Newton's Laws of Motion | 牛顿定律考点精讲

📚 Newton’s Laws of Motion | 牛顿定律考点精讲

Newton’s laws of motion form the cornerstone of classical mechanics and are essential for understanding forces, acceleration, and equilibrium in A-Level OCR Physics. This revision guide breaks down every key concept, from inertia and free-body diagrams to friction and connected-object problems, ensuring you are fully prepared for the exam.

牛顿运动定律是经典力学的基石，对于理解 A-Level OCR 物理中的力、加速度和平衡至关重要。本篇复习指南将详细解析从惯性、受力分析图到摩擦力和连接体问题等每一个关键概念，帮助你全面备考。

1. Newton’s First Law and Inertia | 牛顿第一定律与惯性

Newton’s first law states that an object will remain at rest or continue to move at a constant velocity in a straight line unless acted upon by a resultant external force.

牛顿第一定律指出，除非受到合外力的作用，物体将保持静止或沿直线做匀速直线运动。

This tendency of an object to resist changes in its state of motion is called inertia. Inertia is directly proportional to mass; a more massive object has greater inertia.

物体抵抗其运动状态变化的性质称为惯性。惯性与质量成正比；质量越大的物体惯性越大。

For example, a book resting on a table stays at rest because the upward normal contact force and the downward weight balance each other, yielding zero resultant force.

例如，放在桌上的书保持静止，因为向上的接触力与向下的重力相互平衡，合外力为零。

In exam questions, the first law often appears when identifying equilibrium conditions, making it crucial to check that both resultant force and resultant moment are zero.

在考试题目中，第一定律常出现在判断平衡条件的场景，必须确认合外力和合力矩都为零。

2. Equilibrium and Net Force | 平衡与净力

A system is in translational equilibrium when the vector sum of all forces acting on it is zero. This implies the object is either stationary or moving with constant velocity.

当作用在系统上的所有力的矢量和为零时，系统处于平动平衡，此时物体要么静止，要么以恒定速度运动。

To verify equilibrium, resolve all forces into perpendicular components (typically horizontal and vertical) and ensure that ΣF_x = 0 and ΣF_y = 0.

要验证平衡，需将所有力分解为垂直分量（通常为水平和竖直方向），并确保 ΣF_x = 0 且 ΣF_y = 0。

OCR exam problems often involve objects suspended by strings, resting on surfaces, or held by multiple cables where tension, weight, and reaction forces must be balanced.

OCR 试题经常涉及由细绳悬挂、放置在表面或用多根缆绳固定的物体，需要平衡张力、重力和反作用力。

Always begin by drawing a clear free-body diagram, marking all force vectors accurately before setting up your equilibrium equations.

解题时始终先画出清晰的受力分析图，准确标出所有力矢量，然后再建立平衡方程。

3. Newton’s Second Law: F = m a | 牛顿第二定律：F = m a

The second law states that the resultant force on an object is equal to the product of its mass and acceleration, and the acceleration is in the same direction as the resultant force.

第二定律指出，作用在物体上的合外力等于物体质量与加速度的乘积，加速度方向与合外力方向相同。

ΣF = m a

The unit of force is the newton (N), where 1 N = 1 kg m s⁻². This law allows us to calculate unknowns in linear motion once all forces are known.

力的单位是牛顿 (N)，1 N = 1 kg m s⁻²。该定律使我们能够在已知所有力的情况下计算直线运动中的未知量。

In problems with non-zero resultant force, always assign a positive direction and treat acceleration as a vector; components of forces perpendicular to the motion must be accounted for separately.

在处理合外力不为零的问题时，务必设定正方向并将加速度视为矢量；与运动方向垂直的力分量需单独处理。

The second law can be applied to any object or system as long as you consider the net external force and the total mass being accelerated.

只要考虑合外力和被加速的总质量，第二定律就可以应用于任意物体或系统。

4. The Second Law in Momentum Form | 第二定律的动量形式

Newton originally formulated his second law in terms of momentum. Momentum p is defined as p = m v, and the rate of change of momentum is proportional to the resultant force.

牛顿最初是用动量来表述第二定律的。动量定义为 p = m v，动量的变化率与合外力成正比。

F = Δp / Δt

For constant mass, this reduces to F = m (Δv/Δt) = m a. However, the momentum form is especially useful when analysing collisions, explosions, or situations where mass changes.

当质量恒定时，这简化为 F = m (Δv/Δt) = m a。但在分析碰撞、爆炸或质量变化的情况时，动量形式特别有用。

In OCR A-Level Physics, you may be asked to explain how the force experienced by a passenger during a crash relates to the rate of change of momentum, linking the equation to impulse (F Δt = Δp).

在 OCR A-Level 物理中，你可能需要解释碰撞中乘客所受的力如何与动量变化率相关，并将该方程与冲量 (F Δt = Δp) 联系起来。

Remember that impulse equals the area under a force–time graph, and the average force can be found using F = Δp/Δt.

请记住，冲量等于力-时间图下的面积，平均力可以用 F = Δp/Δt 求得。

5. Free-Body Diagrams | 受力分析图

A free-body diagram is a simplified sketch showing all the forces acting on a single object, drawn as arrows originating from a point representing the object’s centre of mass.

受力分析图是一种简化的示意图，将所有作用在单个物体上的力用起点在代表质心点的箭头表示。

Typical forces to include are weight (mg, always vertically down), normal reaction (perpendicular to the contact surface), tension (along a string or cable), friction (opposing relative motion), and applied forces.

通常需标出重力 (mg，始终竖直向下)、法向反力（垂直于接触面）、张力（沿绳子或缆绳方向）、摩擦力（与相对运动方向相反）以及外加力。

Always label each force clearly and, if necessary, resolve weight or other forces into components parallel and perpendicular to the surface before applying Newton’s laws.

务必清晰标注每一个力，如有必要，在应用牛顿定律之前将重力或其他力分解为平行和垂直于表面的分量。

Drawing an accurate free-body diagram is one of the most important steps; many errors in mechanics arise from missing or misorienting a force.

绘制准确的受力分析图是最重要的步骤之一；力学中的许多错误都源于遗漏了某个力或力的方向搞错。

6. Objects on Inclined Planes | 斜面问题

When an object is placed on a smooth inclined plane at an angle θ to the horizontal, its weight can be resolved into two perpendicular components: mg sin θ parallel to the slope and mg cos θ perpendicular to the slope.

当物体放在与水平面成角度 θ 的光滑斜面上时，其重力可分解为两个垂直分量：平行于斜面的 mg sin θ 和垂直于斜面的 mg cos θ。

parallel component = mg sin θ
perpendicular component = mg cos θ

The normal reaction N equals mg cos θ if there are no other vertical forces. The resultant force down the slope is therefore mg sin θ, giving an acceleration a = g sin θ (in the absence of friction).

如果没有其他竖直力的作用，法向反力 N 等于 mg cos θ。因此沿斜面的合力为 mg sin θ，在无摩擦的情况下加速度为 a = g sin θ。

If friction is present, it opposes motion, and the net force becomes mg sin θ − f. The acceleration is then calculated using a = (mg sin θ − f)/m.

如果有摩擦力，它会阻碍运动，此时净力为 mg sin θ − f，加速度则用 a = (mg sin θ − f)/m 来计算。

In OCR questions, you may need to find the angle at which an object just begins to slide, which is related to the coefficient of static friction (tan θ = μ).

在 OCR 考题中，你可能需要求物体刚好开始滑动的角度，这与静摩擦系数有关 (tan θ = μ)。

7. Friction and the Coefficient of Friction | 摩擦力与摩擦系数

Friction is a force that opposes the relative motion or attempted motion between two surfaces in contact. There are two main types: static friction and kinetic (dynamic) friction.

摩擦力是阻碍两个接触表面之间相对运动或相对运动趋势的力。主要有两种类型：静摩擦和动摩擦。

Static friction acts when there is no relative motion, and its magnitude adjusts up to a maximum value given by f_max = μ R, where μ is the coefficient of static friction and R is the normal reaction.

静摩擦在无相对运动时起作用，其大小会在零到最大值之间调节，最大静摩擦力为 f_max = μ R，其中 μ 为静摩擦系数，R 为法向反力。

Once motion begins, kinetic friction takes over, and its magnitude is approximately constant: f_k = μ_k R. For simplicity, OCR often uses μ for both static and kinetic friction unless specifying otherwise.

一旦开始运动，动摩擦就起主导作用，其大小近似恒定：f_k = μ_k R。为简洁起见，除非另有说明，OCR 常使用 μ 同时表示静摩擦和动摩擦系数。

Friction does not always oppose motion in the simple intuitive sense – for example, when a car accelerates, friction from the road on the driving wheels acts in the direction of motion to push the car forward.

摩擦力并不总是简单地阻碍运动——例如，当汽车加速时，路面作用在驱动轮上的摩擦力沿运动方向推动汽车前进。

8. Newton’s Third Law | 牛顿第三定律

Newton’s third law states: if object A exerts a force on object B, then object B simultaneously exerts an equal and opposite force on object A. These forces are of the same type and act on different objects.

牛顿第三定律指出：若物体 A 对物体 B 施加一个力，则物体 B 同时会施加一个大小相等、方向相反的力在物体 A 上。这两个力属于同种类型，且作用在不同物体上。

F_AB = − F_BA

A classic example is a book resting on a table: the book’s weight pulls the Earth upward with the same magnitude as the Earth pulls the book down. Meanwhile, the table pushes up on the book (normal force) and the book pushes down on the table.

一个经典例子是静置在桌上的书：书的重量以相同大小向上拉地球，同时地球以相同大小向下拉书。同时，桌子向上推书本（法向力），书本向下压桌子。

In OCR exams, always identify the ‘Newton’s third law pair’ by checking that the two forces are equal, opposite, act on two different bodies, and are of the same nature. Do not confuse them with balanced forces acting on a single body.

在 OCR 考试中，识别“牛顿第三定律力对”时应检查这两个力是否大小相等、方向相反、作用在两个不同物体上且性质相同。切勿将它们与作用在单个物体上的平衡力混淆。

9. Connected Objects: Tension and Pulleys | 连接体：张力与滑轮

When two objects are connected by a light, inextensible string, they share the same acceleration (assuming the string remains taut) and the magnitude of tension is uniform throughout the string if pulleys are smooth and massless.

当两个物体由轻质且不可伸长的细绳连接时，它们具有相同的加速度（假设绳子保持绷紧），如果滑轮光滑且不计质量，绳中张力大小处处相等。

To solve connected-object problems, apply Newton’s second law either to the whole system or to each object individually. The whole-system approach often eliminates tension from the equation for acceleration.

解决连接体问题时可对整个系统或每个物体单独应用牛顿第二定律。整体法通常能将张力从加速度的表达式中消去。

For example, consider a mass m₁ on a smooth horizontal table connected by a string passing over a pulley to a hanging mass m₂. The system acceleration is a = m₂ g / (m₁ + m₂).

例如，一个质量为 m₁ 的物体放在光滑水平桌面上，通过一根跨过滑轮的细绳与悬挂的质量为 m₂ 的物体相连。系统的加速度为 a = m₂ g / (m₁ + m₂)。

Once the acceleration is known, tension can be found by isolating one mass: T = m₁ a or T = m₂ (g − a). In OCR questions, you may also be asked about the force on the pulley or the effect of a rough table surface.

知道加速度后，可以通过隔离其中一个物体求张力：T = m₁ a 或 T = m₂ (g − a)。在 OCR 试题中，还可能出现求滑轮受力或桌面粗糙带来的影响等问题。

10. Experimental Verification of Newton’s Second Law | 实验验证牛顿第二定律

The classic experiment uses a dynamics trolley on a linear air track or a low-friction ramp, pulled by a falling mass via a string over a pulley. A data logger or ticker-timer records motion.

经典实验采用线性气垫导轨或低摩擦斜面上的动力学小车，通过细绳和滑轮由下落的重物拉动。使用数据采集器或打点计时器记录运动。

To verify F ∝ a, keep the total system mass constant and vary the accelerating force by transferring masses from the trolley to the hanging weight. Measure the acceleration for each force.

要验证 F ∝ a，保持系统总质量不变，通过将砝码从小车转移到悬挂重物上来改变加速力，并测量每个力对应的加速度。

To verify a ∝ 1/m, keep the accelerating force constant and increase the mass of the system by adding masses to the trolley. Plot acceleration against 1/mass to obtain a straight line through the origin.

要验证 a ∝ 1/m，保持加速力不变，通过在小车上增加质量来增大系统质量。绘制加速度相对于 1/质量的图像，应得到一条过原点的直线。

Key precautions include compensating for friction by slightly tilting the track, ensuring the string is horizontal and parallel to the motion, and using light gates for precise timing.

主要的注意事项包括：轻微倾斜轨道以补偿摩擦力，确保细绳水平且与运动方向平行，以及使用光门进行精确定时。

In the analysis, repeated measurements and graphical methods reduce random errors; systematic errors may arise if friction is not fully compensated.

在分析中，重复测量与图像法可以减少随机误差；若摩擦力未完全补偿，则可能产生系统误差。

11. Common Misconceptions and Exam Tips | 常见误区与应试技巧

Misconception 1: Confusing mass and weight. Mass is a scalar measured in kg and remains constant; weight is a force (mg) measured in newtons and depends on the gravitational field strength.

误区一：混淆质量与重量。质量是标量，单位为 kg 且保持不变；重量是一种力 (mg)，单位为牛顿，随引力场强度变化。

Misconception 2: Believing that constant force produces constant speed. According to the second law, a constant resultant force produces constant acceleration, not constant velocity.

误区二：认为恒力产生恒速。根据第二定律，恒定的合外力产生的是恒定的加速度，而不是恒定的速度。

Misconception 3: Assuming action–reaction pairs cancel each other out. They act on different objects, so they do not cancel in the context of a single free-body diagram.

误区三：认为作用力与反作用力会相互抵消。它们作用在不同物体上，因此在单一物体的受力分析中不会抵消。

Exam tip: Always underline the object you are analysing, draw a neat free-body diagram, set a clear sign convention, and write Newton’s second law in its resolved form before substituting numbers.

应试技巧：始终用下划线标出你正在分析的物体，画出清晰的受力分析图，设定明确的正负号规则，并在代入数字前先写出牛顿第二定律的分量形式。

Be especially careful with slope problems: the normal reaction is not always equal to mg; it is mg cos θ, and failing to resolve weight correctly is a very common error.

在处理斜面问题时需格外小心：法向反力并不总是等于 mg，而是 mg cos θ，未能正确分解重力是一个极为常见的错误。

12. Summary and Key Equations | 总结与核心公式

Newton’s laws give a complete framework for analysing forces and motion. Always identify the resultant force, draw a diagram, and apply ΣF = m a or F = Δp/Δt consistently.

牛顿定律为分析力与运动提供了完整的框架。解题时始终找出合外力、绘图，并一致地应用 ΣF

Published by TutorHao | A-Level Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Newton’s Laws of Motion | 牛顿定律考点精讲