Special Relativity Flashcards: Reference Frames, Time, and Length

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1. Carta 1

   Domanda

   What two kinds of coordinates identify an event in an inertial frame?

   Risposta

   A position and a time. A camera shutter closing is one event, and the frame gives the coordinates of that closure.

2. Carta 2

   Domanda

   An instrument is bolted to a pod that coasts past a lab. Which is the instrument’s rest frame?

   Risposta

   The pod frame. The instrument stays at a fixed position in that frame.

3. Carta 3

   Domanda

   A pod recedes from a lamp in vacuum. What speed does the pod measure for light from the lamp?

   Risposta

   $c$, the same speed the lab measures for the light.

4. Carta 4

   Domanda

   A beacon flashes and its light reaches a distant camera. Which event does the camera’s detection timestamp give directly?

   Risposta

   The light’s arrival at the camera. The flash is a separate event at the beacon.

5. Carta 5

   Domanda

   Two events occur beside the same clock at rest in a frame. What interval does that clock record between them?

   Risposta

   The proper time, $\Delta\tau$, between the two events.

6. Carta 6

   Domanda

   In one inertial frame, how can two separated events be timed locally and compared?

   Risposta

   Place a clock at each event location. Keep both clocks at rest and synchronized in the chosen frame, then subtract the event readings.

7. Carta 7

   Domanda

   In which frame is the proper length of a rigid calibration bar measured?

   Risposta

   The bar’s rest frame, where both ends stay at fixed positions.

8. Carta 8

   Domanda

   A probe coasts in a straight line at constant speed relative to an inertial lab. Is the frame attached to the coasting probe inertial?

   Risposta

   Yes. Constant velocity relative to an inertial frame gives another inertial frame.

9. Carta 9

   Domanda

   A detector at rest midway between two stationary lamps receives their vacuum flashes together. When were the flashes emitted in the lamps’ frame?

   Risposta

   At the same time. The paths to the detector have equal length and light travels at the same speed along both.

10. Carta 10

    Domanda

    How do you calculate the Lorentz factor $\gamma$ from the relative speed $v$?

    Risposta

    $\gamma=1/\sqrt{1-(v/c)^2}$, where $c$ is the speed of light in vacuum.

11. Carta 11

    Domanda

    A rod moves along the lab’s track. Which two lab events give the rod’s length in that frame?

    Risposta

    Record the front and rear endpoint positions at the same lab time. Their separation at that time is the lab length.

12. Carta 12

    Domanda

    Two events happen at different lab stations but both happen beside the same clock on a coasting probe. Which clock gives the proper time?

    Risposta

    The probe clock. The events occur at its one fixed probe location.

13. Carta 13

    Domanda

    A detector at rest in a lab receives a flash at lab time $6\,\mu\mathrm{s}$. The light traveled for $2\,\mu\mathrm{s}$ in the lab frame. When was the flash emitted in that frame?

    Risposta

    At $4\,\mu\mathrm{s}$. Subtract travel time from arrival time in the same frame.

14. Carta 14

    Domanda

    What is the Lorentz factor at relative speed $0.60c$?

    Risposta

    $1.25$. The square root in the denominator is $\sqrt{1-0.60^2}=0.80$.

15. Carta 15

    Domanda

    A lab timed two flashes when they were emitted. Which events should a passing pod use to compare the time interval in its own frame?

    Risposta

    The same two emissions. The arrival of either flash at a detector is a separate event.

16. Carta 16

    Domanda

    A moving rod’s front position is recorded first and its rear position one lab second later. Does the difference between the recorded positions give the lab length?

    Risposta

    No. Use endpoint positions at one lab time. The rear has moved during that second.

17. Carta 17

    Domanda

    A clock coasts past an inertial lab and records proper time $\Delta\tau$ between two ticks. What interval $\Delta t$ does the lab assign to those same ticks?

    Risposta

    $\Delta t=\gamma\Delta\tau$. The lab uses synchronized clocks to time the ticks at different positions.

18. Carta 18

    Domanda

    Two flashes at different positions along a test range are simultaneous in the range frame. A pod coasts along the line joining them. Are the emissions simultaneous in the pod frame?

    Risposta

    No, for a nonzero relative speed along that line. The two frames assign different time differences to the same emissions.

19. Carta 19

    Domanda

    If the relative velocity reverses direction without changing speed, what happens to the Lorentz factor?

    Risposta

    It stays the same. The factor depends on $(v/c)^2$.

20. Carta 20

    Domanda

    A bar coasts past an inertial lab with its length perpendicular to its velocity. How does the length measured in the lab compare with the bar’s rest length?

    Risposta

    They are equal. The lab records both ends at the same lab time, and their separation is entirely transverse to the motion.

21. Carta 21

    Domanda

    A pod coasting at $0.80c$ relative to the lab records $9\,\mathrm{s}$ between two ticks of its own clock. How much lab time separates those ticks?

    Risposta

    $15\,\mathrm{s}$. The lab interval is $(5/3)\times9\,\mathrm{s}$.

22. Carta 22

    Domanda

    How do you find the measured length $L$ of an object moving along its length at constant speed, given its proper length $L_0$?

    Risposta

    $L=L_0/\gamma$. Measure both ends at one time in the frame where the object moves.

23. Carta 23

    Domanda

    Two lamps and a detector are at rest in the same frame. Their flashes travel directly through vacuum to the detector and arrive together. If one lamp is farther away, which lamp emitted first in that frame?

    Risposta

    The farther lamp. Both flashes traveled at the same speed, so the longer path took more time.

24. Carta 24

    Domanda

    A boom’s endpoints are measured at the same lab time while it moves lengthwise. Does the boom frame assign the same time to those two measurements?

    Risposta

    No. Simultaneity is frame-dependent for these two events because they occur at different points along the direction of relative motion.

25. Carta 25

    Domanda

    Two ticks of a clock coasting at $0.60c$ relative to the lab are $15\,\mathrm{s}$ apart in lab time. How much time elapsed on the moving clock?

    Risposta

    $12\,\mathrm{s}$. Its proper time is $15\,\mathrm{s}/1.25$.

26. Carta 26

    Domanda

    A $75\,\mathrm{m}$ bar in its rest frame moves lengthwise at $0.80c$ in the lab. What length does the lab measure?

    Risposta

    $45\,\mathrm{m}$. Divide $75\,\mathrm{m}$ by $5/3$.

27. Carta 27

    Domanda

    Two inertial crews coast past one another and each uses clocks synchronized in its own frame. How can each assign a slower rate to the other crew’s clock?

    Risposta

    They compare different pairs of ticks. Each times two ticks of the other crew’s clock with separated clocks synchronized in its own frame.

28. Carta 28

    Domanda

    The nose of a coasting probe passes two checkpoints at rest in an inertial lab. Which frame gives the proper time between those crossings?

    Risposta

    The probe frame. Both crossings happen at its nose, where one clock on the probe can time them.

29. Carta 29

    Domanda

    Two light pulses reach the same detector at the same instant. Do all inertial frames agree that the pulses arrive together?

    Risposta

    Yes. They arrive at one place and time, so their arrivals coincide in a single event. Each frame still assigns its own coordinates to that event.

30. Carta 30

    Domanda

    A bar moves lengthwise at $0.60c$ relative to the lab, which measures its length as $52\,\mathrm{m}$. What is the bar’s proper length?

    Risposta

    $65\,\mathrm{m}$. Multiply the lab length by $1.25$.

30 carte

Special Relativity Flashcards: Reference Frames, Time, and Length

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