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Modern Physics: Number of Cycles from Two Clocks

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In the twin paradox, twin A remains on Earth while twin B travels a distance L, measured in the Earth's inertial frame, at a velocity v to a very distant solar system. In turning around for the return trip, the rocket malfunctions somewhat and achieves only a velocity ½ v. Find formulas for the number of cycles counted by A and B from the two clocks, NA, NB, N'A, and N'B.

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With very thorough explanations and calculations, the problem is solved. The number of cycles from two clocks in modern physics are determined.

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#3)
In the twin paradox, twin A remains on Earth while twin B travels a distance L, measured in the Earth's inertial frame, at a velocity v to a very distant solar system. In turning around for the return trip, the rocket malfunctions somewhat and achieves only a velocity ½ v. Find formulas for the number of cycles counted by A and B from the two clocks, NA, NB, N'A, and N'B.

Solution: Here we can take the number of cycles counted equal to the time measured in respective clocks. NA is the time measured by A's clock during onward journey, NB is the time measured by B's clock during onward journey, N'A is the time measured by A's clock during return journey and N'B is the time measured by B's clock during return journey.

When twin A observes the space craft (onward journey):
Let us consider twin A observes the space craft and measures the time taken by the space craft to travel 'L' distance. Given that the velocity of space ...

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