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Theme A — Space, Time and Motion

A.5.2 Galilean Relativity — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 54 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
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Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

A.5.2 Galilean Relativity — IB PHYSICS HL notes: Apply Galilean transformations to positions and velocities between inertial frames.Newton's laws of motion are the same in all inertial frames — this is Galilean relativity.An object at constant velocity in one frame has a constant…

  • Primed quantities are measured in the moving frame
  • Timers start at t
  • Only x changes
  • Remember one equation, x
  • Same direction
  • Opposite direction

Part 1 of 6Galilean relativity

Galilean relativity
Newton's laws of motion are the same in all inertial frames
  • Newton's laws of motion are the same in all inertial frames this is Galilean relativity.
An object at constant velocity in one frame has a constant, but different, velocity in another.
Time and space were treated as absolute in Newtonian physics.

Part 2 of 6Setting up the frames

Setting up the frames
S is the stationary frame with coordinates (x, y, t).
S' is the moving frame, with coordinates (x', y', t').
v is always the velocity of the moving frame S'.
Primed quantities are measured in the moving frame
  • Primed quantities are measured in the moving frame unprimed in the stationary frame.
Timers start at t
0 when the observers are alongside each other.

Part 3 of 6Galilean transformation equations

QuantityTransformation
Position along motionx' = x − vt, equivalently x = x' + vt
Transverse positionsy = y', z = z'
Timet = t'
Only x changes
  • Only x changes relative motion is along x only.
Remember one equation, x
Remember one equation, x x' + vt — the other follows by rearranging.
No transformation is needed for a measurement taken in the frame where the event occurs.

Part 4 of 6Velocity addition

u
u u' + v and u' = u − v.
  • u is the object's velocity in S, u' its velocity in S' and v the velocity of S'.
Same direction
  • Same direction add: a ball thrown forward at 2 m s-1 from a skateboard at 4 m s-1 is seen at 6 m s-1.
Opposite direction
  • Opposite direction u = v − u'.
Take care over direction
  • Take care over direction the positive direction is that of the velocity v of the moving frame.

Part 5 of 6Using the equations

Using the equations
Sketch the situation and label S, S' and the velocities.
Decide in which frame the quantity is wanted.
Apply x = x' + vt or u = u' + v.
1
A child walking at 2 m s-1 on a train at 15 m s-1: after 10 s she is 20 m from the start in the train frame but 170 m in the platform frame.
2The method fails near the speed of light
  • The method fails near the speed of light see Lorentz transformations.

Part 6 of 6More from the specification

1Cosmic ray muons entering Earth
  • Cosmic ray muons entering Earth unstable atmospheric muons formed in upper atmospheric layers travel downwards toward Earth's ground surface at relativistic velocities.
2Length
  • Resistance is directly proportional to the length of a wire.
3Distance
  • Total length of path travelled, a scalar.
4Gradient
  • Slope of a graph line.
5Reference frame
  • Coordinate system used by an observer.
6Length contraction
  • Shortening of lengths measured along the direction of relative motion.
7Proper length
  • Length measured in the rest frame of the object.
8Space-time interval
  • Invariant quantity (cΔt)2 − (Δx)2.
9Relativistic speed
  • Relativistic speed a speed close to the speed of light, where Galilean velocity addition no longer gives correct results.
10Inertial frames only
  • IB problems use frames moving at constant velocity in straight lines, never accelerating or circling frames.

Key terms

TermMeaning
Galilean relativityNewton's laws take the same form in all inertial frames.
Galilean transformationEquations converting position and time between frames.
Moving frame S'Frame moving at velocity v relative to S.
Velocity additionu = u' + v.
Absolute timeTime identical in all frames.
Inertial frameNon-accelerating frame.

Avoid these mistakes

1
Applying Galilean velocity addition at speeds close to c.
2
Using the wrong sign for v when the object moves in the opposite direction.
3
Forgetting that time is the same in both frames in Galilean relativity.
4
Transforming a measurement already taken in the correct frame.
5
Mixing up which frame is primed.

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