📚 Force and Motion: Key Exam Points for IB & CIE Science | 力与运动：IB与CIE科学考点精讲
A solid understanding of force and motion is essential for success in IB and CIE science examinations. This article breaks down the key concepts, equations, and common pitfalls, providing a bilingual revision guide to help you master kinematics, dynamics, and energy.
深入理解力与运动是IB和CIE科学考试中取得高分的关键。本文梳理核心概念、公式和常见易错点，通过中英双语复习指南帮助你掌握运动学、动力学和能量。
1. Scalars and Vectors | 标量和矢量
Scalar quantities have only magnitude (size) and no direction. Examples include distance, speed, mass, energy and time.
标量只有大小（数值），没有方向。例如距离、速率、质量、能量和时间。
Vector quantities have both magnitude and direction. Examples include displacement, velocity, acceleration, force and momentum.
矢量既有大小又有方向。例如位移、速度、加速度、力和动量。
Distance is the total path length travelled, while displacement is the straight-line distance in a specific direction from start to finish.
距离是运动轨迹的总长度，而位移是从起点指向终点的有向直线距离。
Speed is a scalar; velocity is a vector. The magnitude of velocity is speed, but velocity also tells you the direction of motion.
速率是标量；速度是矢量。速度的大小就是速率，但速度还包含了运动的方向。
2. Distance, Displacement, Speed, Velocity and Acceleration | 距离、位移、速度、速率与加速度
Average speed = total distance / total time. Average velocity = total displacement / total time.
平均速率 = 总路程 / 总时间。平均速度 = 总位移 / 总时间。
Acceleration is the rate of change of velocity. It is a vector: a = Δv / Δt. An object accelerates if it speeds up, slows down, or changes direction.
加速度是速度的变化率。它是一个矢量：a = Δv / Δt。物体加速包括速度大小增加、减小或者方向改变。
Uniform acceleration means the acceleration is constant. Deceleration is negative acceleration.
匀加速指加速度恒定。减速即负加速度。
On a distance–time graph, the gradient gives speed. On a velocity–time graph, the gradient gives acceleration and the area under the graph gives displacement.
在距离-时间图中，斜率表示速率。在速度-时间图中，斜率表示加速度，图线下方的面积表示位移。
3. Equations of Uniformly Accelerated Motion | 匀加速运动方程
For motion with constant acceleration, four kinematic equations link initial velocity u, final velocity v, acceleration a, displacement s and time t.
对于匀加速直线运动，四个运动学方程将初速度 u、末速度 v、加速度 a、位移 s 和时间 t 联系起来。
v = u + at
s = ½ (u + v) t
s = ut + ½ at2
v2 = u2 + 2as
Always check that the acceleration is constant before using these equations. Take care with signs: choose a positive direction and stick to it.
使用这些方程前务必确认加速度恒定。注意正负号：选定一个正方向并始终遵循。
4. Forces and Newton’s Laws | 力与牛顿定律
A force is a push or pull that can change an object’s motion or shape. The SI unit is the newton (N).
力是能改变物体运动状态或形状的推或拉。国际单位是牛顿 (N)。
Newton’s First Law: An object remains at rest or in uniform motion in a straight line unless acted upon by a resultant force. This is also called the law of inertia.
牛顿第一定律：物体将保持静止或匀速直线运动状态，除非受到合外力作用。这也叫惯性定律。
Newton’s Second Law: The resultant force on an object is equal to its mass multiplied by its acceleration: F = ma. Resultant force is the vector sum of all forces acting.
牛顿第二定律：物体所受合外力等于质量乘以加速度：F = ma。合外力是所有作用力的矢量和。
Newton’s Third Law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A. These action–reaction forces act on different bodies.
牛顿第三定律：物体A对物体B施加力时，物体B同时对物体A施加一个大小相等、方向相反的力。作用力与反作用力作用在不同物体上。
5. Mass and Weight | 质量和重量
Mass is the amount of matter in an object; it is a scalar measured in kilograms (kg). Mass does not change with location.
质量是物体所含物质的多少；它是标量，单位千克 (kg)。质量不随位置改变。
Weight is the gravitational force acting on an object: W = mg. It is a vector directed towards the centre of the planet, measured in newtons.
重量是作用在物体上的重力：W = mg。它是一个矢量，方向指向行星中心，单位牛顿。
On Earth, g ≈ 9.8 m/s2 (often approximated as 10 m/s2 in exam problems). On the Moon, g is about 1.6 m/s2.
在地球上，g 约 9.8 m/s2（考试中常取 10 m/s2）。月球上的 g 约为 1.6 m/s2。
6. Momentum | 动量
Momentum is the product of mass and velocity: p = mv. It is a vector with units kg·m/s.
动量是质量与速度的乘积：p = mv。它是矢量，单位 kg·m/s。
The principle of conservation of momentum states that in a closed system with no external forces, total momentum before an event equals total momentum after.
动量守恒定律指出：在没有外力的封闭系统中，碰撞或相互作用前后的总动量保持不变。
Impulse is the change in momentum: Impulse = F Δt = Δp. The same change in momentum can be achieved with a large force over a short time or a small force over a long time.
冲量是动量的变化量：冲量 = F Δt = Δp。增大作用时间可减小作用力，这在安全气囊和缓冲垫中广泛应用。
7. Work, Energy and Power | 功、能和功率
Work is done when a force moves an object in the direction of the force: W = F d cos θ, where θ is the angle between force and displacement. If the force is parallel to displacement, W = F × d. Work is measured in joules (J).
力使物体沿力的方向移动时做功：W = F d cos θ，其中 θ 是力与位移的夹角。当力与位移平行时，W = F × d。功的单位是焦耳 (J)。
Energy is the capacity to do work. Kinetic energy: KE = ½ mv2. Gravitational potential energy: GPE = mgh. Energy is also measured in joules.
能量是做功的能力。动能：KE = ½ mv2。重力势能：GPE = mgh。能量单位也是焦耳。
Power is the rate of doing work or transferring energy: P = W / t. The SI unit is the watt (W), where 1 W = 1 J/s.
功率是做功或能量转移的速率：P = W / t。国际单位是瓦特 (W)，1 W = 1 J/s。
Efficiency = (useful energy output / total energy input) × 100%. No device can be 100% efficient due to energy dissipation as heat.
效率 =（有用能量输出 / 总能量输入）× 100%。由于存在热耗散，没有设备能达到 100% 的效率。
8. Conservation and Transfer of Energy | 能量守恒与转移
Energy cannot be created or destroyed, only transferred or transformed from one form to another. This is the law of conservation of energy.
能量既不能创造也不能消灭，只能从一种形式转移或转化为另一种形式。这就是能量守恒定律。
In a closed system, the total energy remains constant. For a falling object, gravitational potential energy converts to kinetic energy (ignoring air resistance): mgh = ½ mv2.
在封闭系统中，总能量保持不变。对于自由落体（忽略空气阻力），重力势能转化为动能：mgh = ½ mv2。
Energy can be transferred by forces (mechanical work), heating, radiation, and electrical currents. Sankey diagrams are used to represent energy transfers visually.
能量可通过力（机械功）、加热、辐射和电流等方式转移。桑基图用于直观表示能量转移过程。
9. Free Fall and Projectile Motion | 自由落体与抛体运动
Free fall is motion under gravity alone, with no air resistance. All objects in free fall near Earth’s surface accelerate downwards at g (≈ 9.8 m/s2), regardless of mass.
自由落体是仅受重力作用且无空气阻力的运动。在地球表面附近，所有物体自由下落的加速度同为 g (≈ 9.8 m/s2)，与质量无关。
Projectile motion can be analysed by separating horizontal and vertical components. Horizontally, velocity is constant (if air resistance is negligible). Vertically, the motion is uniformly accelerated at g.
抛体运动可通过水平和竖直分量分别分析。水平方向速度恒定（忽略空气阻力），竖直方向为加速度 g 的匀加速运动。
The horizontal and vertical motions are independent. The time of flight depends only on the vertical motion. At the highest point, the vertical velocity is zero, but horizontal velocity remains unchanged.
水平与竖直运动相互独立。飞行时间仅取决于竖直运动。在最高点，竖直分速度为零，但水平分速度保持不变。
10. Friction and Air Resistance | 摩擦力与空气阻力
Friction is a force that opposes motion between two surfaces in contact. It arises from the roughness of surfaces and molecular interactions.
摩擦力是阻碍两个接触表面相对运动的力，来源于表面粗糙度和分子相互作用。
Static friction prevents an object from starting to move; kinetic friction acts when the object is already sliding. Maximum static friction is usually greater than kinetic friction.
静摩擦力阻止物体从静止开始运动；动摩擦力在物体滑动时产生。最大静摩擦力通常大于动摩擦力。
Air resistance (drag) is a frictional force that opposes an object’s motion through air. It increases with speed, cross-sectional area, and fluid density.
空气阻力（拖曳力）是物体在空气中运动时受到的反向摩擦力。它随速度、横截面积和流体密度增加而增大。
Terminal velocity is reached when the downward force of gravity equals the upward drag force, giving zero resultant force and constant velocity.
当向下的重力等于向上的空气阻力时，合外力为零，物体达到收尾速度并匀速下落。
11. Circular Motion | 圆周运动
An object moving in a circle at constant speed is accelerating because its direction is constantly changing. This acceleration is called centripetal acceleration and points towards the centre.
物体以恒定速率做圆周运动时仍具有加速度，因为速度方向不断改变。这个加速度称为向心加速度，方向指向圆心。
ac = v2 / r = ω2 r
where v is the linear speed, ω is the angular speed, and r is the radius.
其中 v 为线速度，ω 为角速度，r 为半径。
The resultant force providing the centripetal acceleration is the centripetal force: Fc = m v2 / r. It is not a new type of force, but a name for the net force directed towards the centre (e.g., tension, gravity, friction).
提供向心加速度的合外力称为向心力：Fc = m v2 / r。向心力并非新型力，而是指向圆心的合力（如拉力、重力、摩擦力等）的统称。
12. Hooke’s Law | 胡克定律
Hooke’s Law states that the extension of an elastic object is directly proportional to the applied force, provided the limit of proportionality is not exceeded: F = k x.
胡克定律指出：弹性物体的伸长量与外加载荷成正比，前提是不超过比例极限：F = k x。
k is the spring constant (stiffness) in N/m, and x is the extension (or compression) from the natural length.
k 是劲度系数（弹簧常数），单位 N/m；x 是相对于原长的伸长量（或压缩量）。
The elastic limit is the point beyond which the material deforms permanently. The extension–force graph is a straight line through the origin only up to the limit of proportionality.
弹性极限是材料开始发生永久形变的点。在比例极限内，伸长量-力图为一条过原点的直线。
Elastic potential energy stored in a stretched spring = ½ F x = ½ k x2. This energy is recoverable as kinetic energy when the spring returns to its original shape.
被拉伸的弹簧储存的弹性势能 = ½ F x = ½ k x2。弹簧恢复原状时，这部分能量可转化为动能。
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