I am wondering if, for a particle moving close to the speed of light (so that we must examine things relativistically rather than classically) does the centripetal force equation $F_c=m\frac{v^2}{r}$ still hold? If not, what is the correct equation for centripetal force?
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Since relativistic momentum p = $\gamma m_0 v$, then:
$\vec{F} = \frac{d\vec{p}}{dt} = \gamma m_0 \frac{d\vec{v}}{dt}$, which, when solved using vectors is equal to: $\gamma m_0 \frac{v^2}{r}$
PhotonBoom
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$\gamma$ is a function of velocity, so your derivative is missing a term. – Javier Mar 31 '14 at 22:58
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Ah you're very right, I'll fix it in a second! – PhotonBoom Mar 31 '14 at 22:58
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Hmmm looking at it again, isn't this perfectly valid assuming constant velocity? Which I assume is what OP was asking for? – PhotonBoom Mar 31 '14 at 23:03
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That's a good point, but then you need to take into account that $F$ is a vector, not a scalar. Otherwise $dv/dt$ would be zero too. – Javier Mar 31 '14 at 23:11
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Fixed! Sorry its a bit late – PhotonBoom Mar 31 '14 at 23:15