Explosions:

An explosion occurs when an object is divided into two or more fragments due to a release of energy. Note that kinetic energy in a system of explosion is not conserved because it involves energy transformation (i.e. kinetic energy changes into heat and acoustic energy).

Modern definitions of momentum:
Momentum in relativistic mechanicsIn relativistic mechanics, in order to be conserved, the momentum of an object must be defined as
where m0 is the invariant mass of the object and ? is the Lorentz factor, given by
where v is the speed of the object and c is the speed of light.

Relativistic momentum can also be written as invariant mass times the object's proper velocity, defined as the rate of change of object position in the observer frame with respect to time elapsed on object clocks (i.e. object proper time). Within the domain of classical mechanics, relativistic momentum closely approximates Newtonian momentum: at low velocity, ?m0v is approximately equal to m0v, the Newtonian expression for momentum.

A graphical representation of the interrelation of relativistic energy E, invariant mass m0, relativistic momentum p, and relativistic mass m = ?m0.The total energy E of a body is related to the relativistic momentum p by

where p denotes the magnitude of p. This relativistic energy-momentum relationship holds even for massless particles such as photons; by setting m0 = 0 it follows that