Force and Motion: Key Exam Points | 力与运动考点精讲

📚 Force and Motion: Key Exam Points | 力与运动考点精讲

Mastering force and motion is essential for success in IB and AQA physics. This article breaks down the most tested concepts, from vector fundamentals to conservation laws, with clear explanations and practical examples you can apply directly to exam questions.

掌握力与运动是 IB 和 AQA 物理考试取得高分的关键。本文逐一剖析高频考点，从矢量基础到守恒定律，通过清晰的解释和实用示例帮助你在考场上直接得分。

1. Scalars and Vectors | 标量与矢量

Scalars have magnitude only, such as distance, speed, mass and energy. Vectors have both magnitude and direction, including displacement, velocity, acceleration and force. Pay attention to sign conventions when vectors act in opposite directions along a line.

标量只有大小，如路程、速率、质量和能量。矢量既有大小又有方向，如位移、速度、加速度和力。当矢量在一条直线上方向相反时，要特别注意正负号规定。

For any vector a with magnitude a and direction θ measured from the positive x‑axis, the components are:

对于任一矢量 a，大小为 a，方向与 x 轴正方向夹角为 θ，其分量为：

aₓ = a cos θ, aᵧ = a sin θ

The resultant of two perpendicular vectors can be found using Pythagoras: R = √(aₓ² + aᵧ²). The angle is given by tan θ = aᵧ / aₓ.

两个相互垂直的矢量的合矢量可用勾股定理求得：R = √(aₓ² + aᵧ²)。方向角满足 tan θ = aᵧ / aₓ。

2. Kinematics Equations | 运动学方程

When acceleration is constant, the four suvat equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). You must define a positive direction and use signs consistently.

当加速度恒定时，四个 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。必须规定正方向并保持符号一致。

v = u + at

s = ut + ½at²

v² = u² + 2as

s = ½(u + v)t

Always check which variables you know and which one you need to find. Choose the equation that involves only one unknown.

始终检查已知量和待求量，选择只含一个未知数的方程。

For free fall near the Earth’s surface, a = g ≈ 9.81 m s⁻², and the acceleration acts downward. If you set upward as positive, then a = –g.

在地面附近的自由落体运动中，a = g ≈ 9.81 m s⁻²，加速度方向向下。如果设定向上为正，则 a = –g。

3. Newton’s First Law | 牛顿第一定律

An object remains at rest or in uniform motion in a straight line unless acted upon by a resultant external force. This law defines inertia and explains why seatbelts are needed: a passenger tends to keep moving forward during a sudden stop.

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。这一定义了惯性，并解释了为何需要安全带：在急刹车时乘客趋向于保持向前的运动。

In equilibrium, the vector sum of all forces is zero: ΣF = 0. This condition can be used to solve problems where objects are stationary or moving with constant velocity.

平衡时，所有力的矢量和为零：ΣF = 0。这一条件可用于求解物体静止或匀速运动的问题。

4. Newton’s Second Law | 牛顿第二定律

The rate of change of momentum of an object is proportional to the resultant force acting on it. For constant mass, this simplifies to the familiar form:

物体动量的变化率与作用在其上的合外力成正比。当质量不变时，可简化为常见形式：

F = ma

Here F is the resultant force in newtons, m is mass in kg, and a is acceleration in m s⁻². The direction of acceleration is the same as the resultant force.

式中 F 为合外力（N），m 为质量（kg），a 为加速度（m s⁻²）。加速度方向与合外力方向相同。

Always draw a free‑body diagram showing all forces acting on the object, then apply ΣF = ma in two perpendicular directions.

始终画出隔离体受力图，标明所有作用力，然后在两个垂直方向上分别应用 ΣF = ma。

Scenario / 情景	Equation / 方程
Object on horizontal surface / 水平面上物体	F − friction = ma
Incline plane (no friction) / 光滑斜面	mg sin θ = ma
Atwood machine / 阿特伍德机	(m₁ − m₂)g = (m₁ + m₂)a

5. Newton’s Third Law | 牛顿第三定律

If body A exerts a force on body B, then body B exerts an equal and opposite force on body A. These two forces are of the same type, act on different bodies, and never cancel each other.

若物体 A 对物体 B 施加一个力，则 B 同时对 A 施加一个大小相等、方向相反的力。这两个力类型相同，作用在不同物体上，绝不能抵消。

Common exam misconception: the normal reaction force and weight do not constitute an action‑reaction pair because they both act on the same object. The correct pair for weight is the gravitational pull of the Earth on the object and the object’s pull on the Earth.

常见考试误区：支持力与重力并不是一对作用力与反作用力，因为它们作用在同一物体上。重力的反作用力是地球对物体的引力与物体对地球的引力。

6. Friction and Drag Forces | 摩擦力与阻力

Friction is a contact force that opposes relative motion or attempted motion. Static friction adjusts up to a maximum value: fₛ ≤ μₛ N. Once motion begins, kinetic friction fₖ = μₖ N acts, where N is the normal contact force.

摩擦力是阻碍相对运动或相对运动趋势的接触力。静摩擦力可调节至最大值：fₛ ≤ μₛ N。一旦开始运动，动摩擦力 fₖ = μₖ N，其中 N 为支持力。

Drag force, such as air resistance, increases with speed. When drag equals the driving force (or weight in free fall), the net force becomes zero and terminal velocity is reached.

空气阻力等阻力随速度增大而增大。当阻力等于驱动力（或自由落体时的重力），合外力为零，物体达到终端速度。

7. Circular Motion | 圆周运动

For an object moving in a circle of radius r with constant speed v, the velocity is tangent to the circle while the acceleration points towards the centre. The centripetal acceleration is:

物体以恒定速率 v 在半径为 r 的圆周上运动时，速度沿切线方向，加速度指向圆心。向心加速度为：

a = v² / r = ω²r

The centripetal force is F = ma = mv² / r = m ω²r. This is not a separate force but the resultant of real forces such as tension, friction or gravity.

向心力为 F = ma = mv² / r = m ω²r。这不是一种独立的力，而是真实力（如张力、摩擦力或引力）的合力。

A standard problem: a car rounding a banked curve. The horizontal component of the normal reaction provides the centripetal force, while the vertical component balances weight.

标准题型：汽车在倾斜弯道上转弯。支持力的水平分量提供向心力，竖直分量与重力平衡。

8. Work, Energy and Power | 功、能与功率

Work done by a constant force is W = F s cos θ, where θ is the angle between the force and the displacement. Energy is the capacity to do work, measured in joules (J).

恒力做功 W = F s cos θ，θ 为力与位移的夹角。能量是做功的本领，单位为焦耳 (J)。

The work‑energy theorem: the net work done on an object equals its change in kinetic energy:

动能定理：合外力对物体做的功等于物体动能的变化量：

W_net = ½mv² − ½mu²

Gravitational potential energy near Earth’s surface is ΔEₚ = mgh (taking a reference level). Elastic potential energy stored in a spring is U = ½kx².

地表附近的重力势能变化量 ΔEₚ = mgh（选取参考面）。弹簧储存的弹性势能为 U = ½kx²。

Power is the rate of doing work: P = W / t = Fv (for constant force in the direction of velocity). Unit: watt (W).

功率是做功的快慢：P = W / t = Fv（恒力与速度同向时）。单位：瓦特 (W)。

9. Momentum and Impulse | 动量与冲量

Linear momentum p = mv is a vector quantity. Impulse J = F Δt is the product of the average force and the time interval during which it acts. Impulse equals the change in momentum:

线动量 p = mv 是矢量。冲量 J = F Δt 是平均力与其作用时间的乘积。冲量等于动量的变化量：

F Δt = Δp = mv − mu

This is especially useful when forces act briefly, such as in collisions or ball strikes. The area under a force–time graph gives the impulse.

该关系在短暂的碰撞或击球情景中尤为有用。力–时间图像下的面积代表冲量。

10. Conservation of Momentum | 动量守恒

In an isolated system (no external forces), the total momentum remains constant. For a collision of two objects:

在孤立系统中（无外力），总动量守恒。对于两个物体的碰撞：

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Collisions can be elastic (kinetic energy conserved) or inelastic (some kinetic energy converted to other forms). In perfectly inelastic collisions, objects stick together and move with a common final velocity.

碰撞可以是弹性（动能守恒）或非弹性（部分动能转化为其他形式）。在完全非弹性碰撞中，物体粘在一起，以共同速度运动。

Explosions are the reverse: a single object splits into fragments. The total momentum before is zero if initially at rest, so the vector sum of fragments’ momenta must be zero.

爆炸是反过程：单个物体分裂成碎片。若初始静止，总动量为零，因此碎片动量的矢量和必为零。

11. Free‑Body Diagrams and Problem‑Solving Strategy | 受力分析与解题策略

A reliable approach to force and motion problems: (1) Identify the object of interest. (2) Draw all forces acting on it. (3) Choose a coordinate system – often aligning one axis with acceleration. (4) Resolve forces into components. (5) Apply ΣF = ma in each direction. (6) Solve algebraically for unknowns.

处理力与运动问题的可靠步骤：(1) 确定研究对象。(2) 画出所有受力。(3) 选择坐标系——常令某一坐标轴与加速度方向一致。(4) 将力分解到坐标轴上。(5) 在各个方向上应用 ΣF = ma。(6) 代数求解未知量。

Check that units are consistent and that your answer is physically reasonable. In multi‑body systems, treat each mass separately and link them using constraints like rope length.

确保单位一致，答案物理上合理。在多体系统中，隔离分析每个物体，并用绳长等约束条件关联。

12. Common Exam Pitfalls and Tips | 常见失分点与应试技巧

Mixing scalar and vector mindsets: always include direction with vector answers unless only magnitude is requested.

混淆标量和矢量思维：除非题目只要求大小，矢量答案必须标明方向。
Forgetting sign conventions: a velocity of −5 m s⁻¹ is just as meaningful as +5 m s⁻¹, depending on your chosen positive direction.

忽略正负号：速度 −5 m s⁻¹ 与 +5 m s⁻¹ 一样有意义，取决于所选正方向。
Applying suvat when acceleration is not constant: suvat only works for uniform acceleration. For varying acceleration, use calculus or graphs if needed.

在加速度变化时使用 suvat：suvat 仅适用于匀加速。若加速度变化，需用微积分或图像。
Confusing centripetal force as an extra force: centripetal force is the resultant of existing forces; never add it as a separate arrow on a diagram.

将向心力当作额外力：向心力是已有力的合力，切不可在受力图上单独加箭头。
Neglecting air resistance in free fall questions: read the question carefully – if “falling at steady speed” is mentioned, drag equals weight.

忽略自由落体中的空气阻力：仔细读题——如提到“匀速下落”，则阻力等于重力。

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Force and Motion: Key Exam Points | 力与运动考点精讲