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The Law of Conservation of Energy 

The law of conservation of energy is now one of the most important and firmly established conservation law of nature, although it has been necessary to recognize that energy may occur in many different forms and is also equivalent to mass. Perhaps the simplest form of energy arises from motion, where the Kinetic Energy of a particle of mass m, moving with speed v, is defined as (1/2)mvv. The total kinetic energy of a system of particles is the sum of the kinetic energies of the individual particles. When work is done on a particle, the total work done on all the particles is equal to the increase in kinetic energy of the whole system. If the net work is zero, kinetic energy is conserved. This network must include work done by internal forces of the particles acting on each other. This is why when a skater spinning with arms outstretched pulls them in, he or she spins faster ( with increased kinetic energy ) because of work done on the body. In this example, angular momentum is conserved because there are no external torques.


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