| English | 의미 |
|---|---|
| reference frame/ˈrefrəns freɪm/ | 참고 좌표계 |
| relative velocity/ˈrelətɪv vəˈlɒsɪti/ | 상대 속도 |
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.
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.
The observer or point of view against which you measure motion is called a ____ frame.
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
A reference frame is the viewpoint; all velocities are stated relative to one.
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.
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)?
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
Same direction, so add them, $1.5 + 25 = 26.5\ \tfrac{\text{m}}{\text{s}}$.
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)?
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
Opposite directions subtract, $25 - 1.5 = 23.5\ \tfrac{\text{m}}{\text{s}}$.
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: $\vec{v}_{BA} = -\vec{v}_{AB}$.
Relative velocity
Add a boat's velocity across a river to the current's velocity to get its velocity relative to the bank.
To combine velocities across frames, you...
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
$\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}$ -- a vector sum (which becomes plain adding or subtracting along one line).
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."
There is one single "true" velocity for an object, the same for every observer.
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
Velocity is always relative to a frame -- different observers measure different velocities for the same object.
Select all true statements about relative motion.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
Velocity is frame-dependent and frames add as vectors; no velocity is absolute.
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 $30 - 2 = 28\ \tfrac{\text{m}}{\text{s}}$.
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.
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.