- #1

Somsak

- 7

- 0

From special relativity, we know that

t=t

For the object moves as a circle with radius r, the velocity v = w r

Therefore, time varying along radius r as

t=t

In this case

ds

Since object will move in shortest path in space-time, Dif[ds

and Dif[r,dr] = 1, the above equation will be

0 =2 dr - 2 w

That means the object will move dr due to time varying along radius r as

dr = w

Or the object will move with accelleration as

dr/dt

This accelleration is look like acting by centrifugal force.

t=t

_{0}/(1-v^{2}/c^{2})^{1/2}For the object moves as a circle with radius r, the velocity v = w r

Therefore, time varying along radius r as

t=t

_{0}/(1-w^{2}r^{2}/c^{2})^{1/2}In this case

ds

^{2}= dr^{2}- c^{2}dt^{2}= dr^{2}- c^{2}dt_{0}^{2 }/(1-w^{2}r^{2}/c^{2})Since object will move in shortest path in space-time, Dif[ds

^{2},dr] = 0,and Dif[r,dr] = 1, the above equation will be

0 =2 dr - 2 w

^{2}r dt_{0}^{2 }/(1-w^{2}r^{2}/c^{2})^{2}That means the object will move dr due to time varying along radius r as

dr = w

^{2}r dt_{0}^{2 }/(1-w^{2}r^{2}/c^{2})^{2}= w^{2}r dt^{2 }/(1-w^{2}r^{2}/c^{2})Or the object will move with accelleration as

dr/dt

^{2 }= w^{2}r /(1-w^{2}r^{2}/c^{2})This accelleration is look like acting by centrifugal force.

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