Kinetic Energy Newton's laws are in principle all we need to understand and predict motion of macroscopic bodies at speeds much less than the speed of light. As mathematical physicists struggled to apply these laws of motion to ever more complicated problems they discovered that while the position forces and acceleration which enter Newton's laws are ever changing there are other quantities characterizing the motion which remain un-changed, which are conserved quantities. From Newton's laws they derived conservation laws which state that certain quantities are constants of motion .
Conservation laws provide powerful insight into mechanics and physics in general.
So powerful in fact that physicists following Newton such as Lagrange, and Hamilton found it more expedient to choose conservation laws as the fundamental axioms of the theory of mechanics. The main content of the rest of this semester will be to teach you the conservation laws and how to use them to understand nature.