Does mechanical energy in the system have mass in any common sense, as e=mc^2 supposed to mean?
Suppose there is a Ringworld-sized wheel with an engine where the sun normally is. The whole thing, with a mass of Jupiter, spins at 700 km/s, which equates to 1/4 mass of the Moon of kinetic energy.
Now, will there be any difference in acceleration provided by the engine in the COG of the structure between the standing still case and spinning case?
Yes, slightly. The mass of the moon is only about 1/400,000th the mass of Jupiter, so the difference won't be much, but there will be one.
And, will there be a difference in gravity-defined trajectory of a distant object flying by the structure,between the same cases?
Yes. Not only will there be a slight change in trajectory due to the added mass from the kinetic energy of the spinning wheel, but there will also be an effect called
frame dragging: An object flying by will not be pulled straight towards the center of mass of the wheel by the wheel's gravity: there will also be a small amount of acceleration in the direction of the wheel's rotation.
In other words, does energy equates to inertial and/or gravitational mass?
Both: In general relativity, gravity *is* inertia, and so gravitational mass is inertial mass.
---------- Post added at 03:34 AM ---------- Previous post was at 02:58 AM ----------
I am no expert in these things, but I think E=mc² refers to the "rest energie" of an object, that is an object not moving relatively to the current reference frame.
Actually the term E=mc² is simplified and only valid for 'non-moving objects'.
Yes and no. Alot of it has to do with definitions of the terms involved, and there can be alot of arguments between physicists over the best language to use to describe what the math behind a theory is doing, whether or not they agree upon what the math is doing.
In any case, the kinetic energies of the parts of a system contribute to the rest mass of the system (the mass of the system in a frame where its center of mass is not moving). The rotational kinetic energy of an object will contribute to its mass. (Not so much in Artlav's scenario, with a velocity of "only" 700 km/s, but when the rotational velocity gets up to .9c, the effects will be significant.)
---------- Post added at 03:47 AM ---------- Previous post was at 03:34 AM ----------
Ive always wondered about this myself. I can think of lots of places in the universe where mass is actively being converted into energy via E=MC^2 but are there places universe in the where energy is actively being condensed into mass?
Yes and no, depending entirely upon your definitions. Generally, it's best to say that energy and mass are (quite literally, in fact) the same thing from two different angles. There is no conversion, just a change of viewpoint.
But you can consider particle accelerators to "convert" energy into mass. They'll take two particles (for example, a proton and an anti-proton), get them up to very high speed, and smash them together, resulting in a particle considerably more massive than the combined mass of the originals. (The balance comes from their kinetic energy).
