Linear Momentum · 线性动量
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| linear momentum/ˈlɪnɪə məʊˈmentəm/ | 动量 | dòng liàng |
| vector/ˈvektə/ | 矢量 | shǐ liàng |
| system of particles/ˈsɪstəm ɒv ˈpɑːtɪklz/ | 粒子系统 | lì zi xì tǒng |
A slow truck and a fast bullet
- A truck creeping at walking pace is almost impossible to stop.
- A tiny bullet, moving fast, is also almost impossible to stop.
- Very different objects, yet both carry a lot of the same thing.
- That "quantity of motion" is momentum.
慢速卡车与高速子弹
- 以步行速度缓缓前行的卡车几乎无法阻止。
- 高速运动的小小子弹,也几乎无法阻止。
- 非常不同的物体,却都携带着大量的同一种东西。
- 那种"运动的量"就是动量。
Linear momentum
- Linear momentum 动量 is mass times velocity:
- It measures how hard it is to stop a moving object.
- Both a big mass and a high speed make it large.
线动量
- 动量是质量乘以速度:
- 它衡量阻止一个运动物体有多难。
- 大质量和高速度都会使它变大。
A $4\ \text{kg}$ cart moves at $5\ \tfrac{\text{m}}{\text{s}}$. What is its momentum (in kg·m/s)? · 一辆 $4\ \text{kg}$ 的小车以 $5\ \tfrac{\text{m}}{\text{s}}$ 运动。其动量是多少（单位：kg·m/s）？
$p = mv = 4 \times 5 = 20\ \tfrac{\text{kg}\cdot\text{m}}{\text{s}}$.
Select all · 所有 ways to increase an object's momentum. · 选择所有能增加物体动量的方法。
$p = mv$ grows with mass or speed; stopping it drops the momentum to zero. · $p = mv$ 随质量或速度增大；使其停止会将动量降至零。
A vector
- Momentum is a vector 矢量 -- it points the same way as the velocity.
- Direction matters: two objects moving opposite ways have opposite-sign momenta.
- Momenta add as vectors, not just as numbers.
一个矢量
- 动量是一个矢量——它与速度方向相同。
- 方向很重要:两个反向运动的物体动量符号相反。
- 动量按矢量相加,而不只是按数值相加。
Two objects moving toward each other can have a total momentum of zero. · 两个相向运动的物体可以具有零的总动量。
Momentum is a vector -- opposite directions carry opposite signs, which can cancel to zero. · 动量是一个矢量——相反方向带有相反的符号，可以相互抵消为零。
Momentum is a ____ quantity, pointing the same way as the velocity. · 动量是一个____量，指向与速度相同的方向。
$\vec{p} = m\vec{v}$ is a vector -- it has both size and direction. · $\vec{p} = m\vec{v}$ 是一个矢量——它既有大小也有方向。
Total momentum of a system
- For a system of particles 粒子系统, the total momentum is the vector sum of each one's $m\vec{v}$.
- It also equals the total mass times the velocity of the center of mass.
- This total is what conservation laws will hold fixed.
系统的总动量
- 对于一个粒子系统,总动量是每个粒子 $m\vec{v}$ 的矢量和。
- 它也等于总质量乘以质心的速度。
- 守恒定律将保持这个总量不变。
Linear momentum · 线性动量
Momentum is mass times velocity - at a fixed mass, it grows in step with speed. · 动量是质量乘以速度——在质量固定时，它随速度成比例增长。
A $1\ \text{kg}$ ball at $+4\ \tfrac{\text{m}}{\text{s}}$ and a $2\ \text{kg}$ ball at $-1\ \tfrac{\text{m}}{\text{s}}$. Total momentum (in kg·m/s)? · 一个 $1\ \text{kg}$ 的球以 $+4\ \tfrac{\text{m}}{\text{s}}$ 运动，另一个 $2\ \text{kg}$ 的球以 $-1\ \tfrac{\text{m}}{\text{s}}$ 运动。总动量是多少（单位：kg·m/s）？
$p_{tot} = 1(4) + 2(-1) = 4 - 2 = 2\ \tfrac{\text{kg}\cdot\text{m}}{\text{s}}$ -- add the vectors with their signs. · $p_{tot} = 1(4) + 2(-1) = 4 - 2 = 2\ \tfrac{\text{kg}\cdot\text{m}}{\text{s}}$ ——将它们作为带符号的矢量相加。
Mass and speed together
- A slow truck and a fast bullet can have the same momentum.
- Big mass, small speed can equal small mass, big speed.
- To change momentum, you must change mass or velocity -- which takes a force over time.
质量与速度共同作用
- 慢速卡车和高速子弹可以有相同的动量。
- 大质量、小速度可以等于小质量、大速度。
- 要改变动量,就必须改变质量或速度——这需要力作用一段时间。
Two identical balls move at equal speeds in opposite directions. Which is zero for the pair? · 两个相同的球以相等的速度向相反方向运动。对于这对球来说，什么是零？
Momentum cancels (vector); kinetic energy does not (scalar, always positive). So total momentum is zero, energy is not. · 动量相互抵消（矢量）；动能不会（标量，始终为正）。因此总动量为零，但能量不为零。
A $2\ \text{kg}$ ball moves right at $3\ \tfrac{\text{m}}{\text{s}}$; a $3\ \text{kg}$ ball moves left at $2\ \tfrac{\text{m}}{\text{s}}$.
- Right ball: $p = +6\ \tfrac{\text{kg}\cdot\text{m}}{\text{s}}$; left ball: $p = -6\ \tfrac{\text{kg}\cdot\text{m}}{\text{s}}$.
- Total momentum: $6 - 6 = 0$ -- they cancel because momentum is a vector.
一个 $2\ \text{kg}$ 的球向右以 $3\ \tfrac{\text{m}}{\text{s}}$ 运动;一个 $3\ \text{kg}$ 的球向左以 $2\ \tfrac{\text{m}}{\text{s}}$ 运动。
- 右球:$p = +6\ \tfrac{\text{kg}\cdot\text{m}}{\text{s}}$;左球:$p = -6\ \tfrac{\text{kg}\cdot\text{m}}{\text{s}}$。
- 总动量:$6 - 6 = 0$——因为动量是矢量,它们抵消了。
Momentum is not the same as kinetic energy. Momentum ($mv$) is a vector and can cancel; kinetic energy ($\tfrac{1}{2}mv^2$) is a scalar and never cancels. Two objects can have zero total momentum yet plenty of kinetic energy.
动量和动能不是一回事。动量($mv$)是矢量,可以抵消;动能($\tfrac{1}{2}mv^2$)是标量,永不抵消。两个物体可以总动量为零,却拥有大量动能。
Linear momentum $\vec{p} = m\vec{v}$ measures the "quantity of motion" -- a vector pointing along the velocity. The total momentum of a system is the vector sum of the parts. Big mass or high speed makes it large, and opposite directions can cancel.
线动量 $\vec{p} = m\vec{v}$ 衡量"运动的量"——一个沿速度方向的矢量。一个系统的总动量是各部分的矢量和。大质量或高速度都会使它变大,而相反的方向可以抵消。