HKDSE Physics Core
Chapter 5: Momentum | 動量
Billy Sir’s Smart Notes: Master Momentum, Impulse, Collisions, and Explosions.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握動量、衝量、碰撞及爆炸。
1. Momentum | 動量
Momentum is a vector quantity defined as the product of an object’s mass and its velocity. It describes the “quantity of motion” an object has. 動量是矢量，定義為物體質量與速度的乘積，用來描述物體的「運動量」。
⚙️ Formula for Momentum | 動量公式
- Unit: \( \text{kg m s}^{-1} \) or \( \text{N s} \) (單位：千克米每秒 或 牛頓秒)
- Vector Nature: The direction of momentum is the same as the direction of velocity. (矢量特性：動量的方向與速度方向相同)
2. Impulse and Newton’s Second Law | 衝量與牛頓第二定律
Impulse is the effect of a force acting over a period of time, which results in a change in momentum. 衝量是力在一段時間內作用的效果，會導致動量的改變。
⚡ Impulse Formula | 衝量公式
The area under a Force-time (F-t) graph represents the impulse. (力-時間圖下的面積代表衝量。)
⚖️ Newton’s Second Law (Momentum Form) | 牛頓第二定律 (動量形式)
The net force acting on an object is equal to the rate of change of its momentum. (作用於物體的淨力等於其動量的變化率。)
3. Conservation of Momentum | 動量守恆定律
In a closed system where no external net force acts, the total momentum remains constant before and after an event (like a collision). 在沒有外在淨力作用的封閉系統中，事件（如碰撞）前後的總動量保持不變。
🔄 Conservation Formula | 守恆公式
Note: Always define a positive direction (e.g., right is positive) before substituting values, as velocity is a vector! (注意：代入數值前必須定義正方向，因為速度是矢量！)
4. Types of Collisions & Explosions | 碰撞類型與爆炸
| Event Type (事件類型) | Momentum (動量) | Kinetic Energy (動能) | Characteristics (特徵) |
|---|---|---|---|
| Elastic Collision 彈性碰撞 |
Conserved (守恆) | Conserved (守恆) | Objects bounce off each other perfectly with no loss of kinetic energy. (物體完美反彈，沒有動能流失。) |
| Inelastic Collision 非彈性碰撞 |
Conserved (守恆) | Not Conserved (不守恆) | Objects bounce off, but some kinetic energy is lost (converted to heat/sound). (物體反彈，但部分動能流失轉化為熱能或聲能。) |
| Perfectly Inelastic Collision 完全非彈性碰撞 |
Conserved (守恆) | Maximum Loss (最大流失) | Objects stick together and move with a common velocity (\( v \)). \( m_1 u_1 + m_2 u_2 = (m_1 + m_2)v \) (物體黏在一起並以共同速度運動。) |
| Explosion 爆炸 |
Conserved (守恆) | Increases (增加) | Initial momentum is usually zero. Objects fly apart in opposite directions. Chemical/potential energy converts to KE. \( 0 = m_1 v_1 + m_2 v_2 \) (初始動量通常為零，物體向反方向飛出。) |
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