Special Relativity Flashcards: Reference Frames, Time, and Length

اس ڈیک کے کارڈز

1. کارڈ 1

   سوال

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

   جواب

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

2. کارڈ 2

   سوال

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

   جواب

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

3. کارڈ 3

   سوال

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

   جواب

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

4. کارڈ 4

   سوال

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

   جواب

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

5. کارڈ 5

   سوال

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

   جواب

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

6. کارڈ 6

   سوال

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

   جواب

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

7. کارڈ 7

   سوال

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

   جواب

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

8. کارڈ 8

   سوال

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

   جواب

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

9. کارڈ 9

   سوال

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

   جواب

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

10. کارڈ 10

    سوال

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

    جواب

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

11. کارڈ 11

    سوال

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

    جواب

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

12. کارڈ 12

    سوال

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

    جواب

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

13. کارڈ 13

    سوال

    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?

    جواب

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

14. کارڈ 14

    سوال

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

    جواب

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

15. کارڈ 15

    سوال

    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?

    جواب

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

16. کارڈ 16

    سوال

    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?

    جواب

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

17. کارڈ 17

    سوال

    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?

    جواب

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

18. کارڈ 18

    سوال

    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?

    جواب

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

19. کارڈ 19

    سوال

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

    جواب

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

20. کارڈ 20

    سوال

    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?

    جواب

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

21. کارڈ 21

    سوال

    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?

    جواب

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

22. کارڈ 22

    سوال

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

    جواب

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

23. کارڈ 23

    سوال

    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?

    جواب

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

24. کارڈ 24

    سوال

    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?

    جواب

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

25. کارڈ 25

    سوال

    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?

    جواب

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

26. کارڈ 26

    سوال

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

    جواب

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

27. کارڈ 27

    سوال

    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?

    جواب

    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. کارڈ 28

    سوال

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

    جواب

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

29. کارڈ 29

    سوال

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

    جواب

    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. کارڈ 30

    سوال

    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?

    جواب

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

30 کارڈز

Special Relativity Flashcards: Reference Frames, Time, and Length

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