📚 A Systematic Review of Mechanics in Physics | 物理力学知识点系统梳理
Mechanics is the cornerstone of physics, describing how objects move and interact under the influence of forces. From the simplest push and pull to the grand orbits of celestial bodies, the principles of mechanics allow us to model, predict, and engineer the world around us. This article provides a structured revision of the essential mechanics topics covered in advanced physics syllabi, including kinematics, Newton’s laws, work and energy, momentum, circular motion, gravitation, and simple harmonic motion. Each section pairs explanations with key formulae and practical examples to help you build a confident understanding.
力学是物理学的基石，描述物体如何在力的作用下运动与相互作用。从简单的推拉到天体的宏伟轨道，力学原理让我们能够模拟、预测和设计周围的世界。本文系统梳理了高阶物理课程中的核心力学知识点，涵盖运动学、牛顿定律、功与能、动量、圆周运动、引力以及简谐运动。每一节都配有中英对照的解释、关键公式和实例，助你建立起扎实的理解。
1. Scalars, Vectors and Kinematics | 标量、矢量与运动学
In mechanics, physical quantities are divided into scalars (magnitude only, e.g., distance, speed, mass, time, energy) and vectors (magnitude and direction, e.g., displacement, velocity, acceleration, force, momentum). Vectors can be added using the triangle or parallelogram law, and they can be resolved into perpendicular components, typically using trigonometric functions: Fx = F cos θ, Fy = F sin θ.
力学中的物理量分为标量（只有大小，如距离、速率、质量、时间、能量）和矢量（既有大小又有方向，如位移、速度、加速度、力、动量）。矢量可以用三角形法则或平行四边形法则合成，也可以分解为互相垂直的分量，通常借助三角函数：Fx = F cos θ，Fy = F sin θ。
Displacement, velocity and acceleration are the fundamental kinematic descriptors. Average velocity vav = Δs / Δt, instantaneous velocity v = ds/dt. Acceleration a = Δv / Δt. When acceleration is constant, the five SUVAT equations intertwine these quantities with time:
位移、速度和加速度是运动学的基本描述量。平均速度 vav = Δs / Δt，瞬时速度 v = ds/dt。加速度 a = Δv / Δt。当加速度恒定时，五个 SUVAT 方程将这些量与时间联系起来：
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = ½ (u + v) t
s = v t − ½ a t²
These equations only apply when the acceleration is uniform. For free-fall motion near Earth’s surface, a is replaced by g = 9.81 m s⁻² directed downwards. Projectile motion is then separated into horizontal (constant velocity) and vertical (constant acceleration) components, producing a parabolic trajectory.
这些方程仅适用于匀加速情况。近地面自由落体运动中，加速度 a 被向下的 g = 9.81 m s⁻² 取代。抛体运动则分解为水平匀速运动与竖直匀加速运动的合成，其轨迹为抛物线。
To solve projectile problems, resolve the initial velocity u into horizontal (u cos θ) and vertical (u sin θ) parts. Time of flight, maximum height and range can all be derived using the SUVAT equations independently in each direction. Air resistance is typically neglected in these ideal models.
求解抛体问题时，需将初速度 u 分解为水平分量 (u cos θ) 和竖直分量 (u sin θ)。飞行时间、最大高度和射程均可分别对两个方向独立使用 SUVAT 方程导出。理想模型中通常忽略空气阻力。
2. Newton’s Laws of Motion | 牛顿运动定律
Newton’s First Law (law of inertia) states that an object will remain at rest or in uniform straight-line motion unless acted upon by a net external force. This introduces the concept of inertia, the tendency of an object to resist changes in its motion.
牛顿第一定律（惯性定律）指出，除非受到净外力作用，物体将保持静止或匀速直线运动状态。由此引入了惯性的概念，即物体抵抗运动状态变化的性质。
Newton’s Second Law quantifies dynamics: the net force acting on an object is equal to the product of its mass and acceleration, Fnet = m a. Force is measured in newtons (N). It is a vector equation; thus, components along axes can be analysed separately.
牛顿第二定律定量描述了动力学规律：作用在物体上的净力等于其质量与加速度的乘积，Fnet = m a。力的单位为牛顿 (N)。这是一条矢量方程，因此可以沿坐标轴分别进行分量分析。
Newton’s Third Law emphasises that forces always come in pairs: if body A exerts a force on body B, body B simultaneously exerts a force equal in magnitude but opposite in direction on A. These action–reaction forces act on different objects and never cancel each other in a free-body diagram of a single object.
牛顿第三定律强调力总是成对出现：若物体 A 对 B 施加力，则 B 同时对 A 施加大小相等、方向相反的力。这一对作用力与反作用力作用在不同物体上，在单个物体的受力图中绝不能相互抵消。
Common forces examined in mechanics include weight (W = m g), normal contact force, tension in strings, friction (static up to a limit, kinetic f = μ R where μ is the coefficient of friction and R is the normal reaction), and drag or air resistance. Drawing a clear free-body diagram is essential to identify all forces and apply Newton’s laws correctly.
力学中常见的力包括重力（W = m g）、法向接触力、绳中张力、摩擦力（静摩擦有上限，动摩擦 f = μ R，μ 为摩擦系数，R 为法向反作用力）以及空气阻力。清晰地画出受力图是识别所有力并正确应用牛顿定律的关键。
3. Equilibrium and Moments | 力的平衡与力矩
An object is in translational equilibrium when the vector sum of all forces acting on it is zero, ΣF = 0. For rotational equilibrium, the sum of clockwise moments about any pivot must equal the sum of anticlockwise moments, ΣM = 0.
当物体所受所有力的矢量和为零（ΣF = 0）时，它处于平动平衡状态。而要达到转动平衡，对任一转动轴的顺时针力矩之和必须等于逆时针力矩之和，即 ΣM = 0。
The moment of a force about a point is defined as the product of the force and the perpendicular distance from the point to the line of action: M = F d. Moments are measured in newton-metres (N m). The principle of moments is widely used in levers, bridges, and crane problems.
力对某点的力矩定义为力的大小与该点到力作用线的垂直距离的乘积：M = F d。力矩的单位是牛顿·米 (N m)。力矩原理广泛应用于杠杆、桥梁和起重机等问题中。
The centre of gravity of a body is the point at which the entire weight appears to act. For a uniform regular body, it coincides with the geometrical centre. Stability of an object increases when its centre of gravity is low and its base area is large.
物体的重心是其所有重量看似集中的作用点。对于均匀规则物体，重心与几何中心重合。物体的重心越低、底面积越大，其稳定性越高。
In many static problems, resolving forces into perpendicular components and applying both ΣF = 0 and ΣM = 0 simultaneously allows unknown forces or distances to be determined. This is the foundation of statics.
在许多静力问题中，通过将力分解为正交分量并同时应用 ΣF = 0 和 ΣM = 0，可以解出未知力或距离。这正是静力学的基础。
4. Work, Energy and Power | 功、能量与功率
Work is done when a force moves its point of application in the direction of the force: W = F s cos θ, where θ is the angle between the force and the displacement. Work is a scalar quantity measured in joules (J), where 1 J = 1 N m.
当力的作用点沿力的方向发生位移时，力做功：W = F s cos θ，θ 为力与位移的夹角。功是标量，单位为焦耳 (J)，1 J = 1 N m。
Kinetic energy is the energy due to motion: K = ½ m v². Gravitational potential energy near Earth’s surface changes according to ΔU = m g Δh. In a closed system with no external forces, total mechanical energy (K + U) is conserved, though it can change form.
动能是物体由于运动而具有的能量：K = ½ m v²。近地面重力势能的变化为 ΔU = m g Δh。在无外力做功的封闭系统中，机械能总量（K + U）守恒，但其形式可以相互转化。
Power is the rate of doing work or transferring energy: P = W / t. For a constant force acting in the direction of motion, P = F v. The SI unit is the watt (W), where 1 W = 1 J s⁻¹.
功率是做功或转化能量的速率：P = W / t。若力恒定且与运动方向一致，有 P = F v。国际单位是瓦特 (W)，1 W = 1 J s⁻¹。
Efficiency is defined as the ratio of useful output work (or power) to total input work (or power), often expressed as a percentage: η = (useful output / total input) × 100%. Real machines always have losses due to friction, sound or heat.
效率定义为有用输出功（或功率）与总输入功（或功率）之比，常以百分数表示：η = (有用输出 / 总输入) × 100%。实际机器总因摩擦、声音或热而有能量损耗。
5. Momentum and Impulse | 动量与冲量
Linear momentum is the product of an object’s mass and its velocity: p = m v. Momentum is a vector quantity pointing in the same direction as the velocity. It is measured in kg m s⁻¹.
线动量是物体质量与速度的乘积：p = m v。动量是矢量，方向与速度相同，单位为 kg m s⁻¹。
The law of conservation of momentum states that in an isolated system (no net external force), the total momentum before an interaction equals the total momentum afterwards. This principle is extremely useful for analysing collisions and explosions.
动量守恒定律指出，在孤立系统（无净外力）中，相互作用前的总动量等于相互作用后的总动量。这一原理对分析碰撞与爆炸问题极为有用。
Impulse J is the product of the average force and the time interval during which it acts: J = F Δt. Impulse equals the change in momentum: J = Δp = m v − m u. This explains why extending the impact time reduces the force (e.g., airbags, crumple zones).
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