Special Relativity Flashcards: Reference Frames, Time, and Length

Amakhadi akuleli qoqo

1. Ikhadi 1

   Umbuzo

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

   Impendulo

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

2. Ikhadi 2

   Umbuzo

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

   Impendulo

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

3. Ikhadi 3

   Umbuzo

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

   Impendulo

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

4. Ikhadi 4

   Umbuzo

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

   Impendulo

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

5. Ikhadi 5

   Umbuzo

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

   Impendulo

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

6. Ikhadi 6

   Umbuzo

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

   Impendulo

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

7. Ikhadi 7

   Umbuzo

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

   Impendulo

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

8. Ikhadi 8

   Umbuzo

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

   Impendulo

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

9. Ikhadi 9

   Umbuzo

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

   Impendulo

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

10. Ikhadi 10

    Umbuzo

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

    Impendulo

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

11. Ikhadi 11

    Umbuzo

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

    Impendulo

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

12. Ikhadi 12

    Umbuzo

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

    Impendulo

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

13. Ikhadi 13

    Umbuzo

    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?

    Impendulo

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

14. Ikhadi 14

    Umbuzo

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

    Impendulo

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

15. Ikhadi 15

    Umbuzo

    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?

    Impendulo

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

16. Ikhadi 16

    Umbuzo

    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?

    Impendulo

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

17. Ikhadi 17

    Umbuzo

    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?

    Impendulo

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

18. Ikhadi 18

    Umbuzo

    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?

    Impendulo

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

19. Ikhadi 19

    Umbuzo

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

    Impendulo

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

20. Ikhadi 20

    Umbuzo

    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?

    Impendulo

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

21. Ikhadi 21

    Umbuzo

    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?

    Impendulo

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

22. Ikhadi 22

    Umbuzo

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

    Impendulo

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

23. Ikhadi 23

    Umbuzo

    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?

    Impendulo

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

24. Ikhadi 24

    Umbuzo

    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?

    Impendulo

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

25. Ikhadi 25

    Umbuzo

    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?

    Impendulo

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

26. Ikhadi 26

    Umbuzo

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

    Impendulo

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

27. Ikhadi 27

    Umbuzo

    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?

    Impendulo

    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. Ikhadi 28

    Umbuzo

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

    Impendulo

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

29. Ikhadi 29

    Umbuzo

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

    Impendulo

    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. Ikhadi 30

    Umbuzo

    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?

    Impendulo

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

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Special Relativity Flashcards: Reference Frames, Time, and Length

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