Galilean relativity
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Question
What is a reference frame?
Answer
A coordinate grid and clock you measure motion **against**. All motion is **relative** to a chosen frame.
Question
Define an inertial reference frame.
Answer
A frame moving at **constant velocity** (no acceleration). Newton's first law holds in it.
Question
Give one inertial and one non-inertial example.
Answer
Inertial: a train cruising in a straight line at steady speed. Non-inertial: a car going round a bend.
Question
State the Galilean velocity transformation.
Answer
$u' = u - v$ — the object's velocity in the moving frame equals its ground velocity minus the frame's velocity.
Question
State the Galilean position transformation.
Answer
$x' = x - vt$ — position in the moving frame, where v is the frame's speed.
Question
Same direction vs opposite direction — add or subtract?
Answer
Same direction ⇒ **subtract** the speeds; opposite directions ⇒ the speeds **add**.
Question
A person walks at 1.5 m s⁻¹ toward the front of a train moving at 12 m s⁻¹. Ground speed?
Answer
Same direction ⇒ add: $12 + 1.5 = 13.5$ m s⁻¹.
Question
Velocity of car B (east, 20 m s⁻¹) seen from car A (east, 30 m s⁻¹)?
Answer
$u' = u - v = 20 - 30 = -10$ m s⁻¹, i.e. 10 m s⁻¹ westward.
Question
State Galileo's principle of relativity.
Answer
The **laws of mechanics are the same in every inertial frame** — no experiment can detect uniform motion.
Question
Does an absolute rest frame exist?
Answer
**No.** All inertial frames are equivalent; 'at rest' only ever means 'relative to something'.
Question
Where does Galilean velocity addition break down?
Answer
Near the **speed of light** — light travels at the same speed in every frame, so simple addition fails (→ special relativity).
Question
Two trains approach at 25 and 30 m s⁻¹. Relative speed of approach?
Answer
Opposite directions ⇒ add: $25 + 30 = 55$ m s⁻¹.
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Topic 1.5 hub
Galilean and special relativity (HL)
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