Worksheet: Minkowski Diagrams for Galilean Relativity

In this worksheet, we will practice interpreting Minkowski diagrams if Minkowski diagrams were used for Galilean relativity.

Q1:

The above diagram shows what a Minkowski diagram would look like for two reference frames that obey Galilean relativity. Frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡, and frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡. Frame 𝑆 moves at a speed 𝑢 relative to frame 𝑆. Which of the following does the red line show?

  1. An object that is moving at the speed of light in both 𝑆 and 𝑆
  2. An object that is moving at the speed of light in frame 𝑆
  3. An object that is moving at a constant, nonzero speed in both 𝑆 and 𝑆
  4. The world line of an object that is at rest in frame 𝑆
  5. The world line of an object that is moving at speed 𝑢 in frame 𝑆
  6. An object that is moving at the speed of light in frame 𝑆
  7. The world line of an object that is at rest in frame 𝑆
  • Aii
  • Biii and i
  • Cv and iv
  • Dvii and vi
  • Eiii

Q2:

The diagram shows what a Minkowski diagram would look like for two reference frames that obey Galilean relativity. Frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡, and frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡. Frame 𝑆 moves at a speed 𝑢 relative to frame 𝑆. Six events are shown on the diagram: 𝐴, 𝐵, 𝐸, 𝐹, 𝐺, and 𝐻.

Which two events are simultaneous in frame 𝑆?

  • A𝐵 and 𝐸
  • B𝐻 and 𝐺
  • C𝐵 and 𝐺
  • D𝐹 and 𝐴
  • E𝐸 and 𝐴

Which two events are simultaneous in frame 𝑆?

  • A𝐸 and 𝐴
  • B𝐻 and 𝐺
  • C𝐵 and 𝐸
  • D𝐵 and 𝐺
  • E𝐹 and 𝐴

Q3:

The above diagram shows what a Minkowski diagram would look like for two reference frames that obey Galilean relativity. Frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡, and frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡. Frame 𝑆 moves at a speed 𝑢 relative to frame 𝑆. Which of the following does the red line show?

  1. An object that is moving at the speed of light in both 𝑆 and 𝑆
  2. An object that is moving at the speed of light in frame 𝑆
  3. An object that is moving at a constant, nonzero speed in both 𝑆 and 𝑆
  4. The world line of an object that is at rest in frame 𝑆
  5. The world line of an object that is moving at speed 𝑢 in frame 𝑆
  6. An object that is moving at the speed of light in frame 𝑆
  7. The world line of an object that is at rest in frame 𝑆
  • Ai and ii
  • Bv and vi
  • Ciii and iv
  • Di and vii
  • Evii

Q4:

The diagram shows what a Minkowski diagram would look like for two reference frames that obey Galilean relativity. Frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡, and frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡. Frame 𝑆 moves at a speed 𝑢 relative to frame 𝑆. Which of the following does the red line show?

  1. The world line of an object that is moving at speed 𝑢 in frame 𝑆
  2. An object that is moving at the speed of light in both 𝑆 and 𝑆
  3. An object that is moving at the speed of light in frame 𝑆
  4. An object that is moving at a constant, nonzero speed in both 𝑆 and 𝑆
  5. The world line of an object that is at rest in frame 𝑆
  6. The world line of an object that is moving at speed 𝑢 in frame 𝑆
  7. An object that is moving at the speed of light in frame 𝑆
  8. The world line of an object that is at rest in frame 𝑆
  • Avi and iv
  • Biii and vi
  • Cii and vii
  • Diii and viii
  • Ei and v

Q5:

The above diagram shows what a Minkowski diagram would look like for two reference frames that obey Galilean relativity. Frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡, and frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡. Frame 𝑆 moves at a speed 𝑢 relative to frame 𝑆. The red line is the world line of a particle that is moving at the speed of light in frame 𝑆. Which of the following expressions gives the speed of the particle in frame 𝑆?

  • A𝑐+2𝑢
  • B𝑢
  • C𝑐+𝑢
  • D𝑐𝑢
  • E𝑐

Q6:

The diagram shows what a Minkowski diagram would look like for two reference frames that obey Galilean relativity. Frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡 and frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡. Frame 𝑆 moves at a speed 𝑢 relative to frame 𝑆. Six events are shown on the diagram: 𝐴, 𝐵, 𝐸, 𝐹, 𝐺, and 𝐻.

Which two events occur at the same position in 𝑆?

  • A𝐸 and 𝐹
  • B𝐵 and 𝐹
  • C𝐴 and 𝐵
  • D𝐺 and 𝐻
  • E𝐺 and 𝐹

Which two events occur at the same position in 𝑆?

  • A𝐺 and 𝐹
  • B𝐴 and 𝐵
  • C𝐸 and 𝐹
  • D𝐵 and 𝐹
  • E𝐵 and 𝐸

Q7:

The diagram shows what a Minkowski diagram would look like for two reference frames that obey Galilean relativity. Frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡, and frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡. Frame 𝑆 moves at a speed 𝑢 relative to frame 𝑆. Which of the following does the red line show?

  1. An object that is moving at the speed of light in both 𝑆 and 𝑆
  2. An object that is moving at the speed of light in frame 𝑆
  3. An object that is moving at a constant, nonzero speed in both 𝑆 and 𝑆
  4. The world line of an object that is at rest in frame 𝑆
  5. The world line of an object that is moving at speed 𝑢 in frame 𝑆
  6. A line of constant time in both 𝑆 and 𝑆
  7. An object that is moving at the speed of light in frame 𝑆
  8. The world line of an object that is at rest in frame 𝑆
  • Aii and iii
  • Bv and vii
  • Civ and i
  • Dviii
  • Evi

Q8:

The above diagram shows what a Minkowski diagram would look like for two reference frames that obey Galilean relativity. Frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡, and frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡. Frame 𝑆 moves at the speed of light, 𝑐, relative to 𝑆. The red line is the world line of a particle that is moving at the speed of light in frame 𝑆. What is the speed of the particle in frame 𝑆?

Q9:

The above diagram shows what a Minkowski diagram would look like for two reference frames that obey Galilean relativity. Frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡, and frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡. Frame 𝑆 moves at a speed 𝑢 relative to frame 𝑆. The red line is the world line of a particle moving at the speed of light, 𝑐, in frame 𝑆. Which of the following expressions gives the speed of the particle in frame 𝑆?

  • A𝑐+𝑢
  • B𝑐2𝑢
  • C𝑐𝑢
  • D𝑐
  • E𝑢

Q10:

The above diagram shows what a Minkowski diagram would look like for two reference frames that obey Galilean relativity. Frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡, and frame 𝑆 is shown by the axes 𝑥 and 𝑐𝑡. Frame 𝑆 moves at a speed 𝑢 relative to frame 𝑆, where 𝑢 is faster than the speed of light. The red line is the world line of a particle moving at the speed of light, 𝑐, in frame 𝑆. Which of the following statements is true for an observer at rest in frame 𝑆?

  • AThe particle is moving away from the observer at a speed 𝑐2𝑢.
  • BThe particle is moving away from the observer at a speed 𝑐.
  • CThe particle is not moving relative to the observer.
  • DThe particle is moving away from the observer at a speed 𝑐𝑢.
  • EThe particle is moving away from the observer at a speed 𝑢.

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