As with conservation of energy, it would be difficult to overstate the importance of conservation of linear momentum to the field of physics.  As just one of the numerous examples we could use to illustrate the power of momentum conservation, consider the discovery of the atomic nucleus. Much of what we understand about subatomic particles and nuclear structure comes from collision experiments. Initially, though it was clear that an atom contained particles that were both positively and negatively charged, it was unclear how the matter was arranged.  Where the negatively charged electrons and positively charged protons uniformly distributed throughout the volume of the atom or were the charges arranged in some other way?

In a collision experiment performed in 1909, a beam of alpha particles (the nucleus of helium atoms) were fired at a thin sheet of gold foil.  If the charges were uniformly distributed inside the atom, most of the alpha particles would be deflected, but the deflection angles should be small.  Instead, most of the alpha particle were not deflected, but those that were, were deflected at large angles.  In the words of one of the scientists conducting the experiment, “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”  Using their data and the conservation of momentum, the scientist concluded that the positive charge must be concentrated in a very small space within the atom.  Our first indication that there must be a nucleus in an atom came directly from applying the conservation of momentum.