Answer 1:
The answer has to do with special relativity, and
what you mean by the "mass" of a particle.
You'll often hear this explanation: when
the speed of a particle changes, its kinetic
energy changes, and therefore so does its total
energy. But special relativity, and
Einstein's famous formula
E = mc^{2}
tell us that energy and mass are equivalent, so
changing the speed of the particle changes its
mass. This new mass is often called the
relativistic mass M.
Even though that explanation is popular, many
physicists (myself included) don't like it. The
reason is because the formula E = mc^{2}
is really only valid when a particle isn't moving.
When a particle is moving with some momentum p,
the correct formula is
E^{2} = (mc^{2})^{2} +
(pc)^{2}.
This formula gives you the total energy E of a
particle in terms of its rest mass m (that is, the
mass of the particle when it's not moving) and its
momentum p. Because it's only the rest mass m
that appears in the formula, most physicists will
only use the term "mass of the particle" to refer
to the rest mass, and don't really care about the
relativistic mass.
So my short answer to your question would be:
the mass of a particle doesn't change when it's
moving! But its energy certainly does.
