"Greg Neill" escreveu na mensagem
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"El Enrrabadore-mor" wrote in message


[aka "Phantom"?]

Now, energy is the time derivative of the
angular momentum, and that time is an
absolute time.

Huh? The time derivative of angular momentum is torque.
Remember T = dL/dt? Just because the units of Torque
can be equated to Joules does not mean that it is
appropriate to interpret them in such a way. Rotational
kinetic energy is still given by (1/2)*I*w^2, the analog
of the linear (1/2)*m*v^2. I'm surprised that you would
attempt to perpetrate such a flimsy subterfuge.

You've missed the fact that during a given amount
of time a torque T = dL/dt have moved the body a
given angle theta (which is a basic coordinate).

You forget the fact that derivatives are of the form:
d/dt f(x(t)) = x df/dt
x - is an angular displacement

Energy = Torque . angular displacement (dot product)
Power = Torque . angular velocity (dot product)
Power = Time derivative of energy

This is hard stuff.
Uniform circular motion and uniformly accelerated
motions have somehow the same basic equations:
displacement = 1/2 g t^2
velocity = g t
acceleration = g
Gravity is an uniformly accelerated motion.


Also remember that kinetic energy is frame dependent,
even for Newtonian physics, so time dilation poses no
conceptual problems for energy in this regard.

Sure, that's why I keep the point about the
center of rotation being a fixed point in space.

You'll no doubt be even more disturbed to learn that
General Relativity essentially discards nonlocal
conservation of energy.

If so, the mystery is solved.