📚 Momentum and Newton's Laws | 动量与牛顿定律
Newton's laws of motion provide the foundation for understanding how forces change an object's motion, while linear momentum gives us a powerful conserved quantity for analysing collisions and explosions. In CIE A Level Physics, you need to be able to state the three laws, apply them to systems of interacting bodies, and use momentum conservation in one and two dimensions.
牛顿运动定律为理解力如何改变物体的运动提供了基础，而线性动量则为我们提供了一个强大的守恒量，用于分析碰撞和爆炸。在 CIE A Level 物理中，你需要能够陈述三条定律，将它们应用到相互作用的物体系统，并在一维和二维问题中使用动量守恒。
1. Newton's First Law | 牛顿第一定律
An object remains at rest or continues to move with constant velocity unless acted upon by a resultant external force. This means that if the vector sum of all forces acting on a body is zero, its velocity does not change.
除非受到合外力的作用，否则物体会保持静止或继续以恒定速度运动。这意味着如果作用在一个物体上的所有力的矢量和为零，它的速度就不会改变。
In exam terms, constant velocity includes both zero velocity and constant speed in a straight line. A common mistake is to think that a moving object needs a forward force to keep moving; in the absence of friction or drag, no net force is needed.
在考试中，恒定速度包括零速度和直线匀速运动两种情况。一个常见错误是认为运动物体需要向前的力才能继续运动；如果没有摩擦或阻力，就不需要净力。
This law also defines an inertial frame of reference. Any frame in which the first law holds is called an inertial frame; a frame that accelerates relative to an inertial frame is non-inertial and Newton's laws need extra care there.
这条定律还定义了惯性参考系。任何第一定律成立的参考系称为惯性参考系；相对于惯性参考系加速的参考系是非惯性参考系，在那里使用牛顿定律需要额外小心。
For CIE A Level, you should be able to explain everyday examples such as a passenger lurching forward when a bus brakes, or a book remaining on a table because weight and normal contact force balance.
在 CIE A Level 中，你应该能够解释日常例子，例如公交车刹车时乘客向前倾，或者书停在桌面上是因为重力和法向接触力平衡。
2. Newton's Second Law | 牛顿第二定律
The resultant force on a body is proportional to its rate of change of momentum. In symbol form:
作用在物体上的合外力与其动量变化率成正比。用符号表示为：
F = Δp / Δt
more general form F = Δp / Δt is especially useful when mass changes, as in rocket motion.
对于质量恒定的情况，这可以简化为 F = m a，其中 a 是产生的加速度。更一般的形式 F = Δp / Δt 在质量变化时尤其有用，例如火箭运动。
Because momentum is a vector, the direction of the resultant force is the same as the direction of the change in momentum. A force perpendicular to velocity changes direction but not speed, which is why circular motion at constant speed still requires a resultant force.
因为动量是矢量，合外力的方向与动量变化的方向相同。垂直于速度的力改变方向但不改变速率，这就是为什么匀速圆周运动仍然需要合外力。
kg m s⁻¹, so F = -3.0 / 0.02 = -150 N. The negative sign shows the force is opposite to the initial velocity.
示例：一个 0.15 kg 的球以 12 m s⁻¹ 撞墙，并在 0.02 s 内以 8 m s⁻¹ 反弹。取初始方向为正，Δp = 0.15 × (-8 - 12) = -3.0 kg m s⁻¹，所以 F = -3.0 / 0.02 = -150 N。负号表示力与初始速度方向相反。
Always define the positive direction clearly. In momentum questions, a sign error can change the final answer completely, even if the physics method is correct.
一定要明确定义正方向。在动量问题中，即使物理方法正确，符号错误也可能完全改变最终答案。
3. Newton's Third Law | 牛顿第三定律
If body A exerts a force on body B, then body B exerts an equal and opposite force on body A. The two forces are of the same type, act along the same line, and act on different bodies.
如果物体 A 对物体 B 施加一个力，那么物体 B 对物体 A 施加一个大小相等、方向相反的力。这两个力属于同一种类型，沿同一直线作用，并且作用在不同的物体上。
A common mistake is to pair weight and normal contact force as a third-law pair. They are equal only in special cases and usually act on the same body. A true third-law pair acts on two different bodies.
一个常见错误是把重力和法向接触力当作第三定律的一对力。它们只在特殊情况下大小相等，而且通常作用在同一个物体上。真正的第三定律力对作用在两个不同物体上。
Third-law pairs are essential in momentum conservation: the internal forces between two interacting bodies are equal and opposite, so they produce equal and opposite changes in momentum. The total momentum of the system therefore remains constant.
第三定律力对在动量守恒中至关重要：两个相互作用物体之间的内力大小相等、方向相反，因此它们产生大小相等、方向相反的动量变化。系统的总动量因此保持不变。
Examples include the Earth pulling the Moon and the Moon pulling the Earth, or a swimmer pushing water backwards while the water pushes the swimmer forwards.
例子包括地球吸引月球、月球也吸引地球，或者游泳者向后推水、水向前推游泳者。
4. Linear Momentum and Impulse | 线性动量与冲量
Linear momentum p is defined as the product of mass and velocity:
线性动量 p 定义为质量与速度的乘积：
p = m v
Momentum is a vector quantity, measured in kg m s⁻¹ or N s. Its direction is the same as the velocity. Always choose a positive direction before doing calculations.
动量是矢量，单位为 kg m s⁻¹ 或
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