Newton's laws of motion: Encyclopedia II - Newton's laws of motion - Relationship to the conservation laws

Newton's laws of motion - Relationship to the conservation laws

The laws of conservation of momentum, energy, and angular momentum are of more general validity than Newton's laws, since they apply to both light and matter, and to both classical and non-classical physics. In the special case of a system of material particles interacting via instantaneously transmitted forces, Newton's second law can be viewed as a definition of force, and the third law can be derived from conservation of momentum.

Newton stated the third law within a world-view that assumed instantaneous action at a distance between material particles. We now know that this is not the way the universe really works, although it may be a good approximation under certain circumstances. For example, the electrons in the antenna of a radio transmitter do not act directly on the electrons in the receiver's antenna. Momentum is handed off from the transmitter's electrons to the radio wave, and then to the receiver's electrons, and the whole process takes time. Conservation of momentum is satisfied at all times, but Newton's laws are inapplicable, because, for example, the second law does not apply to the radio wave.

Some authors refer to a "strong form" of Newton's third law, which requires that, in addition to being equal and opposite, the forces must be directed along the line connecting the two particles (or the centers of mass of the two objects). The strong form does not always hold. For example, the force between two bar magnets will in general not satisfy the strong form. (Although the bar magnets are not point particles, the same applies, for example, to point particles that have magnetic dipole moments.) In cases where the strong form applies (or where the forces involved are contact forces), Newton's laws can be used to prove conservation of angular momentum. However, this is somewhat misleading, because conservation of angular momentum is always valid, and Newton's laws are not. For example, conservation of angular momentum is valid for electromagnetic fields and their interactions with material particles, but Newton's laws do not apply to electromagnetic waves, and the strong form of the third law is violated even for static electrical and magnetic interactions.

Conservation of energy was discovered nearly two centuries after Newton's lifetime, the long delay occurring because of the difficulty in understanding the role of microscopic and invisible forms of energy such as heat and infra-red light. For a classical system of material particles, conservation of energy, combined with Galilean relativity, implies conservation of momentum, and conservation of momentum implies Newton's laws.

Adapted from the Wikipedia article "Relationship to the conservation laws", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki