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I wonder how would we go about to calculate centripetal/centrifugal acceleration for relativistic objects moving at near the speed of light , do we use the original acceleration = force/mass, or input gamma factor for it to be , Acceleration = (gamma) force / mass , Acceleration = Force / (gamma) mass Which one is valid ? If both aren't is there a particular way and/or equation to calculate centripetal and centrifugal acceleration for relativistic objects ? How ?

Qmechanic
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A Curious Mind
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1 Answers1

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Swinging a rest-mass M tied to a rope around:

Force measured at that end of the rope to which the mass is tied: $F_2 = \gamma^2*M*a$

Force measured at that end of the rope that is the opposite end to which the mass is tied: $F_1 = \gamma*M*a$

$a$ is the velocity change of mass M per unit of time measured by a clock at the center of the circle formed by the path of the mass M.

stuffu
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  • I do want more clarification regarding whether we can use a = f/(gamma) mass, specifically on whether it is valid or not – A Curious Mind Aug 26 '23 at 15:34
  • @A Curious Mind Transverse acceleration is proportional to force, and inversely proportional to $\gamma*m_0$ , where $m_0$ means rest-mass. Hey, this would make a better answer : ) – stuffu Aug 27 '23 at 06:58
  • Okay then , I heard online that I had to calculate the derivative of the four dimensional momentum , is that true ? Or do we add a gamma and modify the centripetal acceleration equation in a unique way? What do you think? – A Curious Mind Aug 28 '23 at 20:34
  • @A Curious Mind Four-momentum not needed, as force transverse to motion is a simple case. As I said, use gamma times rest-mass ("relativistic mass") as the m in the a=F/m. And use F as F, unless you have a F felt by a road when a runner makes a turn, and you want to know g force felt by the runner. – stuffu Aug 29 '23 at 13:09