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

线性动量是一个矢量，既有量值又有方向。动量向量的方向是物体的速度方向。测量动量的国际单位制是千克米秒一。

动量是一个非常有用的计算量，因为它在封闭系统中是守恒的。

动量变化率

为了改变物体的动量，必须对它施加一个力。所需的净力等于动量的变化率。在符号中，我们可以写为：

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:

冲量|冲量动量定理

让我们考虑两个物体之间的碰撞。e、 发球时网球拍与球的碰撞。对于观众来说，碰撞似乎是瞬间的，但事实并非如此。如果你用高速摄影机，录下一个网球发球，然后放慢速度，你会注意到球拍和球接触了一段时间，在此期间球拍和球都会变形。在此期间，球拍对球施加的力不是恒定的。

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 ():

正如我们在上面看到的，

上述表达式有时被称为冲量动量定理。

冲量单位为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

线性动量示例

软管中的水对墙壁施加的力

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:

负号表示墙对水施加的力在左边（图中）。水对墙壁施加的力必须具有相同的大小，但作用方向相反（根据牛顿第三定律）。所以，水对墙的作用力是：

例1

质量为0.058公斤的网球向上抛向空中，用球拍水平击球。在与球拍接触0.01s后，球以54m s-1的水平速度离开。计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***