📚 A-Level CIE Physics: Forces and Motion Revision Notes | A-Level CIE 物理：力与运动 考点精讲
This revision guide covers the essential topics in A-Level CIE Physics: Forces and Motion. You will explore kinematics, dynamics, momentum, energy, and rotational forces. Each section unpacks core principles and equations required for the exam, with clear explanations and worked concepts to strengthen your understanding.
这份复习指南涵盖 A-Level CIE 物理中力与运动的核心考点。我们将探讨运动学、动力学、动量、能量和旋转力。每一节都拆解了考试必备的基本原理和公式，通过清晰的讲解和概念分析帮助巩固理解。
1. Scalars and Vectors | 标量与矢量
Scalars possess magnitude only, such as distance, speed, mass, and time. Vectors have both magnitude and direction, for example displacement, velocity, acceleration, and force. When adding vectors, we must consider direction; perpendicular vectors are combined using Pythagoras’ theorem or trigonometry.
标量只有大小，例如距离、速率、质量和时间。矢量既有大小又有方向，如位移、速度、加速度和力。矢量相加时必须考虑方向；互相垂直的矢量可用勾股定理或三角函数合成。
Resolving a vector into perpendicular components simplifies analysis. For a force F at angle θ to the horizontal, the horizontal component is F cos θ, and the vertical component is F sin θ. In free-body diagrams, all forces acting on an object are drawn, and equilibrium occurs when the net force in any direction is zero.
将一个矢量分解为垂直分量能简化分析。对于与水平方向成 θ 角的力 F，水平分量为 F cos θ，垂直分量为 F sin θ。在受力分析图中，标出物体所受的全部力，当任何方向上的合力为零时，物体处于平衡状态。
2. Kinematic Equations | 运动学方程
For uniformly accelerated motion in a straight line, the four key equations (SUVAT) are used. The symbols represent: s – displacement, u – initial velocity, v – final velocity, a – constant acceleration, t – time. The equations are derived from the definitions of velocity and acceleration.
对于匀加速直线运动，使用四个关键方程（SUVAT）。符号含义：s – 位移，u – 初速度，v – 末速度，a – 恒定加速度，t – 时间。这些方程由速度和加速度的定义推导而来。
v = u + at
s = ut + ½ at²
v² = u² + 2as
s = ½ (u + v) t
When solving problems, identify known and unknown quantities, choose the equation that excludes the unused variable. Always check that acceleration is constant; if not, these equations cannot be directly applied. Sign conventions must be consistent, for example taking upward as positive and downward as negative.
解题时，先确定已知量和未知量，选择不含多余变量的方程。务必确保加速度恒定，否则不能直接使用这些方程。符号规则必须一致，例如取向上为正，向下为负。
3. Projectile Motion | 抛体运动
Projectile motion is two-dimensional motion under constant gravitational acceleration, assuming no air resistance. The horizontal and vertical motions are independent. Horizontally, velocity remains constant (aₓ = 0); vertically, acceleration is g = 9.81 m s⁻² downwards. Thus the path is parabolic.
抛体运动是在恒定重力加速度作用下的二维运动，忽略空气阻力。水平与竖直运动相互独立。水平方向速度恒定（aₓ = 0）；竖直方向加速度为 g = 9.81 m s⁻² 向下。因此轨迹为抛物线。
To solve problems, resolve the initial velocity u into horizontal component u cos θ and vertical component u sin θ. Apply kinematic equations separately to the vertical motion to find time of flight, maximum height, or range. Range R = (u² sin 2θ) / g for level ground.
解题时将初速度 u 分解为水平分量 u cos θ 和竖直分量 u sin θ。对竖直方向单独应用运动学方程，可求出飞行时间、最大高度或水平射程。在水平地面上，射程 R = (u² sin 2θ) / g。
4. Newton’s Laws of Motion | 牛顿运动定律
Newton’s First Law: An object remains at rest or in uniform motion in a straight line unless acted upon by a resultant external force. This introduces the concept of inertia, which is proportional to mass.
牛顿第一定律：任何物体都保持静止或匀速直线运动状态，除非受到合外力的作用。这引入了惯性的概念，惯性与质量成正比。
Newton’s Second Law: The resultant force on an object is equal to the rate of change of its momentum. For constant mass, F = ma, where F is in newtons, m in kilograms, and a in m s⁻². This vector equation means acceleration is in the direction of the resultant force.
牛顿第二定律：物体所受合外力等于其动量的变化率。当质量恒定时，F = ma，F 的单位是牛顿，m 是千克，a 是 m s⁻²。这个矢量方程表明加速度方向与合外力方向一致。
Newton’s Third Law: When body A exerts a force on body B, body B exerts an equal and opposite force on body A. These action-reaction forces act on different bodies, so they do not cancel. They arise in pairs of the same type (e.g. gravitational, contact).
牛顿第三定律：当物体 A 对物体 B 施加力时，物体 B 同时对物体 A 施加大小相等、方向相反的力。这对作用力与反作用力作用在不同物体上，因此不会抵消。它们成对出现且为同种类型（如万有引力、接触力）。
5. Linear Momentum and Impulse | 动量和冲量
Linear momentum p is the product of mass and velocity: p = mv (unit kg m s⁻¹). It is a vector quantity. The rate of change of momentum equals the resultant force: F = Δp / Δt. This is a more general statement of Newton’s Second Law.
线性动量 p 是质量与速度的乘积：p = mv（单位 kg m s⁻¹）。动量是矢量。动量变化率等于合外力：F = Δp / Δt。这是牛顿第二定律的更普遍表述。
Impulse J is the change in momentum caused by a force acting over a time interval: J = FΔt = Δp. The area under a force-time graph equals the impulse. When forces are large and act over a short time (e.g. collisions), they are called impulsive forces.
冲量 J 是力在一段时间间隔内引起的动量变化：J = FΔt = Δp。力-时间图下方的面积等于冲量。当力很大且作用时间很短时（如碰撞），称为冲力。
6. Conservation of Momentum | 动量守恒
In a closed system with no external resultant forces, total linear momentum is conserved. This is a fundamental principle used in collision and explosion problems. The total momentum before an event equals the total momentum after: Σp_initial = Σp_final.
在一个没有合外力的封闭系统中，总线性动量守恒。这是解决碰撞和爆炸问题的基本原理。事件前的总动量等于事件后的总动量：Σp_初始 = Σp_最终。
For two colliding bodies, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. Remember that momentum is a vector; assign positive and negative directions consistently. Explosions are reverse collisions: initial momentum is zero, so fragments move apart with equal and opposite momenta.
对于两个碰撞物体，m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。动量是矢量，需始终如一地指定正负方向。爆炸是反向碰撞：初始动量为零，因此碎片以大小相等、方向相反的动量分开。
7. Work, Energy and Power | 功、能和功率
Work done W by a constant force is W = Fs cos θ, where s is displacement and θ is the angle between force and displacement. Energy is the capacity to do work; both are scalar quantities measured in joules (J). Kinetic energy Eₖ = ½ mv², and gravitational potential energy Eₚ = mgh (near Earth’s surface).
恒力做功 W = Fs cos θ，其中 s 是位移，θ 是力与位移的夹角。能量是做功的本领；两者都是标量，单位是焦耳 (J)。动能 Eₖ = ½ mv²，重力势能 Eₚ = mgh（近地表）。
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. In problems, the work-energy principle ΔEₖ = net work done is powerful for finding speeds without using kinematics. Power P is the rate of work: P = W / t = Fv for constant force and velocity in the same direction.
能量守恒定律指出能量既不能创造也不能消灭，只能转移或转化。解题时功能原理 ΔEₖ = 合力做的净功这一方法，可绕过运动学直接求速率。功率 P 是做功的速率：P = W / t = Fv，适用于恒力且力与速度同向的情形。
8. Elastic and Inelastic Collisions | 弹性与非弹性碰撞
In an elastic collision, both momentum and kinetic energy are conserved. These are idealised collisions; real-world collisions of macroscopic objects are usually inelastic. Relative speed of approach equals relative speed of separation in perfectly elastic collisions: u₁ − u₂ = v₂ − v₁ (for one-dimensional).
在弹性碰撞中，动量和动能都守恒。这是理想化的碰撞；现实世界中宏观物体的碰撞通常是非弹性的。在完全弹性碰撞中，接近速度大小等于分离速度大小：u₁ − u₂ = v₂ − v₁（一维情况）。
In inelastic collisions, momentum is conserved but kinetic energy is not conserved—some is converted to heat, sound, or deformation. A perfectly inelastic collision results in the bodies sticking together and moving with a common velocity. The loss in kinetic energy can be calculated using Eₖ_initial − Eₖ_final.
在非弹性碰撞中，动量守恒但动能不守恒——部分转化为热、声或形变能。完全非弹性碰撞中物体粘在一起并以共同速度运动。动能损失可通过 Eₖ_初 − Eₖ_末 计算得出。
9. Moments and Equilibrium | 力矩与平衡
The moment of a force about a pivot is the product of the force and the perpendicular distance from the pivot to the line of action: moment = Fd. It measures the turning effect and is measured in newton metres (N m). Clockwise and anticlockwise moments are assigned opposite signs.
力对支点的力矩等于力与支点到力的作用线的垂直距离的乘积：力矩 = Fd。它衡量转动效果，单位是牛顿·米 (N m)。顺时针和逆时针力矩分别赋予相反符号。
For a body in rotational equilibrium, the principle of moments applies: total clockwise moment = total anticlockwise moment about any point. For complete static equilibrium, both resultant force and resultant moment must be zero. This is applied to beam problems and ladder problems.
对于转动平衡的刚体，力矩原理适用：对任意点的顺时针力矩之和等于逆时针力矩之和。要实现完全静力平衡，合外力与合力矩都须为零。这应用于横梁和梯子等问题。
10. Forces in Circular Motion | 圆周运动的力
Uniform circular motion involves constant speed but continuously changing velocity direction, hence there is a centripetal acceleration directed towards the centre. The magnitude is a = v² / r = ω²r, where v is linear speed, r is radius, and ω is angular speed (ω = Δθ / Δt).
匀速圆周运动速率恒定，但速度方向不断改变，因此存在指向圆心的向心加速度。其大小为 a = v² / r = ω²r，其中 v 是线速度，r 是半径，ω 是角速度（ω = Δθ / Δt）。
According to Newton’s Second Law, the resultant force towards the centre is the centripetal force: F = mv² / r = mω²r. This is not a new type of force but is provided by existing forces such as tension, friction, gravity, or the normal reaction. For a car rounding a curve, friction supplies the centripetal force; for a satellite, gravity provides it.
根据牛顿第二定律，指向中心的合外力即为向心力：F = mv² / r = mω²r。向心力并非新型力，而是由已有的力（如张力、摩擦力、重力或法向反力）提供。汽车转弯时由摩擦力充当向心力；人造卫星由万有引力提供。
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