Re: Circular motion in SR


"rbwinn" <rbwinn3@xxxxxxxx> wrote in message
news:1cb68793-bbce-4909-8347-5508945487f7@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Mar 16, 1:34 pm, Eric Gisse <jowr...@xxxxxxxxx> wrote:
On Mar 16, 5:12 am, rbwinn <rbwi...@xxxxxxxx> wrote:





On Mar 15, 9:55 pm, Eric Gisse <jowr...@xxxxxxxxx> wrote:

On Mar 15, 7:29 pm, rbwinn <rbwi...@xxxxxxxx> wrote:

On Mar 14, 9:38 pm, Eric Gisse <jowr...@xxxxxxxxx> wrote:

On Mar 14, 7:03 pm, rbwinn <rbwi...@xxxxxxxx> wrote:

On Mar 14, 5:29?pm, mL <mL.bey...@xxxxxxxxxxxxx> wrote:

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?

OK, you have a central force field, ?F_ = f(r)n_ , where the
unit
vector n_ points towards a fix point.

Use the equation dE/dt = F_.v_, to show that the energy E and
the speed
v = |v_| are constants when the particle moves in a circle r =
R.

?> 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?

The force-equation is wrong. For cases with constant rest mass
m, you
have in general,

? ?F_ ?= (gamma)ma_ + (gamma)^3 m(v_.a_)v_ /c^2 ,

which for circular motion, r = R, reduces to

? ?f(R) = (gamma)m a, ?where ?a = v^2/R,

- note that v_.a_ = 0, i.e. a_ // n_, according to comments
above.

/mel

My question about all of this is, since a clock in rotation
supposedly
runs slower than a clock around which the moving clock is
rotating,
then since the Lorentz equations give the velocity as being the
same
in both frames of reference, does the altitude of the rotating
clock
differ from one frame of reference to the other?
This is not a complicated question. Scientists have claimed that
they put a clock in a satellite and recovered it, and the clock
from
the satellite showed less time than an identical clock on earth,
so
this proved that Einstein's theory was true.
Any way you look at it, the velocity of the moving clock is the
same from either frame of reference according to Einstein's
theory.
So with the distance contraction, the circumfrence of the orbit
is
less from the frame of reference of the satellite than from the
frame
of reference of the earth. How does a shorter orbit relate to
the
altitude of the satellite?
I have posted this question many times, and, so far, science
seems to be silent about this, just as they are silent about
many
things with regard to Dr. Einstein's famous theory.
Robert B. Winn

Science has no problem with the concepts. Your whining is
misguided -
USENET seems to be silent with these things because USENET is
tired of
explaining things to you just to have the explanation ignored.
USENET
has figured out that decades of stupidity cannot be fixed.- Hide
quoted text -

- Show quoted text -

Eric,
Here is what I think.

We don't care.

Here is an idea you might be interested in, Eric. There was a
scientist years ago named Galileo who derived these transformation
equations.

x'=x-vt
y'=y
z'=z
t'=t

If you are describing transmission of light, all you have to do is
just say

x=wt
x'=wn'
n'=t(1-v/w)
where w is velocity of light, and n' is time according to a clock in
S'. This way you do not have a distance contraction, the value of pi
is always 3.14..., and time never goes backwards. Of course, a
scientist might not be enthusiastic about a world that boring.
Robert B. Winn

Show me how Maxwell's equations behave under that coordinate
transformation. Are they invariant?- Hide quoted text -

- Show quoted text -
----------------------------------------
Eric,
Well, to be honest, I don't know. I have never even studied
Maxwell's equations. However, I would note one thing. James Clerk
Maxwell died in 1879, and Albert Einstein did not come up with his
theory until 1905. So what transformation equations were being used
by Maxwell?
You tell me, were Maxwell's equations invariant under the
Galillean transformation equations?
Robert B. Winn
----------------------------------------

As I recall there problem with Maxwell's equations prior to relativity was
that there was a preferred frame in which they were valid, i.e. the aether
frame. Maxwell's equations were not invariant under a Galilean
transformation. For that reason scientists used to think that there was a
preferred inertial frame, the aether frame.

Pete


.

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