Euler's laws of motion each governed by Newton’s laws of motion, then Euler’s equations can be derived from Newton’s laws. Euler’s equations can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle distribution. The total body force applied to a continuous body with mass , mass density , and volume , is the volume integral integrated over the volume of the body: where is the force acting on the body per unit mass (dimensions of acceleration, misleadingly called the "body force"), and is an infinitesimal mass element of the body. Body forces and contact forces acting
Newton's laws of motion "Momentum, energy and angular momentum cannot be created or destroyed." Because force is the time derivative of momentum, the concept of force is redundant and subordinate to the conservation of momentum, and is not used in fundamental theories (e.g., quantum mechanics, quantum electrodynamics, general relativity, etc.). The standard model explains in detail how the three fundamental forces known as gauge forces originate out of exchange by virtual particles. Other forces, such as gravity and fermionic degeneracy pressure, also arise from the momentum conservation. Indeed, the conservation of 4-momentum in inertial motion via curved space-time results in what we call gravitational