Mechanical kinetic energy is ?

Answer 1

(1/2) m v^2
as long as you stay away from the speed of light.
Watch out for spinning bodies. It is still (1/2) m v^2 but for each particle in a spinning mass. It comes out to (1/2) I omega^2 where I is the moment of inertia and omega is the angular velocity. It is still the same thing because for each particle v = omega R and I = m R^2
so (1/2) m v^2 = (1/2) (I/R^2)(omega^2 R^2) = (1/2) I omega^2