📚 IB Physics: Newton’s Laws – Key Concepts Explained | IB 物理：牛顿定律 考点精讲
Newton’s laws of motion form the cornerstone of classical mechanics and are central to the IB Physics syllabus. Understanding these laws allows us to predict and explain the motion of objects under the influence of forces, from a falling apple to complex pulley systems. This revision guide breaks down every essential concept, common pitfalls, and examination techniques for both SL and HL students.
牛顿运动定律是经典力学的基石，也是 IB 物理考试的核心内容。掌握这些定律，我们可以预测并解释从下落的苹果到复杂的滑轮系统中物体在力作用下的运动。本考点精讲将为 SL 和 HL 同学逐一梳理所有核心概念、常见易错点以及应试技巧。
1. Newton’s First Law & Inertia | 牛顿第一定律与惯性
Newton’s first law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by a net external force. This property of matter is called inertia. The greater an object’s mass, the greater its inertia and the more it resists changes to 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。物质的这种属性称为惯性。物体的质量越大，惯性越大，就越难改变其运动状态。
In IB problems, ‘uniform motion’ means constant velocity, which implies zero net force. Do not confuse velocity with speed; direction matters. A car turning at constant speed is accelerating because its direction changes, so a net force must be present.
在 IB 考题中，“匀速运动”指速度恒定，这意味着净力为零。切忌将速度和速率混淆；方向至关重要。一辆以恒定速率转弯的汽车处于加速状态（方向改变），因此必定存在净力。
Common misconception: students often think a continuous force is needed to keep an object moving. Actually, in the absence of friction or drag, an object would continue moving indefinitely without any force.
常见误区：同学们常以为需要持续施加力才能让物体保持运动。实际上，若没有摩擦或阻力，物体无需任何力即可无限期地运动下去。
2. Newton’s Second Law (F = ma) | 牛顿第二定律 (F = ma)
The second law quantifies the relationship between net force, mass and acceleration: ΣF = m a. The acceleration is directly proportional to the net force and inversely proportional to the mass. The direction of acceleration is the same as the direction of the net force.
第二定律定量描述了净力、质量和加速度之间的关系：ΣF = m a。加速度与净力成正比，与质量成反比；加速度的方向与净力的方向相同。
In IB exams, you must always use the net force in F = ma. If several forces act on a body, calculate the vector sum first. The equation can also be written in terms of momentum: F = Δp / Δt, where p = m v is linear momentum. This form is especially useful when mass changes or in impulse scenarios.
IB 考试中必须使用净力代入 F = ma。若物体受到多个力作用，要先求出矢量和。该方程也可用动量表述：F = Δp / Δt，其中 p = m v 为线动量。当质量变化或涉及冲量时，这种形式尤为有用。
Be careful with units: force in newtons (N), mass in kg, acceleration in m/s². In free-fall, weight W = m g always acts downward. The acceleration due to gravity g is approximately 9.81 m s⁻² unless otherwise stated.
注意单位：力用牛顿 (N)，质量用 kg，加速度用 m/s²。在自由落体中，重力 W = m g 始终竖直向下。除非另有说明，重力加速度 g 取约 9.81 m s⁻²。
3. Newton’s Third Law (Action-Reaction) | 牛顿第三定律 (作用力与反作用力)
Newton’s third law states that if body A exerts a force on body B, then body B exerts an equal and opposite force on body A: FA on B = -FB on A. These forces act on different bodies, are of the same type, and occur simultaneously.
牛顿第三定律指出：若物体 A 对物体 B 施加一个力，那么物体 B 也会对物体 A 施加一个大小相等、方向相反的力：FA on B = -FB on A。这两个力作用在不同物体上，性质相同，且同时产生。
Exam tip: when identifying action-reaction pairs, never add them together to cancel in a free-body diagram. They act on different objects, so they cannot balance each other on the same object. A book on a table: the book exerts a downward force on the table (action), the table exerts an upward normal force on the book (reaction).
考试技巧：识别作用与反作用力对时，切勿将其加在一起在受力图中抵消。它们作用在不同物体上，不可能在同一物体上相互平衡。例如桌面上的书：书对桌子施加向下的力（作用力），桌子对书施加向上的支持力（反作用力）。
4. Free-Body Diagrams | 受力分析图
Drawing accurate free-body diagrams (FBDs) is essential for solving mechanics problems. Represent the object as a point or a box and draw all forces acting on that object with labelled arrows, ensuring they originate from the object’s centre.
绘制准确的受力分析图是解决力学问题的关键。将物体表示为一个点或方块，并画出所有作用在该物体上的力，用带标签的箭头表示，确保箭头起点位于物体中心。
Typical forces to include: weight (W or Fg) downwards, normal reaction (N or R) perpendicular to surfaces, tension (T) along strings, friction (f) opposing motion, applied forces (Fapp), and spring forces. Always define a convenient coordinate system; align one axis with the direction of acceleration.
常见力包括：重力 (W 或 Fg) 竖直向下，法向反作用力 (N 或 R) 垂直于接触面，绳子张力 (T) 沿绳方向，摩擦力 (f) 阻碍相对运动，外加作用力 (Fapp)，以及弹簧力。务必选定便捷的坐标系，将其中一个坐标轴沿加速度方向放置。
Do not include forces exerted by the object on its surroundings. If a surface is inclined, resolve weight into components: parallel to slope (m g sin θ) and perpendicular (m g cos θ).
不要将物体施加给外界的力画入。若为斜面，需要分解重力：平行于斜面的分量为 m g sin θ，垂直于斜面的分量为 m g cos θ。
5. Equilibrium and Net Force | 平衡与净力
An object is in translational equilibrium when the net force acting on it is zero: ΣF = 0. This means the object is either at rest or moving with constant velocity. For two-dimensional problems, the condition must hold separately for perpendicular axes: ΣFx = 0 and ΣFy = 0.
当物体所受净力为零时，物体处于平动平衡状态：ΣF = 0。这意味着物体要么静止，要么匀速运动。在二维问题中，该条件必须分别在垂直坐标轴上成立：ΣFx = 0 且 ΣFy = 0。
When analysing equilibrium systems (e.g., a sign hanging from two strings), resolve forces into components and set up simultaneous equations. Sketches and neat labelling are vital. IB questions often ask for the tension in cords or the magnitude of an unknown force.
分析平衡系统（如悬挂于两根绳子上的标牌）时，需将力分解为各分量并联立方程组求解。清晰标注的简图至关重要。IB 考题常要求计算绳索中的张力或某个未知力的大小。
6. Friction Forces | 摩擦力
Friction opposes relative motion or attempted motion between two surfaces in contact. It is categorized into static friction (no relative motion) and kinetic (sliding) friction. Static friction varies up to a maximum value: fs ≤ μs N. Kinetic friction is roughly constant: fk = μk N, where N is the normal reaction force.
摩擦力阻碍两接触面之间的相对运动或相对运动趋势，分为静摩擦力（无相对运动）和动（滑动）摩擦力。静摩擦力从零变化到最大值：fs ≤ μs N。动摩擦力则近似恒定：fk = μk N，其中 N 为法向反作用力。
Important: the coefficient of static friction μs is usually larger than μk. If an object is on the verge of slipping, fs = μs N. In many problems, you must first check whether the applied force exceeds the maximum static friction to determine if motion occurs.
要点：静摩擦系数 μs 通常大于动摩擦系数 μk。物体即将滑动时，fs = μs N。在许多题目中，需要先检验外加力是否超过最大静摩擦力，以判断物体是否开始运动。
7. Tension and Pulley Systems | 张力与滑轮系统
Tension is the pulling force transmitted along a string, rope or cable. In ideal (light, inextensible) strings, tension is uniform throughout. For massless, frictionless pulleys, tension is the same on both sides of the pulley. Real pulleys with mass may alter the tension.
张力是沿绳、索或缆传递的拉力。在理想（轻质、不可伸长）绳中，张力处处相等。对于无质量、无摩擦的理想滑轮，滑轮两侧的张力大小相同。若滑轮有质量，则张力可能发生变化。
To solve pulley problems, draw separate FBDs for each mass and apply ΣF = m a. For a system where two masses are connected by a string passing over a frictionless pulley, the acceleration magnitude is the same for both masses. Use sign conventions consistently with the chosen direction of motion.
求解滑轮问题需为每个物体单独画受力分析图，并使用 ΣF = m a。若两物体通过跨过无摩擦滑轮的绳子相连，则两者加速度大小相同。以选定的运动方向为基准，始终使用一致的符号约定。
8. Spring Force (Hooke’s Law) | 弹簧力 (胡克定律)
The force exerted by a spring is proportional to its extension or compression from its natural length, as described by Hooke’s law: F = -k x. Here k is the spring constant (stiffness) measured in N m⁻¹, and x is the displacement from equilibrium. The negative sign indicates the restoring force opposes the displacement.
弹簧产生的力与其相对于原长的伸长量或压缩量成正比，即胡克定律：F = -k x。其中 k 为劲度系数（刚度），单位 N m⁻¹；x 为偏离平衡位置的位移。负号表示回复力与位移方向相反。
In IB problems, springs may be combined with masses on inclined planes or in vertical oscillations. Be aware that when a mass hangs stationary from a spring, the extension is such that k x = m g. The elastic potential energy stored is ½ k x², but this article focuses on the force aspect.
在 IB 题目中，弹簧常与斜面上的物体或竖直振动结合。注意，当物体挂在弹簧下方静止时，伸长量满足 k x = m g。弹簧储存的弹性势能为 ½ k x²，但本文重点探讨力的部分。
9. Momentum and Impulse | 动量与冲量
Linear momentum p is the product of mass and velocity: p = m v. Momentum is a vector; its direction matches velocity. The impulse J of a force is the change in momentum: J = Δp = F Δt, valid when the force is constant. The area under a force-time graph represents impulse.
线动量 p 是质量与速度的乘积：p = m v。动量是矢量，方向与速度相同。力产生的冲量 J 等于动量的变化量：J = Δp = F Δt（适用于恒力）。力-时间图像下的面积表示冲量的大小。
For varying forces, impulse is the integral of force over time, but IB usually assesses impulse via area calculation or average force. Remember: impulse can increase or decrease momentum; it is not a ‘force’ but a product of force and time interval.
对于变力，冲量是力对时间的积分，但 IB 通常通过面积计算或平均力来考查。记住：冲量可以是增加或减少动量；它并非“力”，而是力与时间间隔的乘积。
10. Conservation of Momentum | 动量守恒
If no net external force acts on a system, the total momentum of the system remains constant: Σpbefore = Σpafter. This principle is fundamental for analyzing collisions and explosions. In IB, you must be able to apply conservation of momentum in one and two dimensions.
若系统不受净外力作用，系统总动量守恒：Σp前 = Σp后。这是分析碰撞和爆炸过程的基本原理。IB 要求考生能在一维和二维情境中应用动量守恒。
Explosions: a stationary object initially has zero total momentum; after explosion, fragments move such that the vector sum of momenta is zero. Collisions can be elastic (kinetic energy conserved) or inelastic (kinetic energy not conserved). Momentum is conserved in both types as long as external net force is zero.
爆炸：原本静止的物体总动量为零；爆炸后，碎片的总动量矢量和仍为零。碰撞分为弹性碰撞（动能守恒）和非弹性碰撞（动能不守恒）。只要外净力为零，动量在两种碰撞中均守恒。
11. Connected Bodies and Systems | 连接体与系统
When multiple objects are connected (by strings or in contact), you can treat the whole system as a single entity if they move together with the same acceleration. The internal forces (e.g., tension) cancel when considering the entire system, simplifying the application of Newton’s second law.
当多个物体连接在一起（通过绳子或相互接触）并以相同加速度运动时，可以将整个系统视为一个整体。当对系统整体应用牛顿第二定律时，系统内力（如张力）相互抵消，使计算大为简化。
After finding the system’s acceleration, you can isolate one body to find internal forces. This ‘system-then-individual’ approach is highly efficient for tug-of-war, stacked blocks, and train-coupling problems. Always verify the direction of acceleration and keep coordinate axes consistent.
求出系统加速度后，再隔离其中一个物体以求解系统内力。这种“先整体后隔离”的策略在处理拔河、叠放物块、火车车厢耦联等问题时极为高效。务必核实加速度方向并保持坐标轴的一致性。
12. Exam Tips and Common Mistakes | 考试技巧与常见错误
Top exam tips for IB Newton’s laws: (1) Always write down knowns and unknowns before starting; (2) Draw a clear free-body diagram even if not explicitly asked; (3) Use vector notation or distinguish directions with signs; (4) Check whether mass is in kg; (5) In collision questions, momentum is a vector—subtract or add components carefully.
IB 牛顿定律应试锦囊：(1) 动笔前先列出已知量和未知量；(2) 即使题目未明确要求，也画出清晰的受力分析图；(3) 使用矢量符号或用正负号区分方向；(4) 检查质量是否以 kg 为单位；(5) 碰撞题中，动量是矢量——注意分量的加减。
Common mistakes: confusing mass and weight; forgetting that normal force is not always equal to m g (e.g., on inclined planes or in accelerating lifts); incorrectly applying F = ma to individual pieces of a system without considering net force; adding action-reaction pairs in a single free-body diagram. Avoid these by rigorous practice and diagram drawing.
常见错误：混淆质量与重量；忘记法向力并非总是等于 m g（例如斜面上或加速升降机中）；对系统中的一部分直接用 F = ma 而未考虑所受合力；在单个受力图中加入作用与反作用力对。通过严格练习和绘图，可避免这些失误。
Finally, master the skill of interpreting force-time and momentum-time graphs. The slope of a momentum-time graph gives the net force; the area under a force-time graph gives impulse. These graphical interpretations are frequently tested in IB Paper 1.
最后，熟练掌握解读力-时间图和动量-时间图的技能。动量-时间图的斜率给出净力；力-时间图下的面积给出冲量。这些图像分析技巧在 IB 试卷一中频繁出现。
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