Time Dilation: Showing Relation b/w Intervals

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SUMMARY

The discussion focuses on the relationship between time intervals for a stationary clock and a moving clock in a rotating disk, specifically using the formula for time dilation in special relativity. The time intervals are expressed as (△ t'-△ t)/(△ t) ~ r²w²/2c², where w is the angular speed, r is the distance from the center, and c is the speed of light. A participant highlights the importance of substituting the linear speed v with rω in the time dilation formula. The discussion emphasizes the straightforward application of established principles of special relativity to derive the relationship.

PREREQUISITES
  • Understanding of special relativity principles, particularly time dilation.
  • Familiarity with angular velocity and its relation to linear speed.
  • Knowledge of the formula for time dilation involving linear speed v.
  • Basic grasp of mathematical manipulation of physical equations.
NEXT STEPS
  • Study the derivation of the time dilation formula in special relativity.
  • Explore the relationship between angular velocity and linear speed in rotating systems.
  • Investigate practical applications of time dilation in rotating frames of reference.
  • Learn about the implications of time dilation in high-speed scenarios, such as in particle physics.
USEFUL FOR

Physics students, educators, and professionals interested in the applications of special relativity, particularly in contexts involving rotating systems and time dilation effects.

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For a disk that rotates with angular speed w, there is a clock at the center(at rest), adn one at distance r, with speed rw,. I need to show that frome time dilation in special relativity, time inervals (△ t) for the clock at rest, and (△ t') for the moving clock are related by
(△ t'-△ t)/(delta t) ~ r²w²/2c²

I got a minus sign in front, by using the time dilation.
 
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I don't see what the difficulty is? You know the formula for time dilation using linear speed v, don't you?
You say that the speed is rω. Plug that into the formula.
 

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