Rotational Kinetic Energy · 转动动能
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| rotational kinetic energy/rəʊˈteɪʃənl kɪˈnetɪk ˈenədʒi/ | 转动动能 | zhuǎn dòng dòng néng |
A spinning flywheel stores usable energy
- A heavy flywheel, spun up fast, can power a machine for minutes after the motor stops.
- It isn't going anywhere — yet it clearly holds energy in its spin.
- A rotating body has rotational kinetic energy 转动动能, just as a moving one has translational.
- Swap mass for rotational inertia and speed for angular speed, and the formula follows.
旋转的飞轮储存着可用的能量
- 一个沉重的飞轮,被快速转起来后,能在马达停止后还驱动机器数分钟。
- 它哪也没去——却显然把能量握在它的旋转里。
- 旋转的物体拥有转动动能,正如运动的物体拥有平动动能。
- 把质量换成转动惯量、速度换成角速度,公式就出来了。
The rotational kinetic energy formula
- A spinning body stores $E_k = \tfrac12 I \omega^2$.
- It is the exact twin of $\tfrac12 m v^2$, with $I$ for mass and $\omega$ for speed.
- Like all energy it is a scalar, measured in joules.
- Faster spin or larger rotational inertia both store more energy.
转动动能公式
- 旋转的物体储存 $E_k = \tfrac12 I \omega^2$。
- 它是 $\tfrac12 m v^2$ 的精确孪生,以 $I$ 代替质量、$\omega$ 代替速度。
- 像所有能量一样,它是标量,单位是焦耳。
- 更快的旋转或更大的转动惯量都储存更多能量。
Spin stores energy · 旋转储存能量
Change how fast the angle sweeps to feel how spin rate feeds the rotational kinetic energy. · 改变角度扫过的速度，感受旋转速率如何提供转动动能。
A wheel with $I = 4\ \text{kg}\cdot\text{m}^2$ spins at $\omega = 3\ \tfrac{\text{rad}}{\text{s}}$. What is its rotational kinetic energy, in joules? · 具有$I = 4\ \text{kg}\cdot\text{m}^2$的轮子以$\omega = 3\ \tfrac{\text{rad}}{\text{s}}$旋转。其转动动能是多少焦耳？
$E_k = \tfrac12 I\omega^2 = \tfrac12 (4)(9) = 18\ \text{J}$.
Which is the formula for rotational kinetic energy? · 哪个是转动动能的公式？
It is · 它是 $\tfrac12 I\omega^2$ — the rotational twin of $\tfrac12 mv^2$. · 它是 $\tfrac12 I\omega^2$ ——$\tfrac12 mv^2$ 的旋转对应物。
Rotational kinetic energy is measured in . · 转动动能的测量单位是。
It is an energy, so it is measured in joules. · 因为它是一种能量，所以用焦耳计量。
It depends on ω squared
- Because of the $\omega^2$, doubling the spin rate stores four times the energy.
- This is why flywheels are spun as fast as their strength allows.
- Rotational inertia matters too, in direct proportion — double $I$, double the energy.
- Mass placed far from the axis (large $I$) makes a very effective energy store.
它取决于 ω 的平方
- 因为有 $\omega^2$,旋转速率加倍就储存四倍的能量。
- 这就是为什么飞轮被转到其强度所允许的最快。
- 转动惯量也有影响,且成正比——$I$ 加倍,能量加倍。
- 把质量放在远离轴处(大 $I$)就成为非常有效的储能器。
If a flywheel doubles its angular speed, its rotational kinetic energy becomes: · 如果一个飞轮的角速度加倍，其转动动能变为：
$E_k \propto \omega^2$, so doubling $\omega$ gives four times the energy. · $E_k \propto \omega^2$，因此将$\omega$加倍会使能量变为四倍。
Select all · 所有 ways to increase a flywheel's stored rotational kinetic energy. · 选择所有增加飞轮储存的转动动能的方法。
Higher $\omega$ or larger $I$ (mass at the rim) raises $\tfrac12 I\omega^2$. Colour has no effect. · 更高的$\omega$或更大的$I$（边缘处的质量）会增加$\tfrac12 I\omega^2$。颜色没有影响。
Flywheels as batteries
- Some buses and race cars store braking energy in a spinning flywheel, then reuse it.
- The energy goes in as $\tfrac12 I\omega^2$ and comes back out to drive the wheels.
- No chemicals, no wear — just a very fast, well-balanced disk.
- It is a neat mechanical "battery" built on this one formula.
飞轮当电池
- 一些公交车和赛车把刹车能量储存在旋转的飞轮里,然后再利用。
- 能量以 $\tfrac12 I\omega^2$ 进去,又出来驱动车轮。
- 没有化学物质、没有磨损——只是一个非常快、平衡良好的圆盘。
- 这是建立在这一个公式上的一块巧妙的机械"电池"。
A spinning flywheel can be used to store energy and release it later. · 旋转的飞轮可用于储存能量并在稍后释放。
The energy $\tfrac12 I\omega^2$ is stored in the spin and can drive a machine afterward. · $\tfrac12 I\omega^2$能量储存在旋转中，之后可以驱动机器。
Use rotational inertia $I$ and angular speed $\omega$ in $\tfrac12 I\omega^2$, never plain mass and linear speed. A rolling object has both kinds of kinetic energy at once (lesson 6.5) — don't forget the spinning part.
在 $\tfrac12 I\omega^2$ 中用转动惯量 $I$ 和角速率 $\omega$,绝不要用普通质量和线速率。滚动的物体同时拥有两种动能(第 6.5 节)——别忘了旋转的那部分。
A wheel of rotational inertia $I = 4\ \text{kg}\cdot\text{m}^2$ spins at $\omega = 3\ \tfrac{\text{rad}}{\text{s}}$.
- $E_k = \tfrac12 I\omega^2 = \tfrac12 (4)(3^2) = \tfrac12 (4)(9) = 18\ \text{J}$.
Double the spin to $6\ \tfrac{\text{rad}}{\text{s}}$ and $E_k = \tfrac12(4)(36) = 72\ \text{J}$ — four times as much.
一个转动惯量 $I = 4\ \text{kg}\cdot\text{m}^2$ 的轮子以 $\omega = 3\ \tfrac{\text{rad}}{\text{s}}$ 旋转。
- $E_k = \tfrac12 I\omega^2 = \tfrac12 (4)(3^2) = \tfrac12 (4)(9) = 18\ \text{J}$。
把旋转加倍到 $6\ \tfrac{\text{rad}}{\text{s}}$,$E_k = \tfrac12(4)(36) = 72\ \text{J}$——是原来的四倍。
Rotational kinetic energy is $E_k = \tfrac12 I\omega^2$, the spin twin of $\tfrac12 mv^2$. It grows with the square of angular speed, so doubling $\omega$ stores four times the energy. Flywheels use it as a mechanical energy store.
转动动能是 $E_k = \tfrac12 I\omega^2$,$\tfrac12 mv^2$ 的旋转孪生。它随角速率的平方增长,所以 $\omega$ 加倍储存四倍能量。飞轮用它作为机械储能器。