We're not talking about "relativistic speeds" but c.
In this case what you wrote here:
The centripetal force required to maintain circular motion of a body moving at relativistic speeds is
F = γm_{0}v^{2}/r
where v is the instantaneous tangential velocity
is meaningless since you cannot define γ
Accelerating leptons to 0.99c in a circular path is an engineering problem, but the physics is no big deal. It's the recurring decimal point that distinguishes between difficult and impossible. Your equation is awaited with bated breath.
If physics "is no big deal" why didn't you write the equation I asked you?
Ok, I'll write it:
F = γ
^{3}m
_{0} * a
m
_{0} = proper mass
F = tangential force
a = tangential acceleration
Now compare the two equations:
1) F = γm
_{0} v
^{2}/r (centripetal = radial force).
2) F = γ
^{3}m
_{0} * a (tangential force)
and then tell me which is here the mass that goes to infinity according to the sentence you wrote:
Since a massive object will have infinite mass at c
I mean, the mass you are referring to is γm
_{0} or is γ
^{3}m
_{0}?
Is it still meaningful to talk about relativistic mass, in this context? Wouldn't be better to talk about m
_{0} = m only and say that it doesn't change with velocity?
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