AS AQA Physics: Motion and Forces | AS AQA 物理：运动与力

📚 AS AQA Physics: Motion and Forces | AS AQA 物理：运动与力

Motion and forces form the foundation of the AS AQA Physics specification. From kinematic equations to Newton’s laws and momentum, this topic consistently appears across multiple-choice, short-answer and extended-response questions in the OxfordAQA International AS examinations.

运动与力是 AS AQA 物理考纲的基础。从运动学方程到牛顿定律与动量，这一主题始终贯穿牛津AQA国际AS考试的客观题、简答题与论述题。

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1. Scalars and Vectors | 标量与矢量

A scalar quantity has magnitude only, while a vector quantity has both magnitude and direction. Common scalars include mass, speed, energy and time; common vectors include displacement, velocity, acceleration and force.

标量只有大小，矢量既有大小又有方向。常见标量包括质量、速率、能量和时间；常见矢量包括位移、速度、加速度和力。

To add vectors, use the tip-to-tail method or resolve them into perpendicular components. For two perpendicular components Aₓ and Aᵧ, the resultant magnitude is found using Pythagoras’ theorem:

矢量相加可采用首尾相接法，或将矢量分解为互相垂直的分量。对于两个垂直分量 Aₓ 和 Aᵧ，合矢量大小由勾股定理求得：

|A| = √(Aₓ² + Aᵧ²), tan θ = Aᵧ / Aₓ

Resolution of vectors is essential when analysing motion on slopes or forces at angles — resolve every vector along two perpendicular axes before applying equations.

在处理斜面运动或成角度的力时，矢量分解至关重要——先将每个矢量沿两个互相垂直的坐标轴分解，再代入方程运算。

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2. Displacement, Velocity and Acceleration | 位移、速度与加速度

Displacement (s) is the straight-line distance from a reference point in a specified direction, measured in metres (m). Velocity (v) is the rate of change of displacement, and acceleration (a) is the rate of change of velocity.

位移（s）是从参考点沿指定方向到物体位置的直线距离，单位为米（m）。速度（v）是位移随时间的变化率，加速度（a）是速度随时间的变化率。

Define average velocity and average acceleration as:

平均速度与平均加速度的定义如下：

v = Δs / Δt, a = Δv / Δt

Since velocity is a vector, changing direction alone — even at constant speed — constitutes acceleration, such as in uniform circular motion. In the AS course, an object accelerating while moving in a straight line has its speed changing, while acceleration due to gravity near the Earth’s surface is taken as g = 9.81 m s⁻².

由于速度是矢量，仅改变方向——即使速率不变——也会产生加速度，如匀速圆周运动。在AS课程中，直线运动物体加速时速率改变；地球表面附近的重力加速度取 g = 9.81 m s⁻²。

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3. SUVAT Equations | 匀变速直线运动方程

For motion with constant acceleration, the following SUVAT equations apply. They connect displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t):

对于匀变速直线运动，以下SUVAT方程适用。它们联系了位移（s）、初速度（u）、末速度（v）、加速度（a）和时间（t）：

v = u + at

s = (u + v)t / 2

s = ut + ½at²

v² = u² + 2as

Choose the equation that contains the three known quantities and the unknown you need. Always define a positive direction before substituting values — this avoids sign errors, especially in projectile and free-fall problems.

选择包含三个已知量和待求量的方程。代入数值前务必先规定正方向——这能避免符号错误，尤其在抛体和自由落体问题中。

For free fall under gravity, set a = g = 9.81 m s⁻². If an object is released from rest, u = 0. When an object is thrown upwards, its velocity at the highest point is zero.

自由落体运动中取 a = g = 9.81 m s⁻²。若物体从静止释放，则 u = 0；若物体竖直上抛，最高点处速度为零。

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4. Motion Graphs | 运动图像

Graphical analysis of motion is a core skill. On a displacement–time graph, the gradient gives the velocity. On a velocity–time graph, the gradient gives the acceleration, and the area under the graph gives the displacement.

运动图像分析是核心技能。在位移—时间图像中，斜率表示速度；在速度—时间图像中，斜率表示加速度，图像与时间轴围成的面积表示位移。

Graph | 图像	Gradient | 斜率	Area | 面积
s–t | 位移—时间	Velocity | 速度	— | —
v–t | 速度—时间	Acceleration | 加速度	Displacement | 位移
a–t | 加速度—时间	— | —	Velocity change | 速度变化量

A curved s–t graph indicates changing velocity; a straight-line v–t graph indicates constant acceleration. When a v–t graph is curved, its acceleration changes, and you must draw a tangent to find the instantaneous acceleration.

弯曲的 s–t 图像表示速度在改变；直线的 v–t 图像表示匀变速运动。当 v–t 图像为曲线时，加速度在变化，须作切线求瞬时加速度。

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5. Newton’s First and Second Laws | 牛顿第一、第二定律

Newton’s first law states that an object remains at rest or moves at constant velocity unless acted upon by a resultant (net) force. This explains the concept of inertia: a tendency to resist changes in motion.

牛顿第一定律指出：物体在不受合外力作用时，将保持静止或匀速直线运动状态。这解释了惯性的概念：物体抵抗运动状态改变的性质。

Newton’s second law states that the resultant force on an object equals the rate of change of momentum, which for constant mass simplifies to:

牛顿第二定律指出：物体所受合外力等于其动量变化率；当质量恒定时，可简化为：

F = ma

Here F is the resultant force (N), m is the mass (kg) and a is the acceleration (m s⁻²). One newton is the force that gives a mass of 1 kg an acceleration of 1 m s⁻². Note that mass here is inertial mass — a measure of how difficult it is to change an object’s velocity.

其中 F 为合外力（N），m 为质量（kg），a 为加速度（m s⁻²）。1 牛顿即使 1 kg 的物体产生 1 m s⁻² 加速度所需的力。此处的质量指惯性质量——衡量改变物体运动状态难易程度的量。

In exam problems, always find the resultant force by adding all forces along the direction of motion. For example, a car of mass 1200 kg with a driving force of 4000 N and a resistive force of 1000 N experiences a resultant force of 3000 N and thus accelerates at 2.5 m s⁻².

在考试问题中，始终沿运动方向将所有力求和后得到合外力。例如，一辆质量为 1200 kg 的汽车，牵引力 4000 N，阻力 1000 N，则合外力为 3000 N，加速度为 2.5 m s⁻²。

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6. Newton’s Third Law | 牛顿第三定律

Newton’s third law states that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These forces act on different objects, are equal in magnitude and opposite in direction, and are of the same type.

牛顿第三定律指出：若物体 A 对物体 B 施力，则物体 B 同时对物体 A 施加大小相等、方向相反的力。这对力作用在不同物体上，大小相等、方向相反，且属于同种性质的力。

A common exam trap is to confuse Newton’s third law pairs with balanced forces. For a book resting on a table, the weight (Earth pulls the book down) and the normal contact force (table pushes the book up) are balanced forces acting on the same object — they are not a third-law pair. The third-law pair to the book’s weight is the gravitational pull the book exerts on the Earth.

常见的考试陷阱是将牛顿第三定律的相互作用力与平衡力混淆。书静止在桌上时，重力（地球向下拉书）与支持力（桌子向上推书）是作用在同一物体上的平衡力——它们不是第三定律作用力对。与书所受重力构成第三定律作用力对的是书对地球的万有引力。

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7. Weight and Free-Body Diagrams | 重力与受力分析图

Weight is the gravitational force acting on an object, calculated as W = mg. Unlike mass, weight depends on the local gravitational field strength and changes from the Earth to the Moon. A free-body diagram shows all forces acting on a single body — draw arrows from the centre of the object, with lengths proportional to the magnitudes.

重力是作用在物体上的万有引力，计算公式为 W = mg。与质量不同，重力取决于当地引力场强度，因此在地球与月球上会改变。受力分析图展示单个物体所受的全部力——箭头从物体中心画出，长度与力的大小成比例。

W = mg

When analysing an object on an inclined plane, resolve the weight into a component perpendicular to the plane (mg cos θ) and a component parallel to the plane (mg sin θ). The normal contact force acts perpendicular to the plane and balances mg cos θ when there is no acceleration perpendicular to the slope.

分析斜面上的物体时，把重力分解为垂直斜面的分量（mg cos θ）和平行斜面的分量（mg sin θ）。支持力垂直于斜面，在无垂直斜面方向的加速度时与 mg cos θ 平衡。

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8. Momentum and Impulse | 动量与冲量

Momentum (p) is the product of mass and velocity, p = mv. The impulse of a constant force is the product of force and the time for which it acts, Ft, and impulse equals the change in momentum:

动量（p）是质量与速度的乘积，p = mv。恒力的冲量是力与其作用时间的乘积 Ft，且冲量等于动量的变化量：

Ft = Δp = mv − mu

This is the impulse–momentum principle. In a collision or impact, extending the contact time reduces the average force — hence airbags and crumple zones in cars protect passengers.

这就是冲量—动量定理。在碰撞或冲击中，延长接触时间可减小平均作用力——因此汽车的安全气囊和溃缩区能保护乘客。

In a closed system, total momentum is conserved during collisions and explosions. For two objects of masses m₁ and m₂ before and after a collision:

在封闭系统中，碰撞和爆炸过程中总动量守恒。对于质量分别为 m₁ 和 m₂ 的两个物体，碰撞前后有：

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Remember that momentum is a vector. In two-dimensional problems, conserve momentum separately along each axis. For elastic collisions, kinetic energy is also conserved; for inelastic collisions, some kinetic energy is transferred to other forms.

Published by TutorHao | AS Physics Revision Series | aleveler.com

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