Newton's Laws of Motion and Forces | 牛顿运动定律与力

📚 Newton’s Laws of Motion and Forces | 牛顿运动定律与力

Newton’s laws of motion form the foundation of classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. Mastering these laws is essential for solving problems in AP Physics 1, from analyzing a block on an incline to understanding planetary orbits.

牛顿运动定律构成了经典力学的基础。它们描述了物体与其所受作用力之间的关系，以及物体对这些力的运动响应。掌握这些定律对于解决AP物理1中的各种问题至关重要，从分析斜面上的物块到理解行星轨道。

1. Introduction to Newton’s Laws | 牛顿定律简介

Sir Isaac Newton published his three laws of motion in 1687 in the Philosophiæ Naturalis Principia Mathematica. These laws apply to objects we encounter daily, provided speeds are much less than the speed of light and sizes are much larger than atoms. AP Physics 1 focuses on the application of these laws to point particles and rigid bodies in linear and circular motion.

艾萨克·牛顿爵士于1687年在《自然哲学的数学原理》中发表了他的三大运动定律。这些定律适用于我们日常遇到的物体，只要速度远低于光速且尺寸远大于原子。AP物理1侧重于将这些定律应用于质点和刚体的直线与圆周运动。

2. Newton’s First Law: Inertia | 牛顿第一定律：惯性

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This property of matter is called inertia. Inertia is directly related to mass: the greater the mass, the greater the tendency to resist changes in motion.

静止的物体将保持静止，匀速直线运动的物体将保持匀速直线运动状态，除非受到不平衡力的作用。物质的这一属性被称为惯性。惯性与质量直接相关：质量越大，抵抗运动状态变化的趋势越强。

3. Inertial Reference Frames | 惯性参考系

Newton’s first law defines a special set of reference frames called inertial frames. An inertial frame is one in which an object with zero net force moves with constant velocity (including zero velocity). The surface of the Earth is approximately an inertial frame for many experiments, though its rotation introduces small fictitious forces like the Coriolis effect.

牛顿第一定律定义了一组特殊的参考系，称为惯性参考系。惯性系是指在其中合力为零的物体以恒定速度（包括零速度）运动的参考系。对于许多实验，地球表面近似为惯性参考系，尽管其自转引入了如科里奥利力等微小的虚拟力。

4. Newton’s Second Law: ΣF = m a | 牛顿第二定律：合力 = 质量 × 加速度

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This is written as ΣF = m a, where ΣF is the vector sum of all forces, m is mass, and a is acceleration. Both net force and acceleration are vectors pointing in the same direction. In AP Physics 1, you will often resolve forces into components using F_x = m a_x and F_y = m a_y.

物体的加速度与作用在其上的合力成正比，与其质量成反比。这可以写作 ΣF = m a，其中 ΣF 是所有力的矢量和，m 是质量，a 是加速度。合力与加速度均为矢量，方向相同。在AP物理1中，你会经常把力分解为分量，使用 F_x = m a_x 和 F_y = m a_y。

ΣF = m a

5. Newton’s Third Law: Action-Reaction | 牛顿第三定律：作用力与反作用力

For every action force, there is an equal and opposite reaction force. If object A exerts a force on object B, then object B exerts a force of the same magnitude but opposite direction on object A. These forces act on different objects and therefore do not cancel. For example, the Earth pulls on the Moon with a gravitational force, and the Moon pulls back on the Earth with an equal force.

对于每一个作用力，都有一个大小相等、方向相反的反作用力。如果物体A对物体B施加一个力，那么物体B对物体A施加一个大小相同但方向相反的力。这两个力作用在不同的物体上，因此不会相互抵消。例如，地球对月球施加万有引力，月球也以同样大小的力拉回地球。

6. Common Forces in Mechanics | 力学中的常见力

Weight (gravitational force): F_g = m g, directed toward the center of the Earth. Normal force (N): the support force perpendicular to the contact surface. Tension (T): the pulling force transmitted through a string or rope. Friction (f): a force that opposes relative motion. Spring force (F_s): given by Hooke’s Law, F_s = -k x, where k is the spring constant and x is displacement from equilibrium. These forces will appear repeatedly in free-body diagrams.

重量（重力）：F_g = m g，方向指向地心。法向力（N）：垂直于接触面的支持力。张力（T）：通过绳子或绳索传递的拉力。摩擦力（f）：阻碍相对运动的力。弹簧力（F_s）：由胡克定律给出，F_s = -k x，其中 k 是劲度系数，x 是偏离平衡位置的位移。这些力将在受力图中反复出现。

F_g = m g ; F_s = -k x

7. Drawing Free-Body Diagrams | 绘制受力图

A free-body diagram (FBD) is a simplified sketch showing all forces acting on a single object. Replace the object with a dot, and draw vectors for every force, labeling them clearly (e.g., F_g, N, T, f). Do not include forces exerted by the object on other bodies. Choose a coordinate system and decompose forces into components. Mastery of FBDs is the first step to applying Newton’s second law.

受力图（FBD）是一种简化的示意图，显示作用在单个物体上的所有力。将物体用一个点代替，为每个力画出矢量，并清楚地标注（如 F_g、N、T、f）。不要包括物体施加给其他物体的力。选择坐标系并将力分解为分量。掌握受力图是应用牛顿第二定律的第一步。

8. Equilibrium and Net Force | 平衡与合力

If an object is in equilibrium, its acceleration is zero, so the net force must be zero. This gives two conditions: ΣF_x = 0 and ΣF_y = 0. Static equilibrium means the object is at rest; dynamic equilibrium means it moves with constant velocity. Both cases are described by the same equations. Solving equilibrium problems involves setting up component equations from the FBD and solving for unknown forces.

如果物体处于平衡状态，其加速度为零，因此合力必须为零。这给出两个条件：ΣF_x = 0 和 ΣF_y = 0。静态平衡意味着物体静止；动态平衡意味着它以恒定速度运动。两种情况都由相同的方程描述。解决平衡问题需要从受力图建立分量方程，并求解未知力。

ΣF_x = 0 , ΣF_y = 0

9. Solving Problems with Newton’s Second Law | 应用牛顿第二定律解题

For non-equilibrium situations, acceleration is not zero. Write ΣF_x = m a_x and ΣF_y = m a_y. Identify the direction of acceleration and choose coordinate axes to simplify calculations (often aligning one axis with acceleration). Use kinematics equations if needed to relate acceleration to displacement and velocity. Always double-check that all forces are included and that the sign conventions are consistent.

对于非平衡情况，加速度不为零。写出 ΣF_x = m a_x 和 ΣF_y = m a_y。确定加速度方向并选择坐标轴以简化计算（通常使一个轴与加速度方向对齐）。如果需要，使用运动学方程将加速度与位移和速度联系起来。务必仔细检查所有力都已包含，且符号惯例一致。

10. Friction: Static and Kinetic | 摩擦力：静摩擦与滑动摩擦

Friction arises from surface interactions. Static friction f_s prevents relative motion up to a maximum value: f_s ≤ μ_s N. Kinetic friction f_k acts when surfaces slide: f_k = μ_k N. The coefficient of static friction μ_s is typically greater than μ_k. The direction of friction always opposes the relative motion or attempted motion. In AP problems, always determine whether the object is moving before deciding which friction formula to use.

摩擦力源于表面相互作用。静摩擦力 f_s 可阻止相对运动，最大值为 f_s,max = μ_s N；滑动摩擦力 f_k 在表面滑动时作用：f_k = μ_k N。静摩擦系数 μ_s 通常大于 μ_k。摩擦力的方向总是与相对运动或相对运动趋势相反。在AP问题中，始终先判断物体是否运动，再决定使用哪种摩擦公式。

f_s,max = μ_s N ; f_k = μ_k N

11. Inclined Planes and Pulleys | 斜面与滑轮

For a block on a frictionless incline, the component of weight along the incline is m g sinθ, and the normal force is m g cosθ. For systems with pulleys, assume ideal massless, frictionless pulleys and inextensible strings; tension is uniform throughout the string. Apply ΣF = m a to each mass separately and link their accelerations through the string constraint. Practice with Atwood machines and blocks connected over a pulley on an incline.

对于位于光滑斜面上的物块，重力沿斜面的分量为 m g sinθ，法向力为 m g cosθ。对于滑轮系统，假设理想无质量、无摩擦的滑轮和不可伸长的绳子；绳中张力处处相等。分别对每个质量应用 ΣF = m a，并通过绳子的约束条件将它们的加速度联系起来。练习阿特伍德机和通过滑轮连接在斜面上的物块等经典问题。

12. Uniform Circular Motion and Centripetal Force | 匀速圆周运动与向心力

An object moving in a circle at constant speed experiences a centripetal acceleration directed toward the center: a_c = v² / r. By Newton’s second law, there must be a net force toward the center: F_c = m a_c = m v² / r. The centripetal force is not a new type of force; it is the net radial component of real forces like tension, gravity, or friction. Guarantee that you identify the force(s) providing the centripetal requirement in circular motion problems.

以恒定速率做圆周运动的物体具有指向圆心的向心加速度：a_c = v² / r。根据牛顿第二定律，必须存在指向圆心的合力：F_c = m a_c = m v² / r。向心力不是一种新型力；它是真实力（如张力、重力或摩擦力）的径向分量的合力。在圆周运动问题中确保你识别出提供向心力的力。

a_c = v² / r , F_c = m v² / r

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Newton’s Laws of Motion and Forces | 牛顿运动定律与力