HKDSE Physics Core 2
Chapter 2: Newton’s Laws | 牛頓運動定律
Billy Sir’s Smart Notes: Master the Three Laws of Motion, Force Analysis, and Connected Bodies.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握牛頓三大定律及相連物體系統。
1. Newton’s First Law of Motion | 牛頓第一定律
An object will remain at rest or travel in uniform velocity unless it is acted by a net force. 除非受到淨力作用，否則物體將保持靜止或作勻速直線運動。
🛡️ Inertia & Mass | 慣性與質量
- Inertia (慣性): The tendency to remain at rest or to move in uniform velocity.
- Mass (質量): Mass is a measure of inertia. An object with a larger mass has a greater inertia, meaning it has a greater tendency to remain in its initial state of motion.
- To keep a body moving with uniform motion, no net force is needed. A net force is only needed to change the velocity (cause acceleration).
2. Newton’s Second Law of Motion | 牛頓第二定律
Whenever a body experiences a net force, there must be an acceleration. Newton’s Second Law states the relationship between the net force and acceleration. 當物體受到淨力作用時，必會產生加速度。
🚀 The Core Equation | 核心公式
1 Newton (N) is defined as the force required to give a 1 kg body an acceleration of 1 m s\(^{-2}\).
| Scenario (情境) | Net Force Equation (淨力方程) |
|---|---|
| Free fall motion 自由落體 (Neglecting air resistance) |
\( W = mg \implies mg = ma \implies a = g \) |
| Smooth inclined plane 光滑斜面 |
\( W \sin\theta = ma \implies a = g \sin\theta \) |
| Rough inclined plane (sliding down) 粗糙斜面 (向下滑) |
\( W \sin\theta – f = ma \implies a = g \sin\theta – \frac{f}{m} \) |
3. Newton’s Third Law of Motion | 牛頓第三定律
To every action force, there exists an equal in magnitude and opposite in direction reaction force. 每一個作用力，都有一個大小相等、方向相反的反作用力。
⚖️ Properties of Action-Reaction Pairs | 作用力與反作用力的特性
- The two forces are equal in magnitude.
- The two forces are in opposite direction.
- The two forces are acting on two different bodies (They cannot cancel each other out!).
- The two forces are of the same nature (e.g., both are gravitational, or both are contact forces).
- Action and reaction must occur at the same time.
4. Connected Bodies | 相連物體
When two or more bodies are connected together (e.g., by a string), they share the same motion characteristics. 當兩個或以上物體相連時，它們共享相同的運動特徵。
🔗 Key Principles | 關鍵原則
Connected bodies must have the same magnitude of:
- Displacement (位移)
- Velocity (速度)
- Acceleration (加速度)
⚙️ Finding the Common Acceleration | 尋找共同加速度
Treat the entire system as a single combined mass to find the common acceleration first:
🧵 Finding Internal Forces (e.g., Tension) | 尋找內部力 (如張力)
After finding the common acceleration \(a\), isolate one of the blocks and apply Newton’s Second Law to that specific block.
For block P being pulled by tension \(T\):
For block Q being pulled by force \(F\) and held back by tension \(T\):
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