Conservation laws are the cornerstone of physics. Some examples are energy conservation, momentum conservation, angular momentum conservation, charge conservation, baryon number conservation...
A quantity that is conserved is one that does not change as a function of time.
The law of conservation of energy states:
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This statement is by far the most important in this chapter. For now we will only deal with mechanical energy, but in later chapters we will also add other energy forms, such as heat. In fact, the first law of thermodynamics is nothing but a reformulation of the above conservation law for energy with the inclusion of heat.
Well, what is this conservation law good for? Can we use it to perform useful calculations? We will utilize this conservation law exactly for this purpose for the remainder of this chapter, and hopefully you will then see how useful it can be to think in terms of conserved quantities such as energy.
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