📚 Force and Motion Revision Notes for IB CCEA Science | IB CCEA 科学：力与运动 考点精讲
This comprehensive revision guide covers the essential topics in Force and Motion for IB and CCEA Science specifications. From vector analysis and kinematics to Newton’s laws, momentum, and circular motion, every key concept is explained with clear examples and dual-language annotations to help you master the fundamentals and tackle exam questions with confidence.
这份全面的复习指南涵盖了 IB 和 CCEA 科学大纲中力与运动的核心主题。从矢量分析和运动学到牛顿定律、动量和圆周运动，每个关键概念都配有清晰的示例和中英双语注释，帮助你掌握基础并自信地应对考试。
1. Scalar and Vector Quantities | 标量与矢量
Scalar quantities have magnitude only, such as mass (kg), time (s), speed (m/s), distance (m), and energy (J). Vector quantities have both magnitude and direction, including displacement, velocity, acceleration, force, and momentum.
标量只有大小，例如质量(kg)、时间(s)、速率(m/s)、路程(m)和能量(J)。矢量既有大小又有方向，包括位移、速度、加速度、力和动量。
When adding vectors, you must consider direction. For perpendicular vectors, use the Pythagorean theorem to find the resultant magnitude: R = √(A² + B²). The direction can be found with tan θ = opposite/adjacent. For non-perpendicular vectors, resolve each into horizontal and vertical components before summing.
矢量相加时必须考虑方向。对于相互垂直的矢量，使用勾股定理求合矢量的大小：R = √(A² + B²)，方向可由 tan θ = 对边/邻边求得。对于不垂直的矢量，先将每个矢量分解为水平和垂直分量，再分别相加。
R = √(A² + B²) (for right-angled vectors)
2. Equations of Uniformly Accelerated Motion (SUVAT) | 匀加速运动方程 (SUVAT)
The SUVAT equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t) under constant acceleration. You must select the equation that matches the given and unknown quantities.
SUVAT 方程在恒定加速度下将位移(s)、初速度(u)、末速度(v)、加速度(a)和时间(t)关联起来。你必须选择与已知量和未知量匹配的方程。
The four key equations are:
四个关键方程为：
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
These equations only work when acceleration is uniform. In free-fall near Earth’s surface, a = g = 9.81 m/s² (downwards). Remember to assign a consistent sign convention, typically positive upwards.
这些方程仅在加速度恒定时适用。在地球表面附近的自由落体中，a = g = 9.81 m/s²（向下）。请记住要保持一致的符号约定，通常取向上为正。
An object thrown upward has negative acceleration if positive is up, causing it to slow down, stop, and then descend.
如果取向上为正，向上抛出的物体具有负加速度，使其减速、停止，然后下落。
3. Newton’s First Law and Inertia | 牛顿第一定律与惯性
Newton’s First Law states that an object remains at rest or in uniform motion in a straight line unless acted upon by a net external force. This property is called inertia – the tendency of an object to resist changes in its state of motion.
牛顿第一定律指出，除非受到净外力的作用，否则物体将保持静止或匀速直线运动状态。这种特性称为惯性——物体抵抗其运动状态变化的倾向。
The greater an object’s mass, the greater its inertia. In IB and CCEA exams, you may be asked to explain real-life situations: passengers lurch forward when a bus brakes suddenly; a coffee cup stays on a table when the tablecloth is pulled quickly.
物体的质量越大，惯性越大。在 IB 和 CCEA 考试中，你可能需要解释现实生活中的情景：当公交车突然刹车时乘客向前倾倒；快速抽走桌布时咖啡杯留在桌子上。
No net force means no acceleration. If velocity is constant, resultant force is zero – this is dynamic equilibrium, not just static equilibrium.
无净力意味着无加速度。如果速度恒定，则合力为零——这是动态平衡，而不仅仅是静态平衡。
4. Newton’s Second Law and F = ma | 牛顿第二定律与 F = ma
Newton’s Second Law: The net force on an object is directly proportional to the rate of change of its momentum. For constant mass, this simplifies to F = ma, where F is the net force in newtons (N), m is mass in kg, and a is acceleration in m/s².
牛顿第二定律：物体所受的净力与其动量的变化率成正比。在质量恒定的情况下，这简化为 F = ma，其中 F 是净力（牛顿 N），m 是质量（kg），a 是加速度（m/s²）。
One newton is the force required to give a 1 kg mass an acceleration of 1 m/s². Always identify all forces and find the resultant before applying F = ma.
一牛顿是使 1 kg 质量产生 1 m/s² 加速度所需的力。在应用 F = ma 之前，始终要先确定所有力并求出合力。
For multi-body systems, treat connected objects as a whole to find common acceleration, then isolate individual masses to determine internal forces like tension. Free-body diagrams are essential.
对于多体系统，将连接物体视为一个整体以求得共同加速度，然后隔离单个质量以确定内力，如张力。受力图至关重要。
5. Newton’s Third Law and Action-Reaction Pairs | 牛顿第三定律与作用力-反作用力
Newton’s Third Law: For every action force, there is an equal and opposite reaction force. These forces act on two different bodies, are of the same type, and occur simultaneously.
牛顿第三定律：对于每一个作用力，总存在一个大小相等、方向相反的反作用力。这两个力作用在不同的物体上，属于同一类型，并且同时发生。
A common misconception is that the normal force and weight are an action-reaction pair. They are not; they act on the same body (the object on a surface). A correct pair: the Earth pulls the book down (weight), and the book pulls the Earth up with equal force – but the Earth’s huge mass means its acceleration is negligible.
一个常见的误解是认为法向力和重量是一对作用力与反作用力。它们不是；它们作用在同一物体上（放在表面上的物体）。正确的例子：地球向下拉书本（重力），书本以相等的力向上拉地球——但地球巨大的质量使得它的加速度可以忽略不计。
Rocket propulsion and jet engines are classic applications: exhaust gases are pushed backward, and the rocket is pushed forward.
火箭推进和喷气发动机是经典的应用：废气被向后推出，火箭被向前推动。
6. Free-Body Diagrams and Resolving Forces | 受力图与力的分解
A free-body diagram represents all forces acting on a single object as arrows. These include weight (W = mg), normal reaction (N), friction (f), tension (T), and applied forces. The size and direction of arrows reflect vector nature.
受力图通过箭头表示作用在单个物体上的所有力。这些包括重量(W = mg)、法向反作用力(N)、摩擦力(f)、张力(T)和外加力。箭头的大小和方向反映了矢量性质。
Forces on an inclined plane are resolved into components parallel and perpendicular to the slope. The perpendicular component of weight is mg cos θ, and the parallel component is mg sin θ. Friction often acts up the slope opposing motion.
斜面上的力被分解为平行和垂直于斜面的分量。重量的垂直分量为 mg cos θ，平行分量为 mg sin θ。摩擦力通常沿斜面向上，阻碍运动。
When forces are at angles, use trigonometric methods: horizontal component = F cos θ, vertical component = F sin θ. Equilibrium requires the sum of horizontal components and the sum of vertical components to be zero.
当力不在同一直线上时，使用三角函数方法：水平分量为 F cos θ，垂直分量为 F sin θ。平衡要求水平分量之和与垂直分量之和均为零。
7. Momentum and Impulse | 动量与冲量
Linear momentum (p) is the product of mass and velocity: p = mv, measured in kg m/s. It is a vector quantity. The change in momentum is caused by a net force acting over a time interval, which is impulse.
线动量(p)是质量与速度的乘积：p = mv，单位为 kg m/s。它是一个矢量。动量的变化是由净力在一段时间间隔内的作用引起的，这称为冲量。
Impulse = F Δt = Δp = m(v – u)
The area under a force-time graph gives the impulse, which equals the change in momentum. Cushioning in car safety features (airbags, crumple zones) increases the impact time, reducing the average force for the same change in momentum.
力-时间图下的面积等于冲量，即动量的变化。汽车安全装置（安全气囊、褶皱区）中的缓冲作用增加了碰撞时间，从而在相同的动量变化下降低了平均作用力。
The principle of conservation of momentum states that in an isolated system (no external forces), total momentum before collision equals total momentum after collision. This applies to both elastic and inelastic collisions, though kinetic energy is only conserved in elastic ones.
动量守恒定律指出，在一个孤立系统（无外力）中，碰撞前的总动量等于碰撞后的总动量。这适用于弹性碰撞和非弹性碰撞，但动能仅在弹性碰撞中守恒。
For a collision: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. Remember to use velocity, not speed, and include signs for direction.
对于碰撞：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。记住使用速度而不是速率，并包含表示方向的符号。
8. Work, Energy, and Power | 功、能与功率
Work done (W) is the product of force and displacement in the direction of the force: W = F d cos θ. The unit is the joule (J). Work transfers energy; when work is done against friction, it is dissipated as thermal energy.
功(W)是力与沿力方向的位移的乘积：W = F d cos θ。单位为焦耳(J)。功伴随着能量转移；当克服摩擦力做功时，能量以热能的形式耗散。
Kinetic energy (K.E.) = ½mv². Gravitational potential energy (G.P.E.) = mgΔh. These can be converted into each other in isolated systems, but total mechanical energy is conserved only when no non-conservative forces (e.g. friction, air resistance) do work.
动能(K.E.) = ½mv²。重力势能(G.P.E.) = mgΔh。在孤立系统中，它们可以相互转化，但只有当没有非保守力（如摩擦、空气阻力）做功时，总机械能才守恒。
Power is the rate of doing work or transferring energy: P = W / t = F v (for constant force and velocity). The unit is the watt (W), equivalent to J/s.
功率是做功或能量转移的速率：P = W / t = F v（对于恒力和恒定速度）。单位是瓦特(W)，等于 J/s。
In inclined plane problems, use energy methods to find final speed: loss in G.P.E. = gain in K.E. + work done against friction.
在斜面问题中，使用能量方法求解末速度：重力势能的减少 = 动能的增加 + 克服摩擦所做的功。
9. Terminal Velocity and Drag Forces | 终端速度与阻力
Drag forces (air resistance or fluid friction) increase with speed. For a falling object, when the upward drag force equals the downward weight, the net force becomes zero, and the object falls at constant terminal velocity.
阻力（空气阻力或流体摩擦）随速度增大而增大。对于下落的物体，当向上的阻力等于向下的重力时，净力为零，物体以恒定的终端速度下落。
The sequence of motion for a skydiver: initially, weight > drag, accelerates downwards. As speed increases, drag grows, reducing acceleration. Eventually drag = weight, terminal velocity reached. On opening a parachute, drag dramatically increases, causing deceleration until a new lower terminal speed is achieved.
跳伞者的运动顺序：最初重力 > 阻力，向下加速。随着速度增加，阻力增大，加速度减小。最终阻力 = 重力，达到终端速度。打开降落伞后，阻力急剧增大，导致减速，直到达到一个新的较低的终端速度。
Viscous drag in liquids often follows Stokes’ law for small spheres at low speeds, but for larger objects or higher speeds, drag is roughly proportional to velocity squared. The terminal velocity equation can be derived by equating drag and weight.
液体中的粘滞阻力在低速小球情况下常遵循斯托克斯定律，但对于较大的物体或较高的速度，阻力大致与速度的平方成正比。可通过令阻力等于重力推导终端速度方程。
This topic links directly to Newton’s second law: resultant force = weight – drag, and acceleration decreases until zero. Free-body diagrams at various points in the fall are common exam questions.
这个主题与牛顿第二定律直接相关：合力 = 重力 – 阻力，加速度减小直到为零。下落过程中各个时刻的受力图是常见的考试题目。
10. Uniform Circular Motion and Centripetal Force | 匀速圆周运动与向心力
An object moving in a circular path at constant speed experiences an acceleration directed towards the centre, called centripetal acceleration. This requires a net centripetal force. The velocity vector is always tangent to the circle, so direction changes constantly.
以恒定速率做圆周运动的物体具有指向圆心的加速度，称为向心加速度。这需要一个净向心力。速度矢量始终与圆相切，因此方向不断变化。
Centripetal acceleration: a = v²/r = ω²r
Centripetal force: F = mv²/r = mω²r
Centripetal force is not a separate type of force; it is provided by tension (as in a string), gravity (orbit), friction (car rounding a curve), or the normal component on a banked track.
向心力不是一种单独的力；它由张力（如绳子）、重力（轨道）、摩擦力（汽车转弯）或倾斜赛道上的法向力分量提供。
In the context of IB and CCEA, you may analyse a conical pendulum, a car on a banked curve, or the forces on a bucket of water swung in a vertical circle. At the top of a vertical circle, the minimum speed is given by mg = mv²/r, so v = √(gr).
在 IB 和 CCEA 的背景下，你可能需要分析锥摆、倾斜弯道上的汽车或在竖直平面内甩动的水桶所受的力。在竖直圆轨道顶部，最小速度由 mg = mv²/r 给出，即 v = √(gr)。
Remember that in circular motion, the speed may be constant, but velocity is not, and therefore it is an accelerated motion. The work done by centripetal force is zero because force is perpendicular to displacement.
请记住，在圆周运动中，速率可能是恒定的，但速度不是，因此它是一种加速运动。向心力所做的功为零，因为力始终与位移垂直。
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