Linear Momentum · 线性动量
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| momentum/məʊˈmentəm/ | 动量 | dòng liàng |
A slow truck and a fast pebble — equally unstoppable
- A truck rolling at walking pace is very hard to stop. So is a small pebble fired from a slingshot.
- One has huge mass, the other huge speed — but both carry a lot of momentum 动量.
- Momentum measures the "quantity of motion" packed into a moving object.
- It is the idea that makes collisions and recoil predictable.
慢速卡车和高速石子——同样难以阻挡
- 以步行速度滚动的卡车很难停下。用弹弓射出的一颗小石子也是如此。
- 一个有巨大的质量,另一个有巨大的速度——但两者都携带很多动量。
- 动量量度一个运动物体所含的"运动的量"。
- 正是这个概念让碰撞和反冲变得可预测。
Momentum is mass times velocity
- Momentum is $\vec p = m\vec v$ — mass multiplied by velocity.
- It is a vector: it points the same way the object moves.
- Its units are $\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$ (there is no special name).
- Double the mass or double the speed, and you double the momentum.
动量是质量乘以速度
- 动量是 $\vec p = m\vec v$——质量乘以速度。
- 它是一个矢量:它指向物体运动的方向。
- 它的单位是 $\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$(没有专门的名称)。
- 质量加倍或速度加倍,动量就加倍。
Compare two momenta · 比较两个动量
Change each mass and speed and read off the momentum p = mv of each object. · 改变每个物体的质量和速度，读取动量 p = mv。
What is the momentum of a $1500\ \text{kg}$ car moving at $20\ \tfrac{\text{m}}{\text{s}}$, in $\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$? · 一辆质量为 $1500\ \text{kg}$ 的汽车以 $20\ \tfrac{\text{m}}{\text{s}}$ 的速度运动，其动量是多少，单位为 $\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$？
$p = mv = 1500 \times 20 = 30\,000\ \text{kg}\cdot\tfrac{\text{m}}{\text{s}}$.
Momentum equals mass times . · 动量等于质量乘以。
$\vec p = m\vec v$ — mass times velocity. · $\vec p = m\vec v$ — 质量乘以速度。
If you double an object's speed without changing its mass, its momentum: · 如果你在不改变质量的情况下将物体的速度加倍，其动量会：
Momentum is linear in speed ($p = mv$), so doubling $v$ doubles $p$ — unlike kinetic energy, which quadruples. · 动量与速度呈线性关系（$p = mv$），因此将$v$加倍会使$p$加倍 — 不像动能那样变为四倍。
Why momentum is useful
- The larger an object's momentum, the harder it is to stop or turn.
- A big truck and a fast bullet can need the same effort to halt.
- Momentum, unlike kinetic energy, depends on speed to the first power, not the square.
- That makes it the natural bookkeeping quantity for impacts.
动量为何有用
- 物体的动量越大,越难停下或转向。
- 一辆大卡车和一颗快子弹可能需要同样的努力才能停下。
- 与动能不同,动量取决于速度的一次方,而不是平方。
- 这使它成为处理碰撞时天然的记账量。
Select all · 所有 true statements about momentum. · 选择关于动量的所有正确陈述。
Momentum · 动量 $= mv$ is a vector, linear (not squared) in speed, so mass and speed can trade off. · 动量$= mv$是矢量，与速度呈线性（非平方）关系，因此质量和速度可以相互补偿。
Direction counts
- Because momentum is a vector, its sign matters in one dimension.
- Two objects with the same speed but opposite directions have opposite momenta.
- When you add momenta, add them as vectors — they can partly cancel.
- A system's total momentum is the vector sum of every object's $m\vec v$.
方向很重要
- 因为动量是矢量,在一维中它的符号很重要。
- 两个速率相同但方向相反的物体,动量相反。
- 相加动量时,要按矢量相加——它们可以部分抵消。
- 一个系统的总动量是每个物体 $m\vec v$ 的矢量和。
Momentum is a vector, so its direction matters. · 动量是矢量，因此其方向很重要。
$\vec p = m\vec v$ points along the velocity; opposite directions give opposite signs. · $\vec p = m\vec v$沿速度方向；相反方向给出相反的符号。
Two identical $2\ \text{kg}$ balls move at $3\ \tfrac{\text{m}}{\text{s}}$ in · 入 opposite directions. What is the total momentum, in $\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$? · 两个相同的$2\ \text{kg}$球以$3\ \tfrac{\text{m}}{\text{s}}$向相反方向运动。总动量是多少，单位为$\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$？
$+6$ and $-6$ cancel: total momentum $= 0$. The vectors sum to zero. · $+6$和$-6$抵消：总动量$= 0$。矢量和为零。
Momentum is a vector, so direction cannot be ignored. Two identical balls moving at the same speed in opposite directions have a total momentum of zero, even though each one clearly has momentum. Always keep track of signs.
动量是一个矢量,所以不能忽略方向。两个相同的球以相同速率朝相反方向运动,它们的总动量为零,尽管每一个显然都有动量。永远要记住符号。
Find the momentum of a $1500\ \text{kg}$ car moving at $20\ \tfrac{\text{m}}{\text{s}}$.
- $p = mv = 1500 \times 20 = 30\,000\ \text{kg}\cdot\tfrac{\text{m}}{\text{s}}$, in the direction of motion.
A $0.02\ \text{kg}$ bullet would need a speed of $1.5$ million $\tfrac{\text{m}}{\text{s}}$ to match it — which is why the car is "unstoppable" by comparison.
求一辆 $1500\ \text{kg}$ 的车以 $20\ \tfrac{\text{m}}{\text{s}}$ 运动的动量。
- $p = mv = 1500 \times 20 = 30\,000\ \text{kg}\cdot\tfrac{\text{m}}{\text{s}}$,沿运动方向。
一颗 $0.02\ \text{kg}$ 的子弹需要 $150$ 万 $\tfrac{\text{m}}{\text{s}}$ 的速度才能与之相当——这就是为什么相比之下车"不可阻挡"。
Momentum is the quantity of motion, $\vec p = m\vec v$ (a vector, in $\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$). A large mass or a large speed gives large momentum, so a slow truck and a fast pebble can match. Because it is a vector, direction and sign matter.
动量是运动的量,$\vec p = m\vec v$(矢量,单位 $\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$)。大质量或大速度都给出大动量,所以慢卡车和快石子可以相当。因为它是矢量,方向和符号都很重要。