g., connected particles, pulleys), write F = ma for each object, taking into account tension and weight.
惯性质量定义为合外力与加速度的比值：m = F / a。它反映了改变物体速度的难易程度。在多体系统（如连接体、滑轮）中，对每个物体列出 F = ma，并考虑张力和重力。
Draw free-body diagrams, label all forces, and apply Newton’s second law. If surfaces are smooth, friction is negligible; if rough, include friction opposite to motion.
画受力分析图，标出所有力，并应用牛顿第二定律。如果接触面光滑，摩擦力可忽略；如果粗糙，则加入与运动方向相反的摩擦力。
7. Momentum and Impulse | 动量与冲量
Linear momentum p is the product of mass and velocity: p = mv. Momentum is a vector, unit kg m/s. Impulse is the change in momentum, also equal to average force multiplied by time: Impulse = Δp = FΔt. This follows from F = ma = mΔv/Δt.
线动量 p 是质量与速度的乘积：p = mv。动量是矢量，单位为 kg m/s。冲量是动量的变化量，也等于平均力乘以时间：冲量 = Δp = FΔt。这可由 F = ma = mΔv/Δt 导出。
The area under a force–time graph represents impulse. In collisions, a large force acting over a short time can cause the same impulse as a smaller force over a longer time.
力–时间图下的面积代表冲量。在碰撞过程中，短时间内作用的大力与长时间作用的小力可以产生相同的冲量。
8. Conservation of Momentum | 动量守恒
In an isolated system (no external resultant force), total momentum before an interaction equals total momentum after. This principle is crucial for collision and explosion problems: m1u1 + m2u2 = m1v1 + m2v2.
在孤立系统（无合外力）中，相互作用前的总动量等于作用后的总动量。该原理对于碰撞与爆炸问题至关重要：m1u1 + m2u2 = m1v1 + m2v2。
Collisions can be elastic (kinetic energy conserved) or inelastic (kinetic energy not conserved, objects may stick together). Momentum is conserved in both types. For perfectly inelastic collisions, final velocities are equal.
碰撞可分为弹性碰撞（动能守恒）和非弹性碰撞（动能不守恒，物体可能粘在一起）。两种碰撞动量都守恒。完全非弹性碰撞中，末速度相等。
9. Types of Forces | 力的种类
Common forces in AS dynamics include weight (W = mg), normal reaction, tension, friction (static and kinetic), air resistance (drag), and spring force (Hooke’s law: F = kx). Each force has a specific cause and direction, and must be included in equilibrium or acceleration equations.
AS动力学中常见的力包括：重力 (W = mg)、法向反作用力、张力、摩擦力（静摩擦和动摩擦）、空气阻力（拖曳力）以及弹力（胡克定律：F = kx）。每种力有特定的成因和方向，必须纳入平衡或加速度方程。
Tension is the same throughout a light inextensible string passing over a smooth pulley. Friction f ≤ μR, where R is normal contact force and μ the coefficient of friction.
轻质不可伸长的绳子跨过光滑滑轮时，各处张力相等。摩擦力 f ≤ μR，其中 R 为法向接触力，μ 为摩擦系数。
10. Free-Body Diagrams | 受力分析图
A free-body diagram isolates one object and shows all forces acting on it with arrows indicating direction and relative magnitude. It is an essential step before applying Newton’s laws. Do not include forces exerted by the object on its surroundings.
受力分析图将单个物体隔离，并用箭头标出所有作用其上的力，表示方向与相对大小。这是应用牛顿定律前必不可少的一步。不要包含该物体对外界施加的力。
For an object on an inclined plane, weight is resolved into components parallel (mg sin θ) and perpendicular (mg cos θ) to the slope. Normal reaction equals mg cos θ if there is no acceleration perpendicular to the plane.
对于斜面上的物体，重力分解为平行于斜面 (mg sin θ) 和垂直于斜面 (mg cos θ) 的分量。若垂直于斜面方向没有加速度，法向反力等于 mg cos θ。
11. Friction and Drag Forces | 摩擦力与阻力
Friction opposes relative motion or tendency of motion between surfaces. Static friction prevents motion; kinetic friction acts during sliding. The maximum static friction is fmax = μsR; kinetic friction is fk = μkR, usually slightly less than μsR.
摩擦力阻碍接触面间的相对运动或相对运动趋势。静摩擦力阻止运动开始；动摩擦力在滑动时起作用。最大静摩擦力 fmax = μsR；动摩擦力 fk = μkR，通常略小于 μsR。
Drag forces (e.g., air resistance) increase with speed and depend on shape and cross-sectional area. Terminal velocity occurs when resultant force becomes zero, so acceleration ceases—weight balances drag.
阻力（如空气阻力）随速度增大而增加，并与形状和横截面积有关。当合力变为零时，加速度停止，最终达到终端速度——重力与阻力平衡。
12. Worked Examples | 例题解析
Example 1: A car accelerates uniformly from 10 m/s to 25 m/s over 5 seconds. Calculate (a) acceleration, (b) distance travelled. Solution: (a) a = (v – u)/t = (25 – 10)/5 = 3.0 m/s². (b) s = (u + v)t/2 = (10+25)×5/2 = 87.5 m.
例题 1：一辆汽车从 10 m/s 匀加速到 25 m/s，用时 5 秒。求 (a) 加速度, (b) 行驶距离。解：(a) a = (v – u)/t = (25 – 10)/5 = 3.0 m/s²。(b) s = (u + v)t/2 = (10+25)×5/2 = 87.5 m。
Example 2: A block of mass 5 kg slides down a 30° incline with negligible friction. Find acceleration. Solution: component of weight down slope = mg sin 30° = 5×9.81×0.5 = 24.525 N. a = F/m = 24.525/5 = 4.91 m/s².
例题 2：质量 5 kg 的滑块沿一倾角 30° 光滑斜面下滑。求加速度。解：重力沿斜面分量为 mg sin 30° = 5×9.81×0.5 = 24.525 N。a = F/m = 24.525/5 = 4.91 m/s²。
Example 3: Two masses m1 = 3 kg and m2 = 2 kg connected by a light string over a frictionless pulley. Release from rest. Find tension and acceleration. Solution: For m1: 3g – T = 3a; for m2: T – 2g = 2a. Solve: adding gives g = 5a → a = g/5 = 1.962 m/s². T = 2g + 2a = 2×9.81 + 2×1.962 = 23.5 N.
例题 3：两物体 m1 = 3 kg 和 m2 = 2 kg 通过轻绳跨过无摩擦滑轮相连，由静止释放。求绳张力和加速度。解：对 m1：3g – T = 3a；对 m2：T – 2g = 2a。两式相加得 g = 5a → a = g/5 = 1.962 m/s²。T = 2g + 2a = 2×9.81 + 2×1.962 = 23.5 N。
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