A plenary session from the American Association of Physics Teachers' winter meeting in January 2011. Celebrating the centennial of nuclear physics, Steven T. Corneliussen and Fred Dylla discuss Ernest Rutherford's discovery of the atom's nucleus and how it has shaped the course of physics. Against the backgrop of a century's progress in nuclear and particle physics, this talk presents the extraordinary range of applications for the planet's more than 30,000 accelerators, not only in discovery science, but in medicine, industry, energy, the environment, and national security.