Relativity has changed our concept of energy. An object now has energy just because it is there, whether or not it is moving or at some point in a gravitational field or because it is hot.
Our concept of mass also has to change. An object has a rest mass,
the mass of an object when measured by someone at rest relative to the object. If the object is moving its mass increases as
and so does its energy. The energy of an object is
Because the object is moving it has kinetic energy. The familiar equation of kinetic energy
no longer applies. Instead we write kinetic energy as the difference between the energy a particle has when it is at rest and when it is moving.
(1)
If
is much smaller than
as it is for most of us in our small lives here on Earth, then we can use the binomial expansion to rewrite (1) as
since v/c is small
