Re: Circular motion in SR
- From: Albertito <albertito1992@xxxxxxxxx>
- Date: Thu, 13 Mar 2008 13:41:39 -0700 (PDT)
On 13 mar, 16:12, "ram.rac...@xxxxxxxxx" <ram.rac...@xxxxxxxxx> wrote:
I'm trying to write the equations for circular motion according to SR
laws of motion. I'm doing some kind of mistakes, because I'm not
getting real solutions to the equations.
This is what's going on: You have an body of mass m0 circling around a
stationary center point that is a distance of r from the body. There
is a force F that attracts the body towards the center point, making
it move in a circle around it. What's the velocity v of the object?
I've used these equations:
v=sqrt(a*r)
a=F/(m0*gamma^3)
gamma=1/sqrt(1-(v/c)^2)
I keep getting only imaginary solutions for v. What am I doing wrong?
Thanks, Ram.
Yeah you are doing that wrong, your v = sqrt(a*r) is a
tangential speed, but it results that as the body is in
circular rotation, the relative speed between the body
and the center is not that v. That relative speed must be
w=0, because the orbital radius is constant (the body and the
center remain stationary). Thus, the gamma must be actually
gamma = 1/sqrt(1-(w/c)^2) = 1.
The solution can be found considering Thomas precession:
http://en.wikipedia.org/wiki/Thomas_precession
.
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