Linear Momentum ( ) of a body is defined as the product of the body’s mass and velocity.

線性動量是一個向量，既有量值又有方向。動量向量的方向是物體的速度方向。測量動量的國際單位制是千克米秒一。

動量是一個非常有用的計算量，因為它在封閉系統中是守恆的。

動量變化率

為了改變物體的動量，必須對它施加一個力。所需的凈力等於動量的變化率。在符號中，我們可以寫為：

This is a statement of Newton’s second law of motion. In fact, this is closer to the form that Newton himself used to express the law in. As we have seen in our discussion of Newton’s second law when the mass of the body stays c***tant, we can use this equation to recover the more familiar expression of Newton’s second law,  .

For c***idering cases where the mass of a body changes (for rockets, for example), we come up with another expression.  . Using the chain rule, we get:

沖量|沖量動量定理

讓我們考慮兩個物體之間的碰撞。e、 發球時網球拍與球的碰撞。對於觀眾來說，碰撞似乎是瞬間的，但事實並非如此。如果你用高速攝影機，錄下一個網球發球，然後放慢速度，你會註意到球拍和球接觸了一段時間，在此期間球拍和球都會變形。在此期間，球拍對球施加的力不是恆定的。

What is Linear Momentum – A Tennis Serve

Let us assume that the racket and the ball first came to contact at a time  and that the contact lasted until a time  . Taking the equation  , we can rearrange and integrate over the time period to obtain the total force:

If we take the change in momentum to be , we can write

The quantity  is the area under a force vs. time graph. It is also called impulse ():

正如我們在上面看到的，

上述表示式有時被稱為沖量動量定理。

沖量單位為kg m s-1或N s。

If we draw a graph of how the force acting between two bodies in a collision varies over time, we would get the blue curve on the following graph. As we mentioned before, the area under this graph is equal to the impulse. Note that we can come up with an average force, (), such that   .

What is Linear Momentum – Force vs Time Graph

線性動量示例

軟管中的水對牆壁施加的力

Suppose a water pipe with cross-sectional area carrying water at a speed  is aimed horizontally at a wall. We can find the force  exerted on the wall by the water from the pipe:

What is Linear Momentum – Force on a wall by water from a horizontal hosepipe

change in velocity of water. Once the water hits the wall, it travels down the wall, losing all horizontal velocity. Therefore,  .

mass of water per second (the flow rate) , where  is the density of water and  is the volume. Now,  volume of water exiting the pipe per second. Since cross-sectional area is  ,  , where  is the distance travelled by water per second.

Now, we have  . Since  , we have:

負號表示牆對水施加的力在左邊（圖中）。水對牆壁施加的力必須具有相同的大小，但作用方向相反（根據牛頓第三定律）。所以，水對牆的作用力是：

例1

質量為0.058公斤的網球向上拋向空中，用球拍水平擊球。在與球拍接觸0.01s後，球以54m s-1的水平速度離開。計算施加在球上的平均力。

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Image Courtesy:

“serve of girl at tennis” by Jeuwre (Own work) [CC BY-SA 4.0], via Wikimedia Comm***