Reference Frames and Relative Motion · 参考系与相对运动
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| reference frame/ˈrefrəns freɪm/ | 参考系 | cān kǎo xì |
| relative velocity/ˈrelətɪv vəˈlɒsɪti/ | 相对速度 | xiāng duì sù dù |
How fast are you really walking?
- Stroll down the aisle of a moving train at a gentle $2\ \text{km/h}$.
- To the passenger beside you, that is your speed.
- To someone standing outside, you are doing $102\ \text{km/h}$.
- Both are right -- speed depends on who is watching.
你到底走多快?
- 在行驶的火车过道里以轻松的 $2\ \text{km/h}$ 漫步。
- 对你旁边的乘客来说,那就是你的速度。
- 对站在车外的人来说,你在以 $102\ \text{km/h}$ 前进。
- 两者都对——速度取决于谁在观察。
Reference frames
- A reference frame 参考系 is the point of view -- the observer -- you measure motion against.
- Velocity is always measured relative to some frame.
- Change the frame and the numbers change, even for the same motion.
参考系
- 参考系是你用来测量运动的视角——即观察者。
- 速度总是相对于某个参考系测量的。
- 换一个参考系,即使是同一个运动,数值也会改变。
The observer or point of view against which you measure motion is called a ____ frame. · 你用来测量运动的观察者或视角称为____参考系。
A reference frame is the viewpoint; all velocities are stated relative to one. · 参考系是 viewpoint；所有速度都是相对于某个参考系表述的。
Relative velocity
- Relative velocity 相对速度 is found by adding velocities as vectors.
- Your velocity relative to the ground = your velocity in the train + the train's velocity.
- Same direction adds; opposite subtracts; at an angle, use components.
相对速度
- 相对速度通过把速度作为矢量相加来求得。
- 你相对地面的速度 = 你在火车里的速度 + 火车的速度。
- 同向相加;反向相减;成角度时用分量。
You walk forward at $1.5\ \tfrac{\text{m}}{\text{s}}$ in a train moving at $25\ \tfrac{\text{m}}{\text{s}}$. Your speed relative to the ground (in m/s)? · 你在速度为 $1.5\ \tfrac{\text{m}}{\text{s}}$ 的火车上向前行走， $25\ \tfrac{\text{m}}{\text{s}}$。你相对于地面的速度（单位：m/s）是多少？
Same direction, so add them, $1.5 + 25 = 26.5\ \tfrac{\text{m}}{\text{s}}$. · 同向，因此相加，$1.5 + 25 = 26.5\ \tfrac{\text{m}}{\text{s}}$。
Now you walk backward at $1.5\ \tfrac{\text{m}}{\text{s}}$ in the same $25\ \tfrac{\text{m}}{\text{s}}$ train. Your speed relative to the ground (in m/s)? · 现在你正 向后 走， $1.5\ \tfrac{\text{m}}{\text{s}}$ 在同一个 $25\ \tfrac{\text{m}}{\text{s}}$ 火车里。你相对于地面的速度（以米/秒为单位）是多少？
Opposite directions subtract, $25 - 1.5 = 23.5\ \tfrac{\text{m}}{\text{s}}$. · 反向相减，$25 - 1.5 = 23.5\ \tfrac{\text{m}}{\text{s}}$。
The addition rule
- The velocity of A relative to C is $\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}$.
- Chain the frames: A-relative-to-B, then B-relative-to-C.
- Reverse a subscript pair and you flip the sign: $\vec{v}_{BA} = -\vec{v}_{AB}$.
相加法则
- A 相对 C 的速度是 $\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}$。
- 把参考系串起来:A 相对 B,再 B 相对 C。
- 交换一对下标就翻转符号:$\vec{v}_{BA} = -\vec{v}_{AB}$。
Relative velocity · 相对速度
Add a boat's velocity across a river to the current's velocity to get its velocity relative to the bank. · 将船横渡河流的速度与水流速度相加，即可得到其相对于河岸的速度。
To combine velocities across frames, you... · 要跨参考系组合速度，你需要...
$\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}$ -- a vector sum (which becomes plain adding or subtracting along one line). · $\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}$——矢量和（在一维线上变为简单的加或减）。
Pick a smart frame
- Some problems are far easier in the right frame.
- A collision looks simplest in the frame of the center of mass.
- River-crossing problems are easiest split into "relative to water" and "water relative to ground."
选一个聪明的参考系
- 有些问题在合适的参考系里容易得多。
- 碰撞在质心参考系里看起来最简单。
- 过河问题最容易拆成"相对于水"和"水相对于地面"。
There is one single "true" velocity for an object, the same for every observer. · 物体只有一个“真实”的速度，对所有观察者都相同。
Velocity is always relative to a frame -- different observers measure different velocities for the same object. · 速度总是相对于参考系的——不同的观察者在测量同一物体的速度时会得到不同的值。
Select all · 所有 true statements about relative motion. · 选出关于相对运动的所有正确陈述。
Velocity is frame-dependent and frames add as vectors; no velocity is absolute. · 速度依赖于参考系且参考系按矢量相加；没有绝对速度。
You walk forward at $2\ \tfrac{\text{m}}{\text{s}}$ inside a train moving at $30\ \tfrac{\text{m}}{\text{s}}$.
- Relative to the ground you move at $2 + 30 = 32\ \tfrac{\text{m}}{\text{s}}$.
- Walk backward instead and it is $30 - 2 = 28\ \tfrac{\text{m}}{\text{s}}$.
你在以 $30\ \tfrac{\text{m}}{\text{s}}$ 行驶的火车里向前走 $2\ \tfrac{\text{m}}{\text{s}}$。
- 相对地面你以 $2 + 30 = 32\ \tfrac{\text{m}}{\text{s}}$ 运动。
- 如果改为向后走,则是 $30 - 2 = 28\ \tfrac{\text{m}}{\text{s}}$。
There is no single "true" velocity -- only velocity relative to a chosen frame. A ball dropped in a moving bus falls straight down to you but follows a curve to someone outside. Always state (or assume) the frame before quoting a velocity.
不存在唯一的"真实"速度——只有相对于所选参考系的速度。在行驶的公交车里落下的球,对你是直直落下,对车外的人却沿一条曲线。引用速度前,永远先说明(或假定)参考系。
A reference frame is the observer you measure against; velocity is always relative to one. Combine frames with vector addition: $\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}$ (relative velocity). No velocity is absolute -- choosing a smart frame can make a hard problem easy.
参考系是你用来测量的观察者;速度总是相对于某个参考系。用矢量相加来组合参考系:$\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}$(相对速度)。没有速度是绝对的——选一个聪明的参考系能把难题变简单。