📚 IB Science: Forces and Motion – Key Concepts and Exam Tips | IB 科学：力与运动 考点精讲
Understanding forces and motion is at the heart of IB Physics. This revision guide breaks down the essential concepts of kinematics, Newton’s laws, momentum, work, and energy, giving you the tools to solve problems confidently and ace your exam.
理解力与运动是 IB 物理的核心。这份复习指南拆解了运动学、牛顿定律、动量、功和能量的基本概念，为你提供解决问题的工具，让你在考试中自信地取得高分。
1. Describing Motion: Displacement, Velocity, and Acceleration | 描述运动：位移、速度与加速度
In physics, motion is described using vector quantities. Displacement (s) is the straight‑line distance from the starting point in a given direction, while distance is a scalar that measures the total path length. Velocity (v) is the rate of change of displacement, and acceleration (a) is the rate of change of velocity.
在物理学中，运动使用矢量来描述。位移（s）是从起点沿特定方向的直线距离，而路程是测量路径总长的标量。速度（v）是位移的变化率，加速度（a）是速度的变化率。
The instantaneous velocity is the slope of a displacement‑time graph, and the area under a velocity‑time graph gives the change in displacement. For an acceleration‑time graph, the area under the curve equals the change in velocity.
瞬时速度是位移‑时间图的斜率，速度‑时间图下的面积表示位移的变化量。对于加速度‑时间图，曲线下的面积等于速度的变化量。
Always pay attention to sign conventions – positive and negative directions are chosen arbitrarily, but must be consistent throughout your solution.
务必注意正负号的约定——正方向和负方向可以任意选定，但在整个解答过程中必须保持一致。
2. Kinematic Equations for Uniform Acceleration | 匀加速运动学方程
When acceleration is constant, the four kinematic equations (suvat) link displacement, initial velocity, final velocity, acceleration, and time. They are derived from the definitions of velocity and acceleration.
当加速度恒定时，四个运动学方程（suvat）将位移、初速度、末速度、加速度和时间联系起来。它们由速度和加速度的定义推导而来。
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = ½ (u + v) t
Before applying these equations, identify which three quantities are known and which one you need to find. The equation that does not involve the unknown quantity is the one to use. Always check that the acceleration is truly uniform – if not, these equations are invalid.
在应用这些方程之前，先确定已知哪三个量以及需要求哪一个量。选择不含未知量的那个方程。始终要检查加速度是否真的是均匀的——如果不是，这些方程无效。
3. Free Fall and Projectile Motion | 自由落体与抛体运动
An object in free fall experiences constant downward acceleration due to gravity (g ≈ 9.81 m s⁻² on Earth). In problems, air resistance is usually neglected so that the kinematic equations apply directly.
自由落体中的物体受到恒定的向下重力加速度（地球上 g ≈ 9.81 m s⁻²）。在问题中，通常忽略空气阻力，从而直接应用运动学方程。
Projectile motion is analysed by resolving the initial velocity into horizontal and vertical components. The horizontal motion has constant velocity (aₓ = 0), while the vertical motion has constant acceleration aᵧ = −g (if upward is positive). The two components share the same time of flight.
抛体运动通过将初速度分解为水平和竖直分量来分析。水平方向运动具有恒定的速度（aₓ = 0），而竖直方向运动具有恒定的加速度 aᵧ = −g（如果向上为正）。两个方向的分运动具有相同的飞行时间。
Key results: the time to reach maximum height is uᵧ / g, the maximum height is uᵧ² / (2g), and the horizontal range is (u² sin 2θ) / g for a projectile launched and landing on the same horizontal level.
关键结果：达到最大高度的时间为 uᵧ / g，最大高度为 uᵧ² / (2g)，对于在同一水平面上发射和落地的抛体，水平射程为 (u² sin 2θ) / g。
4. Newton’s First Law: Inertia | 牛顿第一定律：惯性
Newton’s first law states that an object will remain at rest or move with constant velocity unless acted upon by a net external force. This property is called inertia – the tendency of an object to resist changes in its 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。这种性质称为惯性——物体抵抗其运动状态变化的倾向。
Mass is a measure of inertia; the greater the mass, the larger the force required to produce a given acceleration. Inertial mass is defined by the ratio F / a.
质量是惯性的量度；质量越大，产生给定加速度所需的力就越大。惯性质量定义为 F / a 的比值。
5. Newton’s Second Law: Force and Acceleration | 牛顿第二定律：力与加速度
The second law quantifies the effect of force: the net force acting on an object is equal to the rate of change of its momentum, which simplifies to F = m a when mass is constant. Net force and acceleration are always in the same direction.
第二定律量化了力的作用：作用在物体上的净力等于其动量的变化率，当质量恒定时简化为 F = m a。净力与加速度的方向总是相同。
This law allows us to predict motion from known forces or to calculate unknown forces from observed acceleration. In IB problems, it is common to resolve forces into components along perpendicular axes and apply ΣF = m a along each axis independently.
该定律使我们能够根据已知的力预测运动，或根据观察到的加速度计算未知的力。在 IB 问题中，通常将力分解为沿相互垂直轴的分量，并分别对每个轴应用 ΣF = m a。
6. Newton’s Third Law: Action‑Reaction Pairs | 牛顿第三定律：作用力与反作用力
Newton’s third law says that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These forces are of the same type, act on different bodies, and never cancel each other out.
牛顿第三定律指出，如果物体 A 对物体 B 施加一个力，那么物体 B 会对物体 A 施加一个大小相等、方向相反的力。这些力属于同种类型，作用在不同物体上，永远不能相互抵消。
A common misconception is to confuse action‑reaction pairs with balanced forces acting on the same object. For example, the normal force from a table on a book and the weight of the book are not an action‑reaction pair – the correct pair for the normal force is the force the book exerts downward on the table.
一个常见的误解是将作用力与反作用力对与作用在同一物体上的平衡力混淆。例如，桌子对书本的法向力和书本的重力并不是一对作用力与反作用力——法向力的正确反作用力是书本向下施加在桌子上的力。
7. Types of Forces: Weight, Tension, Normal, Friction | 力的类型：重力、张力、法向力、摩擦力
Weight (W = m g) is the gravitational force exerted by a planet on an object and always acts towards the centre of the planet. Tension is the pulling force transmitted through a string, rope, or cable when it is taut.
重力（W = m g）是行星对物体施加的万有引力，方向始终指向行星中心。张力是通过拉紧的细绳、绳索或缆绳传递的拉力。
The normal force is the contact force exerted by a surface perpendicular to itself. It adjusts to balance other perpendicular forces or to provide the centripetal force in circular motion. Friction opposes relative motion between surfaces in contact and is proportional to the normal force for sliding friction (f = μ R).
法向力是表面垂直于自身施加的接触力。它会调整自身大小以平衡其他垂直方向的力，或在圆周运动中提供向心力。摩擦力阻碍接触表面之间的相对运动，对于滑动摩擦，其大小与法向力成正比（f = μ R）。
8. Free‑Body Diagrams and Net Force | 受力分析与净力
A free‑body diagram represents all the external forces acting on a single object using arrows drawn from a dot or a box. The lengths of the arrows indicate relative magnitudes. This tool is essential for identifying the net force.
受力分析图使用从一个点或方框画出的箭头来表示作用在单个物体上的所有外力。箭头的长度表示相对大小。这个工具对于确定净力至关重要。
After sketching the diagram, choose a convenient coordinate system, resolve forces into components, and write ΣF = m a for each axis. If the object is in equilibrium, the net force is zero, so the sum of force components in any direction equals zero.
在绘制完图表后，选择一个方便的坐标系，将力分解为分力，并对每个轴写出 ΣF = m a。如果物体处于平衡状态，净力为零，因此任何方向上的分力之和等于零。
9. Momentum and Impulse | 动量与冲量
Linear momentum p is the product of an object’s mass and its velocity: p = m v, a vector quantity with the same direction as velocity. Impulse J is the change in momentum produced by a force acting over a time interval: J = Δp = F Δt (for constant force).
线动量 p 是物体质量与速度的乘积：p = m v，是一个与速度方向相同的矢量。冲量 J 是由力在一段时间间隔内作用所产生的动量变化：J = Δp = F Δt（对于恒力）。
The area under a force‑time graph gives the impulse. Even when the force varies, the impulse‑momentum theorem states that the total impulse equals the change in momentum. This theorem is especially useful for analysing collisions and impacts.
力‑时间图下的面积表示冲量。即使力是变化的，冲量‑动量定理指出总冲量等于动量的变化。该定理在分析碰撞和撞击时特别有用。
10. Conservation of Momentum | 动量守恒
In an isolated system (no external forces), the total linear momentum before and after an interaction remains constant. This principle applies to all collisions and explosions, regardless of whether kinetic energy is conserved.
在孤立系统中（没有外力），相互作用前后的总线动量保持不变。该原理适用于所有碰撞和爆炸，无论动能是否守恒。
In a perfectly inelastic collision, objects stick together and move with a common final velocity. In an elastic collision, both momentum and kinetic energy are conserved – typically possible only for atomic and subatomic particles, though some macroscopic collisions approximate elastic behaviour.
在完全非弹性碰撞中，物体粘在一起并以共同的速度运动。在弹性碰撞中，动量和动能都守恒——通常只有在原子和亚原子粒子中才能实现，尽管某些宏观碰撞可以近似为弹性碰撞。
11. Work, Kinetic Energy, and Power | 功、动能与功率
Work W done by a constant force is the product of the force component along the displacement and the displacement magnitude: W = F s cos θ. Work is a scalar measured in joules (J) and transfers energy to or from an object.
恒力所做的功 W 是力在位移方向上的分量与位移大小的乘积：W = F s cos θ。功是标量，单位为焦耳（J），它将能量传递给物体或从物体传出。
The work‑energy theorem states that the net work done on an object equals its change in kinetic energy: Wₙₑₜ = ½ m v² − ½ m u². Power P is the rate of doing work or transferring energy: P = W / t, with the SI unit watt (W).
功能定理指出，对物体所做的净功等于其动能的变化：Wₙₑₜ = ½ m v² − ½ m u²。功率 P 是做功或能量传递的速率：P = W / t，国际单位是瓦特（W）。
12. Energy Conservation and Efficiency | 能量守恒与效率
The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. The total mechanical energy (kinetic + potential) remains constant if only conservative forces (such as gravity) do work.
能量守恒原理指出，能量不能被创造或消灭，只能从一种形式转化为另一种形式。如果只有保守力（如重力）做功，则总机械能（动能 + 势能）保持不变。
When non‑conservative forces like friction are present, mechanical energy is dissipated as heat. Efficiency is the ratio of useful energy output to total energy input, usually expressed as a percentage. In IB problems, you may be asked to calculate energy transfers in systems with frictional losses.
当存在像摩擦力这样的非保守力时，机械能会以热的形式耗散。效率是有用能量输出与总能量输入的比值，通常以百分比表示。在 IB 问题中，你可能需要计算存在摩擦损耗的系统中的能量转移。
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