I only took high school physics and a Google search isn't returning anything. Could you tell me why a spinning ball weighs more than a stationary ball?
Another comment seems to claim that since E=mc2, rotational energy can be converted to to mass and viola, the earth is heavier because it has more energy! But that doesn't make sense to me.
Maybe frame dragging has something to do with it? Your pulling of space-time through rotation looks the same as your pulling of space-time from gravity so you appear heavier?
Or is it for the same reason that moving bodies are heavier? Every point of the ball is moving and therefore heavier, the fact that it's rotating makes no differece.
"Mass" is an overloaded word. Nowadays, when physicists refer to a particle's mass, they are referring to what may more specifically be called its "rest-mass" or "invariant-mass". This is a property fundamental to the particle, much as how charge or spin is. This value never changes, and it is associated with a certain amount of energy (E=mc^2).
"Relativistic-mass" is the other use of "mass", although I prefer to just use the word "energy". As a particle's velocity increases, its relativistic-mass / energy increases as well, but its rest-mass does NOT. So you take mc^2 + the kinetic energy of the particle, and that gives you the total energy of the particle.
The gravitational force is a function of total energy [1]. This is why gravity bends the trajectories of photons (and other bosons) even though these particles have no rest-mass. The gravitational force between two systems is a function of the total energy of each system regardless of whatever kind of stuff makes up the system.
For an example, consider the earth + moon system. If you were to "weigh" this system, and then weigh the earth and moon separately, you would find that the sum of the individual weights is more than the sum of the two body system. This is because of the binding energy between the earth and the moon (which is negative). It is interesting to note that this potential energy is roughly equivalent to the mass of everyone on earth.
[1] Gravity is really unique in this regard. No other force is like it.
My physics prof used to say "physics is just the study of units". If you're getting a strange answer, you've probably misunderstood the units of measure somewhere.
This is why I feel you need to be really precise when talking about science. As you said, "mass" refers to "rest-mass". So I can't help but feel that your original statement is really just a play on words to try and trick people.
Another comment seems to claim that since E=mc2, rotational energy can be converted to to mass and viola, the earth is heavier because it has more energy! But that doesn't make sense to me.
Maybe frame dragging has something to do with it? Your pulling of space-time through rotation looks the same as your pulling of space-time from gravity so you appear heavier?
Or is it for the same reason that moving bodies are heavier? Every point of the ball is moving and therefore heavier, the fact that it's rotating makes no differece.